Gabriel Morgado

Laurence Signon

Bogdan Nowakowski

Annie Lemarchand

Termination mechanisms of Turing patterns in growing systems

The question of the termination of a periodic spatial structure of Turing type in a growing system is addressed in a chemical engineering perspective and a biomimetic approach. The effects of the dynamical parameters on the stability and the wavelength of the structure are analytically studied and used to propose experimental conditions for which a Turing pattern stops by itself with a decreasing wavelength. The proposed mechanism is successfully checked by the numerical integration of the equations governing the dynamics of the activator and the inhibitor. We conclude that a local increase of the concentration of the reservoir which controls the injection rate of the inhibitor into the system can be used to achieve the appropriate termination of a Turing pattern.

Introduction

During embryonic development, segmented structures of the body such as the spine and the digits are formed by the production of repeated elements. Since the seminal work of Turing [1] accounting for the formation of biological pattern in the framework of reaction-diffusion models, experimental evidences of Turing structures have been given in chemistry [2,3,4] and biology [START_REF] Murray | Mathematical Biology[END_REF][START_REF] Raspopovic | [END_REF]. Recent years have witnessed a growing number of papers where reaction-diffusion principles are proposed to model the formation of biological periodic spatial structures [7,8,9,10,11,12,13]. Following Turing, a two-component chemical system composed of an autocatalytically-produced activator by consumption of an inhibitor that diffuses faster may produce periodic spatial structures such as stripes in one-dimensional (1D) systems and hexagons in 2D. In other words, a Turing pattern emerges by local self-activation and lateral inhibition [14]. The concepts developed to model living systems provide a source of inspiration in chemical engineering [START_REF] Grzybowski | Chemistry in Motion: Reaction-diffusion Systems for Micro-and Nanotechnology[END_REF][START_REF] Dziekan | [END_REF][START_REF] Mikhailov | Design and Control of Self-organizing Chemical Systems[END_REF][START_REF] Ashkenasy | [END_REF]19,21,22]. However, standard models of Turing patterns generate structures in infinite systems and the question of the termination of a striped structure in a finite system arises in a perspective of biomimetism in material science. Specifically, it is desirable to find experimentally achievable conditions creating a finite-size structure, whose growth stops by itself with decreasing oscillation amplitude and respects the decrease of the wavelength during the termination process. To this aim, we use an as simple as possible reaction-diffusion model [23] admitting a Turing structure developing behind a propagating wave front and examine the effect of all parameters on both the stability and the wavelength of the structure [START_REF] Murray | Mathematical Biology[END_REF]22]. We already used a stochastic approach to a Turing pattern [23] and showed that, contrary to intuition, the internal fluctuations may have a constructive effect and stabilize the structure outside the domain of stability predicted by a deterministic description. Here, we adopt a macroscopic approach. Our goal is to select suitable conditions from this systematic approach and to propose termination mechanisms compatible with processing in chemical engineering.

The paper is organized as follows. In section 2, a reaction-diffusion model involving local activation and long-range inhibition is presented. An analytical stability condition and the wavelength expression of the Turing pattern are given. The influence of the parameters of the model on the stability and the wavelength of the pattern are studied in section 3. The analysis of the results leads to the selection of a user-friendly termination mechanism in the framework of chemical engineering. The analytical predictions regarding stability and wavelength are compared to numerical results for the chosen mechanism.

Section 4 contains conclusions. The possibility that the different mechanisms exhibited could be found as termination scenarios in morphogenesis is raised.

Model

We consider the following reaction mechanism inspired from the Schnakenberg model [24] and the Gray-Scott model [25] A

k 1 -→ R 1 (1) 2A + B k 2 -→ 3A (2)
B

k 3 ⇋ k -3 R 2 (3)
where R 1 and R 2 are reservoirs. The concentrations R 1 and R 2 of the reservoirs are assumed to be constant in time. The reaction given in Eq. ( 2) autocatalytically produces species A and consumes species B. Due to the ability of accelerating its own production, species A is called an activator whereas species B, which is consumed by the same process, is called an inhibitor. The macroscopic dynamics of the system is governed by two partial differential equations [9,23]

∂A ∂t = -k 1 A + k 2 A 2 B + D A ∂ 2 A ∂x 2 (4) ∂B ∂t = k -3 R 2 -k 3 B -k 2 A 2 B + D B ∂ 2 B ∂x 2 (5)
for the concentrations A and B of the activator and the inhibitor supposed to have different diffusion coefficients D A and D B . For appropriate rate constant values, such that

∆ = (k -3 R 2 ) 2 -4k 2 1 k 3 /k 2 ≥ 0 (6)
Figure 1: Largest eigenvalue µ of the linear operator M versus square of Fourier mode q 2 . Solid line:

k -3 R 2 = 8.76. Dashed line: k -3 R 2 = 10. Other parameter values: k 1 = 2.92, k 2 = 1, k 3 = 2.19, D A = 1, D B = 10.
the system admits two steady states (A 0 = 0, B 0 = k -3 R 2 /k 3 ) and

A T = k -3 R 2 + √ ∆ 2k 1 ( 7
)
B T = k -3 R 2 - √ ∆ 2k 3 (8)
that are stable with respect to homogeneous perturbations. A linear stability analysis of Eqs. (4,5) reveals that the steady state (A T , B T ) can be destabilized by inhomogeneous perturbations [START_REF] Murray | Mathematical Biology[END_REF]3,9,23]. The Fourier transforms A q (t) = ∞ -∞ A(x, t)e -iqx dx and B q (t) = ∞ -∞ B(x, t)e -iqx dx, where q is the Fourier mode, are introduced. In the Fourier space, the linear stability operator M is given by:

M = k 1 -D A q 2 k 2 A 2 T -2k 1 -k 2 k -3 R 2 k 1 A T -D B q 2 (9)
The eigenvalues of the matrix M obey the characteristic equation µ 2 + αµ + β = 0, with

α = k 1 -k 2 k -3 R 2 k 1 A T -(D A + D B )q 2 and β = 2k 2 1 A T /B T -(k 1 -D A q 2 )(k -3 R 2 /B T + D B q 2 ).
The Turing structure develops if the largest eigenvalue

µ = 1 2 k 1 - k 2 k -3 R 2 k 1 A T -(D A + D B )q 2 + k 1 + k 2 k -3 R 2 k 1 A T + (D B -D A )q 2 2 -8k 1 k 2 A 2 T    (10)
is real and positive [START_REF] Murray | Mathematical Biology[END_REF]3]. Indeed, a system of differential equations, linearized around a homogeneous steady state, is easily solved by diagonalizing the linear operator. Then, the solution is a linear combination of eigenmodes which exponentially depend on time according to the corresponding eigenvalues. A term associated with a real, positive eigenvalue grows in time, leading to trajectories in the concentration space that move away from the fixed point [START_REF] Murray | Mathematical Biology[END_REF]. In the studied system, the destabilization of the steady state occurs in favor of a Turing pattern. Equation (10) imposes conditions on the parameter values. In particular, the diffusion coefficient D B of the inhibitor B must be sufficiently larger than the diffusion coefficient D A of the activator A: The destabilization of the homogeneous steady state (A T , B T ) requires local self-activation, ensured by the autocatalytic production of the activator through the reaction given in Eq. ( 2), as well as long-range inhibition, due to the larger diffusion coefficient of the inhibitor. The mode q max , which maximizes the eigenvalue µ, is the most unstable Fourier mode:

q max = A T (D A + D B ) 2k 1 k 2 D A /D B -k 1 -k 2 k -3 R 2 A T /k 1 D B -D A (11)
In order to account for the termination of the Turing pattern in a growing system, including the fact that the structure ends with a gradually shorter spatial oscillation, we need to find conditions for which the structure tends to lose its stability while its wavelength decreases. The wavelength of the periodic structure is given by:

λ = 2π q max ( 12
)
Turing structure becomes unstable as the value of largest eigenvalue vanishes for the mode q max associated with the maximum of µ:

µ max = 1 2 k 1 - k 2 k -3 R 2 k 1 A T -(D A + D B )q 2 max + k 1 + k 2 k -3 R 2 k 1 A T + (D B -D A )q 2 max 2 -8k 1 k 2 A 2 T    (13)
k 1 = 2.92, k 2 = 1, k 3 = 2.19, k -3 R 2 = 8.76, D B = 10, ∆x = 0.1.
k 1 = 2.92, k 2 = 1, k 3 = 2.19, k -3 R 2 = 8.76, D A = 1, ∆x = 0.1.
with q max given in Eq. (11). Figure 1 illustrates the behavior of µ max for parameter values associated with a stable Turing pattern with µ max > 0. It is also shown that it is sufficient to increase the value of k -3 R 2 to shift the curve µ(q 2 ) down and lose the stability of the Turing pattern.

In the next section we investigate the behavior of λ and µ max as each parameter controlling dynamics varies. Specifically, we aim at identifying diffusion coefficients or rate constants whose variation leads both to a decrease of the wavelength and a destabilization of the Turing structure, i.e. negative values for the maximum of the eigenvalue.

Results

The concentration R 2 of the inhibitor reservoir is first assumed to be homogeneous. 11) and ( 12) for λ and Eq. ( 13) for µ max , the expressions of the steady state (A T , B T ) being given in Eqs. (7) and (8). To facilitate the comparison with the numerical integration of Eqs. ( 4) and ( 5) that will be performed in the following, the wavelength is given in number of spatial cells of length ∆x = 0.1. As shown in Fig. 2, the decrease in the maximum value µ max of the eigenvalue as the diffusion coefficient 1), decreasing the rate constant k 1 tends to increase the concentration of species A. Following Eq. ( 2), increasing the rate constant k 2 of the autocatalytic step tends to increase the concentration of species A and decrease the concentration of species B. This last result seems to be inconsistent with the consequences drawn from the decrease in k 3 or the increase in k -3 R 2 , which result in increasing the concentration of species B according to Eq. ( 3). However, we already stated that increasing B through soliciting the reservoir R 2 results in consuming species The diffusion coefficients and the rate constants characterize dynamics and are intrinsic to the reaction-diffusion system. Nevertheless, it is always possible to imagine spatial variations of the dynamical parameters. Well-chosen variations of the diffusion coefficient D B of the inhibitor and each of the four rate constants of the chemical mechanism could be a priori used to build a termination model. In the framework of the application to developmental biology, steric hindrance and molecular crowding in the tail of an embryo may be invoked to justify the decrease of the diffusion coefficients. In chemical engineer-

D A of species A
k 1 = 2.92, k 2 = 1, k -3 R 2 = 8.76, D A = 1, D B = 10, ∆x = 0.1.
ing, a local increase of temperature could be used to induce a local increase of the rate constants. However, local increase of confinement or temperature is susceptible to simultaneously affect several dynamical parameters [13,22,27,28,29,30,31,32]. Whereas a decrease of D B is desired to destabilize the Turing pattern while decreasing its wavelength, a simultaneous decrease of D A would be detrimental. Similarly, an increase of k 2 and k -3 due to temperature increase could be satisfying but the joint decrease of k 1 and k 3 could blur the effect on the Turing structure. The simplest way to imagine the control of a targeted parameter leading to the desired behavior is to impose well-chosen spatial variations of the reservoir concentration R 2 . Indeed, the product k -3 R 2 plays the role of an apparent rate constant for the backward reaction given in Eq. ( 3) that can be fixed at will in chemical engineering in the case of a single dynamical system with uniquely defined intrinsic parameters.

According to Fig. 7, increasing R 2 tends to destabilize the Turing pattern and decrease its wavelength. We examine if the results deduced from a stability analysis can be used in a dynamical approach. The results of the numerical integration of Eqs. ( 4) and ( 5) for a homogeneous concentration R 2 and a piecewise linear profile are given in Fig. 8. The initial condition is a step function between the steady state (A T , B T ) in the first 10 cells on the left and the steady state (A 0 , B 0 ) in the remaining cells. The initial total number of cells is set at n 0 = 610. Introducing the cell label i = x/∆x, where ∆x is the cell length, and the discrete time s = t/∆t, where ∆t is the time step, we choose:

A(i, s = 0) = A T , B(i, s = 0) = B T , for 1 ≤ i ≤ 10 ( 14
)
A(i, s = 0) = A 0 , B(s, s = 0) = B 0 , for 11 ≤ i ≤ n 0 ( 15
)
To account for the growth of the system and simultaneously avoid boundary effects that may alter the wavelength of the structure [START_REF] Dziekan | [END_REF], we impose a fixed boundary on the left and a free growing end on the right [9,23,26]. For parameter values for which the steady state (A T , B T ) is unstable with respect to inhomogeneous perturbations, a Turing pattern develops after the passage of a chemical wave front. More precisely, according to Eqs.

(4) and ( 5) and due to the no-flux boundary conditions applied on the left boundary, the concentrations in the first cell obey

A(1, s + 1) = A(1, s) -k 1 ∆tA(1, s) + k 2 ∆tA(1, s) 2 B(1, s) + D A ∆t (∆x) 2 (A(2, s) -A(1, s)) (16) B(1, s + 1) = B(1, s) + k -3 R 2 ∆t -k 3 ∆tB(1, s) -k 2 ∆tA(1, s) 2 B(1, s) + D B ∆t (∆x) 2 (B(2, s) -B(1, s)) ( 17
)
so that both A(1, s) and B(1, s) are extremum of the Turing pattern in the first spatial cell i = 1.

Spatial cells are added to the right end of the system at the front speed to counterbalance the progression of the wave front and mimic system growth: At all the discrete times s for which the concentration B(n -600, s) of species B in the n -600 cell becomes

k 1 = 2.92, k 2 = 1, k 3 = 2.19, D A = 1, D B = 10, ∆x = 0.1.
smaller than 0.99B 0 , the total number n of cells is increased by 1. Provided that the front propagates at a speed smaller than ∆x/∆t, this protocol ensures that a layer of about 600 cells remains in the stationary state (A 0 , B 0 ) on the right of the system, so that the propagation of the front is not significantly affected by the finite size of the system.

To draw Fig. 8b, we have chosen the parameter values given in the caption of Figs. 1 and imposed k -3 = 8.76 for the following spatial profile for the concentration R 2 of the inhibitor reservoir:

R 2 = 1, for 1 ≤ i < 500 (18) R 2 = 2.83 × 10 -4 i + 0.858, for 500 ≤ i < 1000 (19) R 2 = 1.14, for 1000 ≤ i ( 20
)
The simulation is stopped at time t end for which the wave front has passed cell i = 1000.

It is worth noting that the Turing pattern is unchanged for larger values of the final integration time. Then, only the position of the concentration gradients associated with the traveling wave evolve in time but the Turing structure has stopped growing and remains in a steady state with a fixed number of wavelengths. As desired, the increase of the concentration R 2 leads to the termination of the Turing structure.

As illustrated in Fig. 7, the Turing structure is expected to be stable in the range 1 ≤ i < 500 for which k -3 R 2 = 8.76 and unstable in the range i ≥ 1000 for which k -3 R 2 = 10. More precisely, according to Eq. ( 13), the maximum of the eigenvalue µ max vanishes for k -3 R 2 = 9.75, i.e. R 2 = 1.11 for k -3 = 8.76, which occurs in spatial cell i = 900. Hence, the Turing pattern is predicted to be stable in the range 0 ≤ i < 900 and unstable beyond this domain. The results shown in Fig. 8b confirm the analytical predictions. The amplitude of the spatial oscillations decreases between i ≃ 500 and i ≃ 1000. The system is in a steady state in the range 1000 ≤ i < 1500.

The increase of R 2 not only destabilizes the Turing structure but also modifies the steady state values and the propagation speed of the wave front. The comparison between Figs.

8a and 8b shows that, as R 2 increases, the wave front propagates faster, A T increases, B T decreases and B 0 increases. As a consequence of the variation of A T and B T , the oscillations of A and B concentrations are not symmetrical in the range 500 ≤ i < 900. The decrease of the wavelength predicted in Fig. 7 is more difficult to check by a qualitative analysis. Using the numerical results illustrated in Fig. 8b, we evaluate the local wavelength by computing the number of cells between two minima of the A concentration profile. The results are given in Fig. 9 and compared to the analytical prediction deduced from Eqs. (11) and (12). The agreement between the numerical and analytical results is very satisfying in the range 600 ≤ i < 900. Oscillations of very small amplitude are observed in Fig. 8b in the range 900 ≤ i < 1000, proving that a very damped Turing structure remains in a small area where instability was predicted. The wavelength of the structure in the range 1 ≤ i < 500 is slightly affected by the increase of R 2 from cell i = 500 but the deviation from the analytical prediction is only 2.5 percent. This small difference is related to the linear approximation used in wavelength evaluation that neglects non-linear terms that may be more important for large structures.

Interestingly, the wavelength is sensitively decreased in the expected area in which the concentration of the reservoir R 2 increases: As shown in Fig. 9, the wavelength is reduced from 72 spatial cells to less than 61, before the structure disappears. We conclude that an increase in the concentration of the reservoir R 2 related to the inhibitor B is sufficient to account for the destabilization of the Turing pattern associated with a decrease of the wavelength. As anticipated by the results given in Fig. 7, according to which an increase of R 2 decreases the wavelength λ and leads to a negative eigenvalue µ max around (A T , B T ), we suggest that an appropriate spatial variation of R 2 can be used in chemical engineering to stabilize the homogeneous steady state and induce a termination of the Turing pattern in a growing system.

Conclusion

In a biomimetic approach, we have addressed the question of the termination of a Turing structure in a growing system. A free boundary is imposed at the growing part, which ensures that the wavelength of the pattern is not perturbed by fixed boundary conditions. After deriving analytical expressions for the stability condition and the wavelength of the structure, we perform a systematic analysis of the effect of all dynamical parameters on the pattern. Apart from the variation of the diffusion coefficient of the activator, a well-chosen variation of the dynamical parameters leads to the desired behavior, i.e. the simultaneous loss of stability and the decrease of the wavelength. In particular, an increase of the effective rate constant k -3 R 2 , where k -3 is the rate constant of the reaction injecting the inhibitor from the reservoir at the concentration R 2 , is associated with a destabilization of the Turing pattern accompanied by a decrease of the wavelength.

Imposing a spatial variation of the concentration of the reservoir R 2 turns out to be an appropriate protocol for chemical engineering. However, the proposed procedure imposes the total length of the structure but not its number of wavelengths. In the framework of developmental biology, for example in the case of the growth of the digits or the spine of the vertebrates, the termination process has to respect the total number of segments 4) and [START_REF] Murray | Mathematical Biology[END_REF]. Solid line: Analytical prediction given in Eq. (12).

for a possible variation in the length of the global structure. Therefore, it is necessary to imagine that the system itself is able to count the number of already formed segments and to trigger the variation of a parameter leading to smaller subsequently formed segments.

If the concept of the Turing structure is kept in the formation of biological patterns, the presented results could be used to suggest such relevant parameters. The local increase of the rate constant k -3 that would be activated when a given number of segments has

Figure 2 :

 2 Figure 2: Top: Scaled wavelength λ/∆x of Turing pattern versus diffusion coefficient D A of species A. Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus D A . Parameter values: k 1 = 2.92, k 2 = 1, k 3 = 2.19, k -3 R 2 = 8.76, D B = 10, ∆x = 0.1.

Figure 3 :

 3 Figure 3: Top: Scaled wavelength λ/∆x of Turing pattern versus diffusion coefficient D B of species B. Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus D B . Parameter values: k 1 = 2.92, k 2 = 1, k 3 = 2.19, k -3 R 2 = 8.76, D A = 1, ∆x = 0.1.

  Figures 2 and 3 show the variations of the wavelength λ and the maximum value µ max of the eigenvalue with one of the diffusion coefficients, the other parameters being constant. The results are deduced from Eqs. (

   show the variations of the wavelength λ and the maximum value µ max of the eigenvalue with rate constants. The variations of λ are given in a bounded interval of rate constant values, in which the Turing pattern is stable. At one of the endpoints of the interval, the eigenvalue µ max vanishes and at the other endpoint, the condition of existence of the steady state (A T , B T ) given in Eq. (6) is no longer satisfied. The two desired behaviors, i.e. the decrease of both λ and µ max , are observed as k 1 decreases, k 2 increases, k 3 decreases, and k -3 R 2 increases. For an assumed homogeneous concentration R 2 of the reservoir, the variations of λ and µ max with R 2 are analogous to the variations with k -3 R 2 . According to the chemical reaction given in Eq. (1), decreasing the rate con-

Figure 4 :

 4 Figure 4: Top: Scaled wavelength λ/∆x of Turing pattern versus rate constant k 1 of the chemical reaction given in Eq. (1). Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus k 1 . Parameter values: k 2 = 1, k 3 = 2.19, k -3 R 2 = 8.76, D A = 1, D B = 10, ∆x = 0.1.

Figure 5 :

 5 Figure 5: Top: Scaled wavelength λ/∆x of Turing pattern versus rate constant k 2 of the chemical reaction given in Eq. (2). Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus k 2 . Parameter values: k 1 = 2.92, k 3 = 2.19, k -3 R 2 = 8.76, D A = 1, D B = 10, ∆x = 0.1.

Figure 6 :

 6 Figure 6: Top: Scaled wavelength λ/∆x of Turing pattern versus rate constant k 3 of the forward chemical reaction given in Eq. (3). Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus k 3 . Parameter values: k 1 = 2.92, k 2 = 1, k -3 R 2 = 8.76, D A = 1, D B = 10, ∆x = 0.1.

Figure 7 :

 7 Figure 7: Top: Scaled wavelength λ/∆x of Turing pattern versus rate constant k -3 R 2 of the backward chemical reaction given in Eq. (3). Bottom: Maximum value µ max of the largest eigenvalue of the linear operator M versus k -3 R 2 . Parameter values: k 1 = 2.92, k 2 = 1, k 3 = 2.19, D A = 1, D B = 10, ∆x = 0.1.

Figure 8 :

 8 Figure 8: Spatial profiles deduced from the numerical integration of Eqs. (4) and (5) for k 1 = 2.92, k 2 = 1, k 3 = 2.19, k -3 = 8.76, D A = 1, D B = 10, ∆t = 10 -4 , t end /∆t = 2000000, ∆x = 0.1. Black dotted line: Imposed concentration R 2 of the reservoir. (a): Homogeneous concentration R 2 = 1, (b): Piecewise linear R 2 profile. Blue dashed line: Concentration of species A versus cell label x/∆x. Red solid line: Concentration of species B versus cell label x/∆x.

Figure 9 :

 9 Figure 9: Spatial variation of the scaled wavelength λ/∆x of Turing pattern versus cell label x/∆x for the parameter values given in the caption of Fig. 8b. Symbols: Results deduced from the numerical integration of Eqs. (4) and[START_REF] Murray | Mathematical Biology[END_REF]. Solid line: Analytical prediction given in Eq. (12).

  already been formed can be straightforwardly proposed. Similarly, the local increase of the rate constant k 2 controlling the autocatalytic production of the activator or the local decrease of the rate constant k 1 or k 3 , associated with the absorption of the activator or the inhibitor by reservoirs, would lead to the desired phenomenon. The local decrease of the diffusion coefficient of the inhibitor offers an alternative. The nature of the mechanism that would trigger such a response of the system when a given number of segments has been created remains an open question.

Acknowledgements

This publication is part of a project that has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 711859 and has benefited from financial resources for science awarded by the Polish Ministry of Science and Higher Education in the years 2017-2021 for the implementation of an international cofinanced project.


Yao Liang
email: liangyao@mail.iggcas.ac.cn

Matthias Delescluse
email: delescluse@geologie.ens.fr

Yan Qiu

Manuel Pubellier

Nicolas Chamot-Rooke

Jun Wang

Xie Nie

Louise Watremez

Sung-Ping Chang

Thibaud Pichot

Dimitri Savva

Florian Meresse

Décollements, Detachments, and Rafts in the Extended Crust of Dangerous Ground, South China Sea: The Role of Inherited Contacts

published or not. The documents may come

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Introduction

The South China Sea (SCS) is an intensely studied marginal basin where extensional processes and structures cannot easily be explained in the light of classic end-member concepts of magma poor and magma rich margins [START_REF] Larsen | Rapid transition from continental breakup to igneous oceanic crust in the South China Sea[END_REF]. In the SCS, successive rifting phases lead to a rather constant crustal thickness [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF] over a particularly wide rifted area [START_REF] Franke | The final rifting evolution in the South China Sea[END_REF]. The SCS margin features both occasional mantle exhumation [START_REF] Mcintosh | Crustal structure and inferred rifting processes in the northeast South China Sea[END_REF][START_REF] Savva | Seismic evidence of hyper-stretched crust and mantle exhumation offshore Vietnam[END_REF] and basaltic magmatism during breakup [START_REF] Larsen | Rapid transition from continental breakup to igneous oceanic crust in the South China Sea[END_REF] with narrow continent-ocean transition [START_REF] Cameselle | The continent-ocean transition on the northwestern South China Sea[END_REF][START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF].

A succession in time of tilting allows distinguishing several thinning events (e.g., [START_REF] Ding | Seismic stratigraphy and tectonic structure from a composite multi-channel seismic profile across the entire Dangerous Grounds, South China Sea[END_REF][START_REF] Franke | The final rifting evolution in the South China Sea[END_REF][START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF] following a stretching event mostly observed in the coastal strip of Guangdong and Guangxi Provinces of China as well as in the Pearl River basin [START_REF] Chan | Polyphase rifting of greater Pearl River Delta region (South China): Evidence for possible rapid changes in regional stress configuration[END_REF]. This early extension along the Eastern SCS margin is generally considered to have started in the Late Cretaceous/Paleocene time [START_REF] Franke | The final rifting evolution in the South China Sea[END_REF][START_REF] Sun | Ressearch on the dynamics of the South China Sea opening: Evidence from analogue modeling[END_REF][START_REF] Sun | 3D analogue modeling of the South China Sea: A discussion on breakup pattern[END_REF], and the main continental rifting phase was a short Late Eocene event (<10 Myr) according to recent drilling results [START_REF] Larsen | Rapid transition from continental breakup to igneous oceanic crust in the South China Sea[END_REF]. Rifting was followed by Oligo-Miocene oceanic spreading from 32 to 15 Ma [START_REF] Briais | Updated interpretation of magnetic anomalies and seafloor spreading stages in the South China Sea: Implications for the Tertiary history of Southeast Asia[END_REF][START_REF] Li | Ages and magnetic structures of the South China Sea constrained by deep tow magnetic surveys and IODP Expedition 349[END_REF][START_REF] Taylor | The tectonic evolution of the South China Basin[END_REF][START_REF] Taylor | Origin and history of the South China Sea Basin[END_REF], or 32 to 20 Ma (e.g., [START_REF] Barckhausen | Evolution of the South China Sea: Revised ages for breakup and seafloor spreading[END_REF]. In the Eastern Basin, breakup occurred abruptly in time and space under the effect of an overall westward propagation of the accreting centers [START_REF] Cameselle | The continent-ocean transition on the northwestern South China Sea[END_REF]. From 33 to 23.5 Ma, spreading first occurred in the eastern Basin only, because of a propagation stalling phase possibly related to far-field boundary conditions ahead of the propagator (Le [START_REF] Pourhiet | Continental break-up of the South China Sea stalled by far-field compression[END_REF]. During that time, the Eastern Basin experienced several southward ridge jumps [START_REF] Ding | Structures within the oceanic crust of the central South China Sea basin and their implications for oceanic accretionary processes[END_REF], after which the spreading head finally propagated to the southwest. This last phase resulted in the opening of the Southwest subbasin (SWSB) between ~23.5 and ~16 Ma [START_REF] Huchon | Propagation of continental break-up in the southwestern South China Sea[END_REF][START_REF] Li | Ages and magnetic structures of the South China Sea constrained by deep tow magnetic surveys and IODP Expedition 349[END_REF][START_REF] Sibuet | Geodynamics of the South China Sea[END_REF] with reduced magma supply [START_REF] Yu | Crustal structure of the Southwest Subbasin, South China Sea, from wideangle seismic tomography and seismic reflection imaging[END_REF][START_REF] Yu | Seiscmic evidence for tectonically dominated seafloor spreading in the Southwest Sub-basin of the South China Sea[END_REF]. These successive rifting/opening events lead to the overall characteristic V-shaped morphology observed today [START_REF] Briais | Updated interpretation of magnetic anomalies and seafloor spreading stages in the South China Sea: Implications for the Tertiary history of Southeast Asia[END_REF][START_REF] Ding | Conjugate margin pattern of the Southwest Sub-basin, South China Sea: Insights from deformation structures in the continent-ocean transition zone[END_REF][START_REF] Huchon | Finite extension across the South Vietnam basins from 3D gravimetric modelling: relation to South China Sea kinematics[END_REF][START_REF] Huchon | Propagation of continental break-up in the southwestern South China Sea[END_REF][START_REF] Li | The propagation of seafloor spreading in the southwestern subbasin, South China Sea[END_REF][START_REF] Taylor | Origin and history of the South China Sea Basin[END_REF]. The SWSB (Figure 1) conjugate margins feature the widest extended continental crust area (hundreds of kilometers), stretched while oceanic propagation stalled in the Eastern Basin (Le [START_REF] Pourhiet | Continental break-up of the South China Sea stalled by far-field compression[END_REF]. Fast breakup propagation resumed only after a stress change [START_REF] Sibuet | Geodynamics of the South China Sea[END_REF] toward a more favorable direction of extension leading to spreading in the SWSB.

Regarding the structural style of rifting, most published seismic lines indicate the presence of listric faults rooting apparently at different structural levels, either in the upper crust or deep into the lower crust. Ductile flow in the lower crust can explain the relative flatness of the Moho and rather constant crustal thickness over hundreds of kilometers [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF]. Meanwhile, areas of exhumed mantle associated with very severe stretching are bounded by tilted blocks of upper crust rafting over a highly thinned lower crust, sometimes welded to the mantle where lower crust has been totally removed (e.g., [START_REF] Savva | Seismic evidence of hyper-stretched crust and mantle exhumation offshore Vietnam[END_REF]. Basin-sized tilted blocks are widespread over the northern margin, including the Xisha Trough, the Bayung Sag, and the Qiongdongnan Basin among others [START_REF] Franke | The final rifting evolution in the South China Sea[END_REF]. The apparent contradiction between a generally distributed extension and more significant but localized extension in a few basins Tectonics raises the question of the possible reactivation of inherited structures such as Mesozoic granites, or even contacts within the sedimentary pile such as erosional surfaces or fold flanks [START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF][START_REF] Yan | Oxygen and lead isotope characteristics of granitic rocks from the Nansha block (South China Sea): Implications for their petrogenesis and tectonic affinity[END_REF].

In this study, we focus on an area located in the north-east of Dangerous Ground, south of the oceanic basins and at the eastern boundary of the Southwest subbasin (Figure 1). The Eocene-Oligocene restored position of the basins in this area would locate them close to the Xisha Trough [START_REF] Gao | Crustal structure and extension mode in the northwestern margin of the South China Sea[END_REF] and other hyperextended basins (Figure 1, green areas) that were abandoned on the northern margin, suggesting that all these basins are genetically linked. At variance with Xisha Trough, which shows important accumulation of Cretaceous and Tertiary sediments and occurrences of mantle or magmatic intrusions [START_REF] Lei | Structure and sediment budget of Yinggehai-Song Hong basin, South China Sea: Implications for Cenozoic tectonics and river basin reorganization in Southeast Asia[END_REF], stretching was less severe in these southern basins since mantle was not exhumed.

We present the reprocessing and the interpretation of multichannel seismic data and coincident refraction data acquired through a Sino-French collaboration between the Guangzhou Marine Geological Survey and Ecole Normale Supérieure in Paris. The coincident profiles cross a rather unexplored basin located between Reed Bank and the Spratly Islands (Nansha Block). We make use of both the deep reflectivity and refraction velocity down to mantle to unravel extensional structures and processes, and discuss them in the local and general framework of the South China Sea opening. We aim to understand why thinning was limited in this area of Dangerous Ground when compared to its northern counterpart. We also take advantage of an area where the frozen early processes of opening were not obliterated by further stretching to try to better understand the early structures and localization processes in the broader framework of extensional tectonics.

Geological Background: Dangerous Ground

The Dangerous Ground (Nansha Qundao in Chinese, we follow here the toponymy of [START_REF] Hutchison | What are the Spratly Islands?[END_REF]) is a set of shoals dotting the southern South China Sea (250 major islands and hundreds more of smaller size), most of them being carbonate buildups that kept up with the subsidence since at least the Miocene [START_REF] Hutchison | What are the Spratly Islands?[END_REF]. The area (135,000 km 2 , about the size of England) broadly stretches along a NE trend from central Luconia in the south to Reed Bank in the north (Figure 1). It is generally seen as the preserved southern passive margin of the South China Sea, which, to some extent, remained away from the south subduction/obduction deformation in Sarawak, Borneo, Sabah, and Palawan.

Based on geodynamic reconstructions supported by the identification of magnetic lineation in the oceanic basins of the South China Sea, it is agreed that massifs that form Dangerous Ground today, together with North Palawan, Reed Bank, and part of the Philippines, were former continental microblocks attached to South China mainland in Cretaceous time (e.g., [START_REF] Holloway | The stratigraphic and tectonic relationship of Reed Bank, North Palawan and Mindoro to the Asia mainland and their significance in the tectonic evolution of the South China Sea basin[END_REF][START_REF] Holloway | North Palawan Block, Philippines-Its relation to Asian mainland and role in evolution of South China Sea[END_REF][START_REF] Taylor | The tectonic evolution of the South China Basin[END_REF][START_REF] Taylor | Origin and history of the South China Sea Basin[END_REF]; and all subsequent reconstructions). These blocks migrated southward in the wake of the opening of South China Sea oceanic basins (East Basin and Southwest Basin), while others, such as the Macclesfield Bank or the Zongsha-Xisha Massif (Figure 1), were abandoned on the northern margin (see [START_REF] Cullen | Rifting of the South China Sea: New perspectives[END_REF], for an update of the physiographic provinces and a review of their tectonic significance). Dangerous Ground evolution is thus tightly linked to the progressive opening of the South China Sea from east to west, that is, rifting and early drifting of the East Basin in Oligocene, stalling phase, westward propagation of the ridge tip, and further opening of the SW subbasin in the Miocene. Dangerous Ground was rifted while the East Basin was opening, until the head of the westward propagating ridge passed through to open to the SW subbasin [START_REF] Franke | The final rifting evolution in the South China Sea[END_REF]. Carbonate built onto the head of tilted blocks, eventually enhancing the "Basin and Range" type morphology recognized today in bathymetry and in the gravity field as short NE trending segments [START_REF] Hutchison | What are the Spratly Islands?[END_REF]. Some of these buildups apparently grew onto transverse structures active during rifting [START_REF] Cullen | Rifting of the South China Sea: New perspectives[END_REF]. First-order features of Dangerous Ground thus relate to the recent (Paleogene) extensive phases, but the area has a far much longer geological history shared with South China.

Based on extensive dredging [START_REF] Hinz | Geology of the Dangerous Grounds, South China Sea, and the continental margin off Southwest Palawan -Results of the Sonne Cruises SO-23 and SO-27[END_REF][START_REF] Tectonics Kudrass | Mesozoic and Cenozoic rocks dredged from the South China Sea (Reed Bank area) and Sulu Sea and their significance for plate-tectonic reconstructions[END_REF][START_REF] Yan | Petrology and geochemistry of Mesozoic granitic rocks from the Nansha micro-block, the South China Sea: Constraints on the basement nature[END_REF]reviewed in Hutchison & Vijayan, 2010), the present-day crystalline basement of Dangerous Ground seems to be mainly composed of an assemblage of metamorphic rocks (up to the amphibolite facies) and igneous bodies (rhyolites, diorites, gabbros) of Mesozoic age. The oldest datable sediment within Dangerous Ground is a Late Triassic/Early Jurassic deltaic sandstone dredged along the wall of a half-graben some 20 km off the 10.1029/2018TC005418 Tectonics seismic section discussed in this paper (Figure 2; [START_REF] Tectonics Kudrass | Mesozoic and Cenozoic rocks dredged from the South China Sea (Reed Bank area) and Sulu Sea and their significance for plate-tectonic reconstructions[END_REF]. Dated paragneiss and schist (104-123 Ma;[START_REF] Tectonics Kudrass | Mesozoic and Cenozoic rocks dredged from the South China Sea (Reed Bank area) and Sulu Sea and their significance for plate-tectonic reconstructions[END_REF] suggest that the latest thermo-metamorphic event took place in the early Cretaceous, before widespread Paleogene extension. A cortege of volcanic arc granites (monzogranite, tonalite, and diorite) was dredged close to the continent-ocean boundary (30 to 50 km off our profile) and dated at 127-159 Ma [START_REF] Yan | Petrology and geochemistry of Mesozoic granitic rocks from the Nansha micro-block, the South China Sea: Constraints on the basement nature[END_REF]. This age range exactly coincides with the peak production of Yenshanian granites in South China [START_REF] Zhou | Petrogenesis of Mesozoic granitoids and volcanic rocks in South China: A response to tectonic evolution[END_REF], strongly supporting that the area of Dangerous Ground was part of a larger Mesozoic granitoid belt of subduction encompassing the margins of South China and East Vietnam [START_REF] Taylor | Origin and history of the South China Sea Basin[END_REF][START_REF] Lapierre | Mesozoic felsic arc magmatism and continental olivine tholeiites in Zhejiang province and their relationship with the tectonic activity in southeastern China[END_REF]see discussion in Breitfeld et al., 2017;[START_REF] Morley | Late Cretaceous-Early Palaeogene tectonic development of SE Asia[END_REF][START_REF] Pubellier | The basins of Sundaland (SE Asia): Evolution and boundary conditions[END_REF]. This belt, produced by the northwestward subduction beneath eastern Asia of one of the plates that formed the paleo-Pacific ocean in Jurassic and Cretaceous (Izanagi plate; e.g., [START_REF] Zahirovic | The Cretaceous and Cenozoic tectonic evolution of Southeast Asia[END_REF], was active from Middle Jurassic to late Cretaceous, with a sharp decrease of magmatism after 90 Ma [START_REF] Zhou | Petrogenesis of Mesozoic granitoids and volcanic rocks in South China: A response to tectonic evolution[END_REF]. The exact shape of this Cretaceous subduction/accretionary boundary is speculative, but may have been close to Dangerous Ground based on the abundance of granitic rocks west of it [START_REF] Li | Possible spatial distribution of the Mesozoic volcanic arc in the present-day South China Sea continental margin and its tectonic implications[END_REF][START_REF] Pubellier | Structural map of the South China Sea, Commission for the Geological Map of the World[END_REF][START_REF] Zhou | Mesozoic paleogeography and tectonic evolution of South China Sea and adjacent areas in the context of Tethyan and Paleo-Pacific interconnections[END_REF]. An important implication is the strong heterogeneity of the Dangerous Ground crust prior to Paleogene extension, both lithological and structural, in the form of tectonic contacts between geological units, rheological boundaries between sediments, metamorphic and granitic bodies, and other mechanical boundaries such as large-scale erosional surfaces or flanks of broad Mesozoic folds [START_REF] Pubellier | Structural map of the South China Sea, Commission for the Geological Map of the World[END_REF][START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF][START_REF] Yan | Late Mesozoic compressional folds in Dongsha Waters, the northern margin of the South China Sea[END_REF].

The mean crustal thickness in Dangerous Ground is 15 to 20 km based on deep seismic, refraction, and gravity inversion [START_REF] Ding | Seismic stratigraphy and tectonic structure from a composite multi-channel seismic profile across the entire Dangerous Grounds, South China Sea[END_REF][START_REF] Gozzard | South China Sea crustal thickness and oceanic lithosphere distribution from satellite gravity inversion[END_REF][START_REF] Peng | Rift-drift transition in the Dangerous Grounds, South China Sea[END_REF][START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF][START_REF] Wei | Shear wave velocity structure of Reed Bank, southern continental margin of the South China Sea[END_REF]. The area thus remained remote from the main zones of extreme stretching/necking that led to Tectonics oceanic spreading in the South China Sea basins. North of Dangerous Ground, transition to the oceanic lithosphere of the SW subbasin is rather abrupt [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF]. South, seismic profiles show tilted blocks beneath the Northwest Borneo Trough facing the Spratly Islands proper and beneath the Reed Bank Basin and West Palawan Basin facing Reed Bank [START_REF] Cullen | Transverse segmentation of the Baram-Balabac Basin, NW Borneo: Refining the model of Borneo's tectonic evolution[END_REF][START_REF] Ding | Crustal Structure across the northwestern margin of South China Sea: Evidence for magma-poor rifting from a wide-angle seismic profile[END_REF][START_REF] Hinz | Geology of the Dangerous Grounds, South China Sea, and the continental margin off Southwest Palawan -Results of the Sonne Cruises SO-23 and SO-27[END_REF][START_REF] Steuer | Oligocene-Miocene carbonates and their role for constraining the rifting and collision history of the Dangerous Grounds, South China Sea[END_REF][START_REF] Yao | Characteristics and evolution of Cenozoic sediments in the Liyue Basin, SE South China Sea[END_REF]. Crustal thickness within these troughs may be as small as 10 km based on gravity modeling and refraction seismic [START_REF] Franke | Seismic images of a collision zone offshore NW Sabah/Borneo[END_REF][START_REF] Hinz | Geology of the Dangerous Grounds, South China Sea, and the continental margin off Southwest Palawan -Results of the Sonne Cruises SO-23 and SO-27[END_REF][START_REF] Milsom | Gravity anomalies and deep structural controls at the Sabah-Palawan margin, South China Sea[END_REF][START_REF] Vijayan | Crustal character and thickness over the Dangerous Grounds and beneath the Northwest Borneo Trough[END_REF]. Thin crust of presumably continental origin is also found further south beneath the Sarawak margin [START_REF] Madon | The structure and stratigraphy of deepwater Sarawak, Malaysia: Implications for tectonic evolution[END_REF]. A thin-crust basin thus runs south of Dangerous Ground, with the same trend and possibly the same type of rotated blocks controlling Tertiary sediment fills. Offshore North Palawan, the equivalent of Dangerous Ground is absent and the thick inverted margin there connects to the oceanic crust of the East Basin, with the Northwest Palawan Basin in between [START_REF] Aurelio | Middle to Late Cenozoic tectonic events in south and central Palawan (Philippines) and their implications to the evolution of the south-eastern margin of South China Sea: Evidence from onshore structural and offshore seismic data[END_REF][START_REF] Franke | The continent-ocean transition at the southeastern margin of the South China Sea[END_REF]. Further south, most of the south Dangerous Ground thin-crust basin is now buried beneath the allochtonous fold-and-thrust belt offshore Sabah [START_REF] Franke | Seismic images of a collision zone offshore NW Sabah/Borneo[END_REF][START_REF] Hesse | The deep-water fold-and-thrust belt offshore NW Borneo: Gravity-driven versus basement-driven shortening[END_REF][START_REF] Schlüter | Tectono-stratigraphic terranes and detachment faulting of the South China Sea and Sulu Sea[END_REF], and the southern margin is either totally lost or present beneath the wedge as crustal salients [START_REF] Sapin | Onshore record of the subduction of a crustal salient: Example of the NW Borneo Wedge[END_REF].

Besides being floored with relatively thin crust, Northwest Borneo Trough and Palawan Trench (Figure 1) have been further depressed as flexural moats ahead of advancing allochtonous wedges, as originally proposed by [START_REF] Hinz | Geology of the Dangerous Grounds, South China Sea, and the continental margin off Southwest Palawan -Results of the Sonne Cruises SO-23 and SO-27[END_REF] [START_REF] Cullen | Nature and significance of the West Baram and Tinjar Lines, NW Borneo[END_REF][START_REF] Hutchison | What are the Spratly Islands?[END_REF][START_REF] Ilao | 3D seismic investigation of the structural and stratigraphic characteristics of the Pagasa Wedge, Southwest Palawan Basin, Philippines, and their tectonic implications[END_REF][START_REF] Madon | The structure and stratigraphy of deepwater Sarawak, Malaysia: Implications for tectonic evolution[END_REF][START_REF] Milsom | Gravity anomalies and deep structural controls at the Sabah-Palawan margin, South China Sea[END_REF]. The carbonates buildups of Dangerous Ground may thus be presently located at the flexural bulge [START_REF] Hall | Contraction and extension in northern Borneo driven by subduction rollback[END_REF][START_REF] Steuer | Oligocene-Miocene carbonates and their role for constraining the rifting and collision history of the Dangerous Grounds, South China Sea[END_REF], and the entire region may have recorded the progression of the nappes.

Data Acquisition and Processing

The joint Guangzhou Marine Geological Survey/Ecole Normale Supérieure project started in 2011 with the acquisition of a 1,000-km-long refraction line shot using the R/V Tan Bao and 50 ocean bottom seismometers (OBS) deployed across conjugate margins and ocean basin of the South China Sea. In a second phase of the project (2011 to 2013), a 1,000-km-long multichannel seismic (MCS) reflection line-coincident with the refraction seismic line-was shot using the DongFang KanTan and Tan Bao research vessels with an ~7,000 cu.in. tuned air gun array and 6-to 8-km-long streamers, respectively. Preliminary results of the refraction data set (Figure 1) provided a first estimate of the velocities, crustal thickness, and Moho depth solely from the refraction data [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF]. The full coincident MCS data set now allows further processing by constraining the basement geometry, a crucial step in refraction modeling that was missing in our preliminary work. We propose here a proper joint interpretation of refraction and reflection profiles of the southernmost portion of the line.

Multichannel Seismic Reflection Data Set

The 230-km-long section of the profile across Spratly Islands processed in this study consists in 4,525, 50-mspaced shots, each of them being recorded on 480 channels with offset ranges from 130 to 6,130 m (R/V DongFang KanTan). The trace record length is 16 s two-way travel time (TWT) with a 2-ms sampling rate. The MCS processing workflow has been designed and performed at Ecole Normale Supérieure using the CGG Geovation 2013 software. The strategy of the workflow aims at imaging deep reflectivity by fine-tuning the multiple attenuation procedure when possible. Figure 3 shows 110 km of the southernmost section of the profile, while Figure S1 shows the remaining 120 km of the processed section across Spratly Islands to the north (see Figure 1a for location).

The analysis and discussion focus on the area south of Spratly Islands (Nansha block; Figure 3), the section across the Spratly Islands proper being more difficult to process and less promising in terms of deep reflectors (Figure S1). The reason is threefold: (1) shallow seafloor with poor sedimentation and narrow half-graben basins bounded by basement highs makes it difficult to correlate horizons, (2) the shallow basement scatters back the source energy resulting in a lesser penetration of the seismic energy and is further responsible for strong multiples and diffractions that are difficult to remove, and (3) the large number of basement highs related to shallow rooting normal faults tilting blocks induces significant lateral variations of the velocity field (see Figure 4b) leading to difficult time migration of the image there (within a CDP gather, all traces of different incident angles are migrated with a 1-D velocity profile).

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Tectonics

On the contrary, Figure 3 shows that the section from 110 to 225 km is much more sedimented and includes only one significant basement high (~165-km marker). Figure 4b helps visualizing this contrast of lateral velocity variations between the north and south of the line.

For the section in Figure 3 that is central to our study, the workflow includes geometry, denoising, bin centering, offset regularization, predictive deconvolution, multiple attenuation (SRME, radon, F-K), highdensity velocity analysis, prestack Kirchhoff time migration, and finally amplitude recovery. The resulting image is described in section 4. For the section of the profile in Figure S1 from 0 to 110 km, the workflow is similar but we were not able to recover the deep reflectivity.

Refraction Data Set

Because we now have access to basement geometry and crustal reflections from the MCS data, we reprocessed the 230-km-long southernmost section of the refraction data from [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF], including OBS 1 to 12 (Figure 2). This refraction section is coincident with the MCS profile presented in Figures 3 and S1 (see also Figure 4). At variance with Pichot et al. who used travel time tomography inversion (Tomo2D), we perform here forward modeling of the sedimentary, crustal, and mantle seismic phases to fully take into account the a priori shallow and deep structures given by the MCS image (Rayinvr, [START_REF] Zelt | Seismic traveltime inversion for 2-D crustal velocity structure[END_REF]. The method also has the advantage to allow modeling of the secondary arrivals. As a result, a significant addition to the travel times picked in [START_REF] Pichot | Deep crustal structure of the conjugate margins of the SW South China Sea from wide-angle refraction seismic data[END_REF] is the inclusion of lower crustal 1). This section, south of the Spratly Islands (Nansha Islands), is the most sedimented, therefore allowing the imaging of deep reflectivity. The section from 0 to 110 km, more difficult to process (see text), is presented in Figure S1 in the supporting information. Vertical axis shows seconds in two-way travel times (sTWT) 10.1029/2018TC005418 Tectonics secondary arrivals that are visible because of the low-velocity gradient of the continental crust in addition to some intracrustal wide-angle reflections. Beyond the additional arrival picks, the many wide-angle reflections in the crust and mantle in some specific areas sometimes made it difficult to accurately interpret the phases (Moho versus deeper mantle reflections versus deep crustal reflections) without the MCS profile. Our MCS processing workflow focusing on deep reflectivity allows us to perform a common interpretation of phases for both independent data sets. The model includes six layers: two layers of tertiary sediments, one layer of metamorphic sediments (subbasement), one upper crustal layer, one lower crustal layer, and the mantle layer. The picked phases associated to each layer are summarized in Table 1. The modeled velocity is shown in Figure 4 and described in section 4. Other details of the 2) and layers (see Table 1). (b) The two-way travel time (TWT) converted model shows strong lateral velocity variations leading to a difficult (1-D) time migration, in particular from 0 to 110 km (Figure S1). Even phase numbers represent refraction phases whereas odd phase numbers are reflection phases. Each phase is associated to a layer number shown in Figure 4. Reflection phases are related to the bottom of the indicated layer.

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Tectonics refraction modeling strategy and tests of robustness of the model are discussed in the supporting information. In particular, Figure S2 displays the diagonal matrix sensitivity test as well as all picks and modeled arrivals for each OBS and the corresponding ray coverage. Figure S3 displays some robustness analysis where some parameters (velocity or depth nodes) of the model corresponding to key features are varied. Finally, Figure S4 shows all record gathers (hydrophones and vertical geophones) with superimposed picked and synthetic travel times.

Imaging Results

Several sedimentary basins (Figures 3,5, and 6, basins A, B, C) and seismic sequence boundaries have been identified. Prerift, synextension, and postrift sediment interpretation is mostly based on seismic characteristics, including reflection frequency, amplitude, continuity, and reflection termination (onlap, downlap, and truncation). For commodity, we divided Figure 3 into two sections: the south of the line with basins A and B and the deeper and wider basin C, separated from A and B by a very narrow basement high immediately north of them. We describe below the main sedimentary units from bottom to top, the crustal reflectivity, and finally detail the coincident refraction velocity model.

Sediments and Seismic Sequence Boundaries

A prerift sedimentary unit (green unit) is identified in basins A and B (Figure 5). Internally, the prerift sedimentary unit is characterized by a rather chaotic facies that would be difficult to differentiate from a crystalline basement if it were not for the presence of sparse and low-amplitude internal reflectors (dashed purple in Figure 5). This layer may represent the old Precambrian basement of the South China block, its Late Proterozoic and Paleozoic cover of mostly Sinian to Devonian clayey and sandy flysch, Devonian quartzite, Carboniferous to Permian limestone, and Triassic sandstone. Atop this unit, a well-expressed acoustic basement shows distributed fault offsets, while subhorizontal wavy (in time domain) reflectors lie at the base of , 1986). We will discuss later the whereabouts of this unit to the north in basin C.

Above the prerift unit lies a sequence (brown units on Figure 5) assumed to correlate with the early basin fill of coarse clastics during the formation of onshore basins from late Cretaceous to late Eocene [START_REF] Chan | Polyphase rifting of greater Pearl River Delta region (South China): Evidence for possible rapid changes in regional stress configuration[END_REF]. Although this unit generally fills passively the depressions, it sometimes thins laterally indicating local block rotation [START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF]. This unit has a rather chaotic to transparent facies with coarse noise.

In all basins, we then observe a stratified unit (light orange) of variable thickness, loosing reflectivity where tilted. Within basins A and B, this unit is affected by numerous and sharp faults, but without clear syntectonic wedges. This would indicate that sedimentation rate was very high and/or extension rates on steep faults were low during deposition.

Above this light orange unit, we observe a strong erosive surface truncating tilted reflectors (best visible on Figure 5 from markers 190 to 215) with a layer of postextension sediments (colorless on Figure 5) sometimes directly lying upon it (markers 190 to 200; Figure 5). On the sides of the rollover structure however, we image a clear synextension sediment unit with a thickness (yellow in Figure 5) decreasing toward the top of blocks bounded by faults, although sedimentary wedges are not extremely developed. In some places, we identify two unconformities and onlaps in the synrift sediments, in accordance with descriptions of the synrift packages observed in other locations in the SCS (e.g., [START_REF] Ding | Crustal Structure across the northwestern margin of South China Sea: Evidence for magma-poor rifting from a wide-angle seismic profile[END_REF][START_REF] Franke | The final rifting evolution in the South China Sea[END_REF]. The continuity of the previously described erosive surface can be followed within the yellow synextension layers, showing that this phase of extension on shallow rooting normal faults took place under very shallow water level.

To the north, in basin C (Figure 6), a similar wedge-shaped synextension layer is also observed, possibly bounded by two coral reefal structures (light purple in figure 6). Thin in basins A and B, postrift Below the yellow synextension unit in basin C (Figure 6), we identify a unit showing chaotic signals typical of sediments having experienced gravity collapse or sliding. From the position of the unit between the basement and the synextension yellow unit, we identify it as being similar to the light orange unit in basins A and B (Figure 5).

Crustal and Mantle Reflectivity

In Figure 3, we indicate the main subbasement reflectors. Reflector D actually represents a thick strip of reflectors interpreted as a shallow décollement-a subhorizontal low-friction surface-where listric faults bounding the above described rollover structure root. Figure 5 shows a more detailed image of the reflectors being a part of this shallow décollement below the green metamorphic sedimentary units. We will discuss in the next section what this décollement becomes in basin C. Deeper in the crust, intracrustal reflectors are labeled Rc1, Rc2, Rc3, and Rc4. Odd Rc numbers correspond to reflectors below basins A and B while reflectors with even Rc numbers are found below basin C. In the following, the second (s) unit stands for two-way travel times. Rc1 reflectors are found ~1-2 s below décollement D while Rc2 reflectors are found ~1-2 s below the acoustic basement of basin C (Figure 3, zooms on Figures 5 and6). Rc1 reflectors are a clear indication of the sedimentary nature of at least some part of the local continental crust. The many reflectors, although with low signal-to-noise ratio, appear subparallel and sometimes tilted. Rc3 is the next reflector being imaged at ~3 s below décollement D (1-s TWT below Rc1; Figure 3) while Rc4 is found at an equivalent ~2-3 s below the acoustic basement of basin C (1 s below Rc2; Figures 3 and6). Finally, weak reflectors M1 and M2 are found around 9 to 11-s TWT corresponding to Moho depths.

Reflectors D and Rc4 are close to the seafloor first multiple. Indeed, Figure 5 shows that some multiple residuals, although weak, are still sometimes visible just above reflector D. These artifacts have the particularity to be overmigrated (migration smiles). We see that the shape of the several reflectors below the artifacts correspond neither to the geometry of the seafloor nor to the shallow post rift sediments. Besides, D reflectors are well migrated and form a complex pattern of sigmoid-shaped geometries. For reflectors D and Rc4, prestack data displayed on, respectively, Figures S5 andS6 show that the reflection events have a very different moveout in CDP gathers when compared to the seafloor multiples. Reflector D and Rc4 stack at a much higher velocity and are visible at a large range of offsets in CDP gathers. The geometry of Rc4 is also not perfectly flat, which is yet the case of the seafloor. We conclude that the crustal reflectivity is real and we will discuss it jointly with the refraction velocity image.

Structure of the Refraction Velocity Field

In Figure 4a, the geometries of the two sedimentary layers down to basement with velocities from 1.5 to 3.5 km/s are entirely defined from the coincident reflection seismic profile (see Figures 5 and6). The lateral variations of the velocity within these sedimentary layers, however, are interpolated between the sparse OBS receivers (18-km spacing). As a result, the velocity structure in the sediments does not always exactly follow the reflectivity (i.e., in basin C), by lack of resolution. This sediment velocity and more importantly the basement geometry are however crucial to properly model the deeper layers.

Layer 3 in Figure 4a, below tertiary sediments, lies between the acoustic basement and the approximate depth of the décollement D. The velocity ranges from 3.5 to 5.5 km/s. The 5-km/s velocity at the outcropping basement around marker 170 (Figure 4) corresponds to the location of the dredged Cretaceous paragneiss.

As the velocity is similar below the rollover structure basement, this was another reason to draw the green layer as we did in Figure 5. The bottom geometry of this layer 3 is mainly inspired by the presence of the D reflectors in the reflection image. However, the velocity contrast between Tertiary sediments and upper crust clearly appears milder in basin A/B when compared to basin C, where there is a direct contact between 3.5-km/s Tertiary sediments and an ~6.2-6.35-km/s basement (Figure 4). In basin C, we find no velocity corresponding to the green metamorphic unit visible in basin A/B. The large basement velocity contrast in basin C is in excellent agreement with the very high amplitude of the basement reflector there (Figure 6). 10.1029/2018TC005418

Tectonics

Velocities higher than 6 km/s correspond to the modeled top of the upper crustal layer, both beneath the Tertiary sediments of basin C and beneath D reflectors. The top upper crustal velocity decreases slightly to 6.1 km/s away from its maximum in basin C area. The base of the upper crust corresponds to some wide-angle intracrustal reflections in the OBS data. However, as in the reflection profile, the refraction data exhibit multiple, unclear crustal reflectors forming bands of reflectivity similar to the Rc3 series (Figure 3). This is the case even further to the north of the Rc3 zone where the reflection image does not show anything clear because the basement high (marker 170; Figure 3) prevents a good imaging of the crust. Consequently, it is difficult to identify a single clear reflector for the base of upper crust in the refraction data. The overall velocity of the crust (including lower and upper layers) is the only robust feature to interpret, not the thickness of the modeled layers that are used solely for construction of the best fitting model with two linear gradients.

The rationale for dividing crustal layers into upper and lower is still that the upper crustal layer has a higher velocity gradient than the lower crustal layer, especially below basin C with 0.08 s -1 for the upper crust to be compared with 0.02 s -1 in the lower crust below. The lower crustal velocity and velocity gradient are especially well constrained by a very long offset secondary arrival phase typical of continental lower crust (Pc2; Figure S4). The top and bottom velocities of the lower crustal layer are, respectively, 6.5-6.8 and 7.0 km/s and are very stable laterally.

Finally, the Moho geometry (or base of the lower crustal layer) is well constrained by many PmP wide-angle reflections that coincide well with the Moho visible in the reflection profile (see Figure 7), especially its 5-km uplift below basin C. The Moho is rather flat elsewhere. Below basin C, crust has thinned from 20 to less than 15 km over a distance of about 50 km. A mantle dome is located off the main axis of the basin (Figure 7c). To explain the presence and location of the dome, a north verging detachment-a long-lived, low-angle normal fault-is the most obvious [START_REF] Wernicke | Unifor-sense normal simple shear of the continental lithosphere[END_REF]. This large crustal detachment controlling the formation of basin C is the dominant feature of this key section of the SCS (Figure 7c). Figure 8 shows a zoomed image of the flat footwall of the detachment and sedimentation above, while Figure 9 shows the hanging wall block surface. The detachment clearly controls the tilt and slide of large blocks of upper crust. We can infer that if a basin was filled by sediments before the main activity of the detachment, this basin would collapse because of the space created by the apparent 15-km Tectonics detachment heave (Figure 6). The basement-sediment interface was indeed destabilized by the tilting, thus resulting in secondary and shallow sedimentary detachments rooting on the basement surface (Figure 8) or mass transport deposits (MTD).

Although the interpretation of the collapsed units is not easy because of the 3-D nature of the events, the aspect of the seismic packages still shows coherency at places and appears to be clear-cut (Figures 7 and8) at their base on the detachment and on the décollement above the hanging wall (dashed surface on Figure 8). We therefore favor the interpretation of early syntectonic sediments left-behind during the activity of the large offset detachment.

Above these slided units, large or tiny localized wedges (yellow units in Figures 7 and8) show a more recent activity in basin C. This last event may be correlated to the final stages of the extension during the sea floor spreading of the SWSB from Early Miocene to late Middle Miocene. This late extension does not seem to be 6 and7). The images show interesting "dome-like" structure below the basement that could be the lateral echoes from a volcano. The feature is located beneath the interpreted carbonate platform (purple) that built between the MMU and the end of extension (blue horizon).

10.1029/2018TC005418

Tectonics accommodated along the main north dipping detachment. Instead, we observe a southward verging shallow fault rooting on the exposed footwall of the detachment (Figure 8).

Structural Contrast Between Basins A/B and C

The geometry of deformation within basins A and B can be entirely explained with faults rooting in a shallow décollement (D), although it is possible that the main rollover bounding fault forming basin B could in fact initially root deeper in the Rc1 reflectors structure (grey fault in Figure 7c). In basin C however, except for the latest phase where small offsets sedimentary faults root in the exposed footwall décollement at the base of the collapsed units (Figure 8), most if not all of the extension was taken onto the deep rooting detachment fault, explaining the size and depth of basin C itself.

Another difference between basin A/B and basin C is the apparent absence of the metamorphic sedimentary unit (green unit; Figures 5 and6) in basin C. This interpretation mainly results from the observation of a high refraction velocity of the footwall and hanging wall basements in basin C (6.2-6.35 km/s) when compared to the basement of basins A/B (around 5 km/s; Figures 4 and7). This high velocity in basin C compares well with velocities just below the décollement D of basins A and B, suggesting that the only difference is the missing layer 3. Based on velocities (Figures 4 and7), we infer that what we interpret as a metamorphic unit re-appears north of basin C in a southward tilted basin (Figure 5).

An inherited contact between the upper crust (Paleozoic sediments and crystalline rocks) and Mesozoic sediments could explain the absence of the green metamorphic sedimentary unit in basin C. A possible candidate could be a former thrust active at the time of formation of the Yanshanian belt [START_REF] Faure | Is the Jurassic (Yanshanian) intraplate tectonics of North China due to westward indentation of the North China block?[END_REF]; see a simplified sketch in Figure 10, phase 0). Dredged Cretaceous metamorphic rocks (paragneiss and phyllites) point to a burial depth of ~20 km at the footwall side of the present-day detachment [START_REF] Tectonics Kudrass | Mesozoic and Cenozoic rocks dredged from the South China Sea (Reed Bank area) and Sulu Sea and their significance for plate-tectonic reconstructions[END_REF], which is another indication for erosion related to orogeny that could have scalped the Mesozoic sediments in basin C before the activity of the detachment. This basin C detachment would then correspond to the reactivation of an inherited, low-angle contact (Figure 10, phase 0), explaining the absence of the green unit today (Figures 6 and7) and the oblique orientation of the basin (Figure 2).

Basin A is a graben filled with a thin synextension brown unit and a thick light orange sedimentary unit that does not show any clear onlap or wedge (Figure 5). We observe that this same light orange unit filled a "proto basin C" before the main activity of the detachment in basin C (Figure 10) that triggered the collapse of these sediments. This suggests a first phase of deformation in all basins before the detachment really fully reactivates the inherited contact (Figure 10).

Phases of Deformation and Relative Chronology

The images presented herein suggest the succession of at least two main extensional phases. A very early phase of deformation is responsible for the distributed small offset basement faulting in basin A/B and also possibly C (small densely spaced black faults in Figures 5,6, and 10). The deformation then develops with the dismantling of the green metamorphic sedimentary unit by mostly steep faults creating proto basins A/B (Figure 10, step 1). Initially, only a coarse sedimentation from the erosion of faulted metamorphic units and other basement highs fills the basins (brown units) with a very low sedimentation rate. This is to be compared with the molasse basins of the south margin of China [START_REF] Chan | Polyphase rifting of greater Pearl River Delta region (South China): Evidence for possible rapid changes in regional stress configuration[END_REF][START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF]. This early phase ends with the steep fault bounded basins being filled with the light orange sedimentary unit (Figure 9, step 2). This unit was also probably deposited in a small proto-basin C.

Although the light orange unit shows tilted reflectors, the reflectors are not showing clear syntectonic wedges. We suggest two hypotheses regarding the deposition of this unit: either (1) low extension rate and high sedimentation rate were accommodated onto nonrotating steep faults or (2) there was really no fault activity in basins A/B. In Figure 10, step 2, at variance with many studies in the area (e.g., [START_REF] Ding | Seismic stratigraphy and tectonic structure from a composite multi-channel seismic profile across the entire Dangerous Grounds, South China Sea[END_REF][START_REF] Peng | Rift-drift transition in the Dangerous Grounds, South China Sea[END_REF][START_REF] Song | Rifting to drifting transition of the Southwest Subbasin of the South China Sea[END_REF], we do not interpret the sedimentary unit just above the acoustic basement (T g ) in basins A/B as the main synrift, as already suggested by [START_REF] Wang | Seismic evidence for Mesozoic strata in the northern Nansha waters, South China Sea[END_REF].

Because we know that the detachment will accommodate a lot of extension later and the green Mesozoic unit still need to undergo boudinage, the observed properties of the light orange unit in basins A/B imply a multiphase extension or only a temporary local gap of extension, possibly under the effect of nearby The erosional surface (dashed red, Figure 5) truncates the tilted subparallel reflectors of the light orange unit on both sides of the rollover structure (see Figure 5). This indicates that the bounding listric faults observed today tilted basins A and B before uplift and erosion.

Step 3a of Figure 10 illustrates this phase of significant We suggest that the synrift unit corresponding to this step has been eroded (Figure 10, step 3a to 3b). The corresponding synrift may however be preserved southwest of our line, where basins A and B seem to be better developed (Figure 2).

The crustal-scale detachment that led to the formation of basin C accommodated ~15 km of horizontal extension (Figures 5 and6). Syntectonic wedged sediments are absent, as expected along a flat (or low-angle) detachment surface. The fact that what appears to be the main rifting phase is finally poorly recorded in the sedimentation record may indicate a short-lived event.

MTDs observed above the detachment surface are most probably composed of sediments deposited during step 2 (Figure 10). An unconformity (dashed red in Figures 8 and9) and possible carbonates (purple in Figures 8 and9) also tops the MTDs. Basin C being located less than 20 km north of basin B, we infer that the unconformity in C is coeval with the erosional event in basins A and B. As we observe the unconformity on average 2-s TWT deeper in basin C today and the burial of the carbonate platform above the relatively thin MTD unit, we conclude that the main detachment activity constitutes a step that postdates step 3a, although an overlap cannot be excluded (see step 3b of Figure 10).

The synextension wedges visible today (yellow unit;Figures 5,6,8,and 9) do not seem to have recorded any of the extension we described until now, explaining why they are not well developed. In basins A and B, the extension recorded in the yellow unit is a rather minor continuation of the rollover tilt of step 3 (see Figure 10, step 4) in shallow water conditions. This extension on the bounding listric faults explains the tilt of the erosional surface observed today (Figure 10, step 4). South of the profile in basin A, shallow faults in the sediments also offset the erosional surface (Figures 5 and 10) but overall do not account for significant finite extension. In basin C, the latest phase of extension (yellow units; Figure 10, step 4) is also a small sag-type gentle tilt. We suggest that it is quite the same in basins A and B, where this last phase of extension looks more significant but could just be the result of the presence of the weak shallow décollement D amplifying final gravity adjustments. Interpreting in too much details recent unconformities as phases of extension in the SCS may be an overinterpretation of very local final adjustments, when actually the really large extension phase is older and barely recorded in sediments. A single detachment fault can potentially explain the mantle dome, the lower crustal thickening, and the surface geometries. The deep fault geometry is however not imaged directly and can be inferred only from the sparse deep reflectors. Reflector Rc4, in particular, is strong in amplitude and is imaged on the footwall side (S) 2 km shallower than on the hanging wall side (N; Figure 7). In both locations it matches quite well the boundary between upper and lower crusts in the refraction velocity model. It could be reasonable to infer that the detachment fault locates in between the two Rc4 reflectors (Figure 11b) to offset them. This first hypothesis also implies that the Rc4 reflectors do not correspond to a décollement level and that the lower crust is not likely to be ductile. The reflectors are then probably inherited from pre-Tertiary events. However, the limited 2-km offset between the south and north Rc4 branches is too small compared to the 15-km surface offset of the detachment (Figure 11b), unless they were first thrust-offset before extension. Besides, in order not to cross the hanging wall-side Rc4 reflector (N), the detachment fault would have to down bend to a 40°dip angle, which may be a bit too steep for a reactivated thrust structure (Figure 11b).

Another possibility is to consider a detachment limited to the upper crust and rooting at the top of the lower crust on a shear zone that could be Rc4 itself. In this case a lower angle of 25-30°would be maintained along the crustal detachment (Figure 11a). Rc4 reflectors would be indicative of ductile flow in the lower crust (Figure 11a), unless solely the midcrust was ductile [START_REF] Mohn | Necking of continental crust in magma-poor rifted margins: Evidence from the fossil Alpine Tethys margin[END_REF][START_REF] Péron-Pinvidic | The final rifting evolution at deep magma-poor passive margins from Iberia-Newfoundland: A new point of view[END_REF]. We however favor interpretations including a warm, fully ductile lower crust [START_REF] Clerc | Rifted margins: Ductile deformation, boudinage, continentward-dipping normal faults and the role of the weak lower crust[END_REF], as it is commonly accepted in the South China Sea. The SCS has many properties of a type II margin in the sense of [START_REF] Huismans | Depth-dependent extension, two stage breakup and cratonic underplating at rifted margins[END_REF] with for instance a limited synrift subsidence that may be due to mantle breakup preceding crustal breakup. In this situation, it seems natural to observe a mantle dome and favor the classic pure shear in the ductile lower crust and simple shear in the upper crust with a detachment rooting at the base of the brittle upper crust (Figure 11a; [START_REF] Wernicke | Unifor-sense normal simple shear of the continental lithosphere[END_REF][START_REF] Weissel | Flexural uplift of rift flank due to mechanical unloading of the lithosphere during extension[END_REF].

If basin C crustal detachment gives good insight on how extension is accommodated at depth around the detachment, we do not image any obvious structures related to extensional process deep below basins A and B, perhaps because of less favorable acoustic conditions (basement of basins A and B is shallower than basin C basement, with more basement geometry lateral variations, poor refraction ray coverage at the edge of the profile). Another hypothesis is that once extension localized on the main detachment, other deep structures in the vicinity were abandoned, in a similar manner than what we show for the shallow structures in Figure 10 (steps 2 and 3b). A third possibility is that this central part of Dangerous Ground (Figure 1) is a thicker and more rigid continental ribbon that poorly deformed while extension localized south in the NW Borneo Trough and Palawan Trench where crustal thickness is lower. In the next section, we will see how to interpret the extensional events summarized in Figure 10 in the framework of the timing of opening of the SCS.

Timing of Extension in the Framework of the South China Sea

Although we could not perform any correlation of our profile horizons with wells, some steps of the relative chronology detailed in section 5.3 and Figure 10 can be dated in light of what has been previously described in the SCS.

Two recent studies [START_REF] Peng | Rift-drift transition in the Dangerous Grounds, South China Sea[END_REF][START_REF] Wang | Seismic evidence for Mesozoic strata in the northern Nansha waters, South China Sea[END_REF] have interpreted seismic profiles acquired close to ours. In [START_REF] Wang | Seismic evidence for Mesozoic strata in the northern Nansha waters, South China Sea[END_REF], sedimentary units below the erosive surface found within basins A and B (dashed red on Figure 5) are all interpreted as being Mesozoic. The main argument is MCS-derived P waves velocities. Although we agree that this unit is not synrift in the strict sense, regarding the age, we favor previous interpretation by [START_REF] Ding | Seismic stratigraphy and tectonic structure from a composite multi-channel seismic profile across the entire Dangerous Grounds, South China Sea[END_REF] and [START_REF] Song | Rifting to drifting transition of the Southwest Subbasin of the South China Sea[END_REF] with a Cenozoic unit. We find that the main velocity contrast is at the base of this unit (basement, top of the green Mesozoic units in Figure 5) and not at the top of it. Refraction velocities obtained for the light orange unit are actually not excessive for regular compacted Cenozoic sediments. A last hint in favor of a late Oligocene-Early Miocene unconformity is the presence of the carbonate platform in basin C. This interpretation is based on the characteristic continuous subparallel reflectors with low-frequency content of the Nido platforms as described by [START_REF] Steuer | Oligocene-Miocene carbonates and their role for constraining the rifting and collision history of the Dangerous Grounds, South China Sea[END_REF]. This would assimilate the unconformity at the base of the platform as the Late Oligocene Breakup 10.1029/2018TC005418

Tectonics

Unconformity and the top of the yellow unit as the Middle Miocene Red Unconformity (blue line in Figure 9) marking the end of opening (see also [START_REF] Morley | Major unconformities/termination of extension events and associated surfaces in the South China Seas: Review and implications for tectonic development[END_REF].

We therefore tentatively assign a Paleocene to Oligocene age to our brown and light orange units. Our profile does not image any clear Paleogene synrift, indeed usually absent close to the continent-ocean transition of the SW subbasin according to [START_REF] Franke | The final rifting evolution in the South China Sea[END_REF]. Overall, this interpretation is in agreement with ages quoted in [START_REF] Madon | The structure and stratigraphy of deepwater Sarawak, Malaysia: Implications for tectonic evolution[END_REF] constrained by wells south of the Dangerous Ground area. They infer that the faulted and tilted unit lying above basement-quite similar to our light orange unit-is Middle Eocene (43 Ma) to Early Oligocene (30 Ma), with an Early Miocene erosional unconformity. Early Miocene carbonates are also found in the vicinity of OBS 1, where the erosion surface almost outcrops, and around OBS 4, where they were dredged along with the paragneiss (Figure 2; see also [START_REF] Tectonics Kudrass | Mesozoic and Cenozoic rocks dredged from the South China Sea (Reed Bank area) and Sulu Sea and their significance for plate-tectonic reconstructions[END_REF] at the detachment footwall side boundary of basin C.

Regarding the timing of the detachment, we suggest in Figure 10 (phase 3b) that its activity starts during or just after the "breakup unconformity/erosional event," which is compatible with a breakup propagation attempt similar to Xisha trough [START_REF] Gao | Crustal structure and extension mode in the northwestern margin of the South China Sea[END_REF] but probably more recent, as is the failed breakup south of Macclesfield Bank, just before seafloor spreading in the SW subbasin (23 Ma; see Figure 1). We infer that the uplift explaining the significant erosional event is due to the thermal effect of the proximity of the propagation head proceeding toward the SWSB. Just after, subsidence is much larger in basin C due to the crustal detachment activity while basins A and B remain between shallow water and subaerial conditions until the end of extension, when postrift sediments are finally deposited.

The age of the first steps of extension is more difficult to estimate. The very early distributed phase corresponding to densely spaced faulting of the basement would correspond to late Cretaceous based on the comparison with small-offset faults found in the Cretaceous series of the Pearl River Basin [START_REF] Chan | Polyphase rifting of greater Pearl River Delta region (South China): Evidence for possible rapid changes in regional stress configuration[END_REF]. The later phase related to the steep faults cutting the Mesozoic unit could be associated to the "stretching phase" [START_REF] Manatschal | Observations from the Alpine Tethys and Iberia-Newfoundland margins pertinent to the interpretation of continental breakup[END_REF][START_REF] Péron-Pinvidic | Structural comparison of archetypal Atlantic rifted margins: A review of observations and concepts[END_REF] affecting the basement reflector in the South China Sea, when it can be observed. A good timing for this stretching phase would be Eocene, when extension is widely recorded in the SCS before Oligocene spreading in the NE subbasin (Figure 10, steps 1 to 2).

Conclusion

Our joint processing and interpretation of MCS reflection and OBS refraction data is able to partially compensate the poor recording of the extension by sediments in this area of Dangerous Ground. We were able to unravel the geometry of a dismantled Mesozoic sedimentary unit and confirm the significance of a crustal detachment. From our interpretation and the relative chronology of events established in the framework of the SCS, we draw several conclusions:

1. The latest phase of extension recorded in Miocene sediments, the only clearly recorded phase, is not very significant when compared to the finite deformation unraveled from the deep seismic image. Most of the extension in the Dangerous Ground area takes place from late Cretaceous to end Oligocene/early Miocene and this main extension is barely recorded in sediments, at least in this profile. 2. Extension seems to heavily reactivate inherited contacts between Paleozoic and Mesozoic units, with block rotation and rafting on décollements when contacts are flat or detachments when contacts are tilted. 3. Structures and basins oblique (NNE-SSW) to the extensional direction (Figure 2) can be explained by the reactivation of contacts bounding the Jurassic-Early Cretaceous arc related granitic plutons now spread in the SCS (Figure 1; see [START_REF] Zhou | Mesozoic paleogeography and tectonic evolution of South China Sea and adjacent areas in the context of Tethyan and Paleo-Pacific interconnections[END_REF][START_REF] Savva | Different expressions of rifting on the South China Sea margins[END_REF]. The basin imaged in our study has an orientation in line with the Zhongnan-Lile fault described separating the Eastern and SW subbasins [START_REF] Ru | Episodic Rifting and subsidence in the South China Sea[END_REF][START_REF] Sibuet | Geodynamics of the South China Sea[END_REF][START_REF] Yao | Characteristics and tectonic meaning of Zhongnan-Lile Fault[END_REF]. 4. The lesser extent of thinning compared to Xisha trough style basins can be explained by the fact that the detachment reactivating the oblique contact is not optimally oriented. 5. Stalling and fast oceanic propagation periods are controlled by far-field dynamics and imply, respectively, homogeneous thinning ahead of the propagator and necking around the propagator (Le [START_REF] Pourhiet | Continental break-up of the South China Sea stalled by far-field compression[END_REF]. However, locally, reactivation of inherited structures control how deformation is accommodated in both homogenous thinning and near-propagator necking situations.

10.1029/2018TC005418 Tectonics

Figure 1 .

 1 Figure 1. (a) The 1,000-km-long seismic line in the South China Sea with positions of the 50 OBSs (Pichot et al., 2014). The 230-km-long section of the profile across Spratly Islands is indicated in red and orange. SWSB = Southwest subbasin, ESB = Eastern sub-basin. (b) Extract of the structural map of the South China Sea (Pubellier et al., 2016). M.B. = Macclesfield Bank (Zhongsha Islands), NWBT = NW Borneo Trough, NWPB = NW Palawan Basin, PKB = Phu Khan Basin, PRMB = Pearl River Mouth Basin, PT = Palawan "Trench," QDN = Quiondongnan Basin, RB = Reed Bank, RBB = Reed Bank Basin, SI = Spratly Islands (Zenghe High, Nansha Islands), XT = Xisha Trough, ZKM = Zongsha-Xisha Massif. The black frame shows the location of Figure 2.

Figure 2 .

 2 Figure 2. Spratly Islands (Nansha Islands) and Reed Bank area (see black frame in Figure 1 for location). Blue diamonds are dredged rocks in the vicinity of the line. OBS locations are indicated with white circles. Yellow areas are tertiary basins, and orange bricks represent reefal platforms, Brown areas with "cross" signs represent Mesozoic granitoïds. Basins A, B, and C visible on Figure 3 are indicated.

Figure 3 .

 3 Figure3. Section of the 230-km-long processed MCS profile from 110 to 225 km (see location on Figure1). This section, south of the Spratly Islands (Nansha Islands), is the most sedimented, therefore allowing the imaging of deep reflectivity. The section from 0 to 110 km, more difficult to process (see text), is presented in FigureS1in the supporting information. Vertical axis shows seconds in two-way travel times (sTWT)

Figure 4 .

 4 Figure 4. Velocity model obtained by forward modeling. (a) Depth model with OBS number indicated (see positions onFigure2) and layers (see Table1). (b) The two-way travel time (TWT) converted model shows strong lateral velocity variations leading to a difficult (1-D) time migration, in particular from 0 to 110 km (FigureS1).

Figure

  Figure 4. Velocity model obtained by forward modeling. (a) Depth model with OBS number indicated (see positions onFigure2) and layers (see Table1). (b) The two-way travel time (TWT) converted model shows strong lateral velocity variations leading to a difficult (1-D) time migration, in particular from 0 to 110 km (FigureS1).

Figure 5 .

 5 Figure 5. Southernmost section of the profile corresponding to the frame outlined in Figure 3b (basins A and B). The images displayed are all prestack time migrated. The images have been cut to ~7-s TWTT. (a) Uninterpreted image. The dashed ellipse shows probable lateral echoes that are not possible to properly migrate in 2-D. (b) Interpreted image. Green units are interpreted prerift metamorphic sediments; brown and light orange units are Paleogene basin fill. Yellow units are synrift, most likely Miocene sediments (see text).

Figure 6 .

 6 Figure 6. Section of the profile corresponding to the frame outlined in Figure 3a crossing basin C. The images displayed are all prestack time migrated. The images have been cut to ~7-s TWTT. (a) Uninterpreted image with frames locating Figures 8 and 9. (b) Interpreted image. Green units are interpreted prerift metamorphic sediments; brown and light orange units are Paleogene basin fill. Yellow units are synrift, most likely Miocene sediments; purple units are interpreted as carbonate platforms (see text).

Figure 7 .

 7 Figure 7. (a) Time converted refraction velocity model superimposed on the time migrated reflection seismic section. Black dashed lines are crustal reflectors seen in (b) the uninterpreted time domain MCS image. Thick black lines are potential faults after interpretation of the position of the reflectors in (c) the depth domain velocity model. The dashed ellipse indicates a migration artifact.

Figure 8 .

 8 Figure 8. Blow-up image of the south of basin C (see Figure 6 for location). Two different images are presented. (a) The interpreted image is the same processing than Figure 6. (b)The bottom image is also obtained with the processing of Figure6, but with a different color scale highlighting amplitude contrasts. Purple unit corresponds to interpreted carbonates built between the mid Miocene unconformity (breakup unconformity) and the end of extension (blue horizon). Yellow unit is interpreted as a Miocene unit while the collapsed light orange unit above basement is Eocene (see text and Figure10).

Figure 9 .

 9 Figure 9. Blow-up image of the north of basin C. Two different images are presented. (a) The interpreted image (top) is the same image than Figure 6. (b) The bottom image is obtained with the processing of Figure 6, but with another color scale highlighting amplitude contrasts differently. Thick dashed black lines represent a décollement level above the hanging wall basement surface. It is continuous with décollement north of basin C (see Figure6 and 7). The images show interesting "dome-like" structure below the basement that could be the lateral echoes from a volcano. The feature is located beneath the interpreted carbonate platform (purple) that built between the MMU and the end of extension (blue horizon).

  favor the second solution with an abandonment of basins A/B fault activity because of the nearby localization of extension on the detachment in basin C. In this situation, the light orange unit fill is synextension in basin C, but not in basin A/B (Figure 10, phase 2). Of course we have no evidence for the synextension nature of the light orange unit in basin C because the unit later collapses there, erasing the information.

Figure 10 .

 10 Figure 10. Sketch of the main phases of extensional deformation since Cretaceous. The yellow star represents dredged paragneiss (Kudrass et al., 1986) indicating a 20-km depth burial ~120 Myr ago. Colors correspond to units interpreted in the seismic profile in Figures 6, 8, and 9. Red faults represent activity of the faults at the indicated age. Dashed red faults are abandoned faults after localization of extension on the detachment (see text). Ages are suggestions discussed in the text. Red arrows indicate vertical motions.

Figure 11 .

 11 Figure 11. Sketch of the main detachment with possible upper and lower crustal thicknesses. (a) Favored model where the detachment is limited to the brittle upper crust and pure shear occurs in the lower crust. (b) Model with a mostly brittle crust and a detachment offsetting the midcrustal reflector (thick dashed black).

Table 1

 1 Details of the Different Picked Phases, Their Uncertainties, RMS Residuals (T RMS ), and Chi-Square Values

	Phase number	Phase name	Associated layer	Number of picks	Picking uncertainty	T RMS	Chi-square
	1	Direct wave	0 (water)	580	0.015	0.014	0.915
	2	Ps1	1 (sediments)	36	0.050	0.040	0.649
	3	PsP	1 (sediments)	325	0.080	0.099	1.530
	4	Ps2	2 (sediments)	228	0.050	0.042	0.704
	5	PbP	2 (sediments)	355	0.080	0.112	1.973
	6	Ps3	3 (metamorphic sediments)	1420	0.060	0.085	2.022
	8	Pc1	4 (upper crust)	4926	0.075	0.095	1.614
	9	PcP	4 (midcrust)	1202	0.100	0.094	0.882
	10	Pc2	5 (lower crust)	2956	0.080	0.091	1.304
	11	PmP	5 (Moho)	3529	0.100	0.080	0.647
	12	Pn	6 (mantle)	2017	0.100	0.109	1.194
		Total		17719		0.091	1.263

Acknowledgments

Ship and seismic equipment was supplied by GMGS. MCS data processing has been performed at ENS. We thank CGG for giving us access to the CGG Geovation 2013 software. The raw seismic data set can be found online (www.geologie.ens.fr/imagerie/). L.Y. was part of a project supported by the Joint Funds of the National Natural Science Foundation of China (grant U1505232). We thank Gaye Bayrakci, Mikael Evain and Weiwei Ding for their helpful comments.