S B Kuksin

N S Nadirashvili

A L Piatnitski

Hölder estimates for solutions of parabolic SPDEs

Keywords:

This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of R n . We suppose that the coefficients of the noise are L p -functions with sufficiently large p. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective Hölder norms have finite momenta of any order.

Introduction

This paper is devoted to L ∞ -and Hölder estimates for solutions of second-order parabolic stochastic partial differential equations (SPDEs) in bounded domains, under the minimal regularity assumptions on the coefficients. In recent years several works focused on the L p -and W l,p -theory for parabolic SPDEs; however, the W l,p -estimates obtained in these works rely on rather strong regularity assumptions on the coefficients. On the other hand, in various qualitative and applied problems the estimates in terms of L ∞ -or even L p -norms of the coefficients are very important. Major progress in this area was achieved by Krylov in [START_REF] Krylov | On L p -theory of stochastic partial differential equations in the whole space[END_REF], where the regularity assumptions were reduced essentially for equations posed in the whole R d .

In our work we propose another technique which allows us to further reduce the regularity assumptions and to treat initial-boundary problems for solutions of SPDEs with additive noise. Although this class of equations is smaller than that in [START_REF] Krylov | On L p -theory of stochastic partial differential equations in the whole space[END_REF], still it is sufficiently large and contains many important operators. Our approach differs essentially from that in [START_REF] Krylov | On L p -theory of stochastic partial differential equations in the whole space[END_REF] and gives rise to a shorter proof of the main results.

In this paper we study SPDEs of the form

du = Audt + N j=1 f j (x, t)dw j t , (x, t) ∈ Q × (0, +∞), u| t=0 = 0, u| ∂Q = 0, (1)
where Q is a smooth bounded domain in R n , w j t are standard independent one-dimensional Brownian motions, and f j (x, t) are progressively measurable L ∞ -or L p -functions; in the latter case p is sufficiently large. Regarding the operator A we assume that A is either a generic second-order uniformly elliptic operator with sufficiently smooth coefficients or is a divergence form uniformly elliptic operator with measurable bounded coefficients. In this paper we prove that a solution of ( 1) is a Hölder-continuous function a.s. and that the corresponding L ∞ -and Hölder norms have finite momenta of any order.

For a stochastically perturbed heat equation (i.e., for (1) with A = ∆) with periodic boundary conditions these estimates were proved by one of the authors in the appendix of [START_REF] Kuksin | A stochastic nonlinear Schrödinger equation 1. A priori estimates[END_REF]. It should be noted that the results of this paper can be generalized to the equations involving the infinitedimensional stochastic term ∞ j=1 f j (x, t)dw j t instead of the finite-dimensional one; L ∞ -convergence (or L p -convergence with sufficiently large p) of the sum ∞ j=1 |f j (x, t)| is then required.

On the basis of the L ∞ -estimates obtained in this work, one can examine the regularity of solutions of some nonlinear SPDEs and prove the solvability of these equations in certain functional spaces (see [START_REF] Kuksin | A stochastic nonlinear Schrödinger equation 1. A priori estimates[END_REF]). When analyzing SPDEs, the L ∞ -estimates of this type can be used in the same way as the classical maximum principle in the case of deterministic equations.

In the first part of the paper we obtain several estimates for Hölder and L ∞ -norms of solutions of deterministic parabolic equations. In what follows we make use of these estimates to derive point-wise bounds for increments of the solution of (1) and to estimate the corresponding function norms.

2 Setting of the problem. Technical estimates.

Let w j t be standard independent Brownian motions defined on a probability space (Ω, F, P), and let (F t ) be the corresponding filtration of σ-algebras. We assume that f j (x, t) are F × B-measurable, (F t )-adapted functions, where B stands for the Borel σ-algebra, and that at least one of the following two assumptions holds:

B ∞ :
|f (x, t)| 1 almost surely (a.s.) for all x and t,

B p : f (•, t) L p (Q) 1
a.s. for every t.

In the following two statements, A is a uniformly elliptic second-order differential operator of the form

A = a ij (x) ∂ ∂x i ∂ ∂x j + b i (x)) ∂ ∂x i + c(x)
with smooth coefficients.

Theorem 2.1. Let B ∞ hold. Then under the above conditions (a) for any k 0 and any T 0, a solution of problem (1) satisfies the estimate

E u k L ∞ (Q T ) C k exp(cT ), (2)
where

Q T = Q × [T, T + 1] and c = max(0, max Q c(x));
(b) the solution u(x, t) is Hölder-continuous a.s., and for any T 0, k 0, and 0 < θ < 1 2 the upper bound

E u k C θ (Q T ) C(k, θ) exp(cT ) (3)
holds.

In estimates (2), (3), and everywhere below, for brevity we write The case of a generic operator that satisfies our assumptions can be reduced to the case from Remark 1 by means of the following change of the unknown function U = exp(-αt)u, with a proper choice of α.

|u| L ∞ (Q T ) instead of |(u| Q T )| L ∞ (Q T ) , etc.
From now on we assume without loss of generality that c(x) 0. For a uniformly elliptic divergence form operator A with bounded measurable coefficients one has the following result.

Theorem 2.3. Let A be a uniformly elliptic divergence form operator with bounded coefficients. Then under the assumption B ∞ , (a) for any k 0 and any T 0, the solution of problem (1) satisfies the estimate

E u k L ∞ (Q T ) C k ;
(b) the solution u(x, t) is a.s. Hölder-continuous, and there is α > 0 depending only on the lower and upper ellipticity constants of A and on the geometry of the domain Q such that for any T 0, k 0, and 0 < θ < α the upper bound

E u k C θ (Q T ) C(k, θ) (4)
holds.

Under the assumption B p with p > d, (c) there exists α 0 > 0 such that estimate (4) holds true for every T 0, k 0, and 0 < θ α 0 .

The proof of these theorems relies on several auxiliary statements. Let us consider the following initial-boundary problem:

∂v ∂t -Av = 0, v t=0 = F (x), v ∂Q = 0, (5)
and denote by S t the corresponding semigroup:

v(•, t) = (S t F )(•), F = F (•).
The following statement deals with a "smooth" operator A.

Lemma 2.1. Let |F (x)| < M . Then, for any θ < 1, the following estimates hold with c > 0:

v(•, t) C θ (Q) c(θ)M t -θ 2 exp(-ct), (6)
|v(x, t + δ) -v(x, t)| c(θ)M t -θ δ θ exp(-ct). ( 7
)
Moreover, if

F L q (Q) M and q > 1, then v(•, t) C θ (Q) c(θ)M t θ 2 -d 2q exp(-ct), (8) |v
(x, t + δ) -v(x, t)| c(θ)M t -θ-d 2q δ θ exp(-ct). (9)
Proof. Denoting by G(x, y, t) the Green function associated with problem (5), we have

G(x, •, t) L p (Q) c(p)t -d/(2q) , 1 p + 1 q = 1 (10)
(see, for example, [START_REF] Friedman | Partial Differential Equations of Parabolic Type[END_REF]). This implies the inequality

v(•, t) L ∞ (R d ) c(p)t -d/(2q) F L q (R d ) (11)
for any F ∈ L q (R d ).

In addition to problem (5), we consider in the domains

Q γ = γQ = {γx : x ∈ Q}, γ 1, the initial-boundary problems ∂V ∂t -A γ V = 0, x ∈ Q γ , V t=0 = F (γx), V ∂Qγ = 0, (12)
where

A γ = a ij (γx) ∂ ∂x i ∂ ∂x j + γ -1 b i (γx) ∂ ∂x i + γ -2 c(γx).
Due to the smoothness of the coefficients of A and of the domain Q, by the standard elliptic estimates one has

∂ ∂t V (x, 1) + |∇ x V (x, 1)| c V (•, 1 2 )
L ∞ (Qγ ) (13)
uniformly in x ∈ Q γ , with the constant c that does not depend on γ (see [START_REF] Ladyzenskaja | Linear and Quasilinear Equations of Parabolic Type[END_REF], [START_REF] Gilbarg | Elliptic Partial Differential Equations of Second-Order[END_REF]). After an appropriate rescaling, the last estimate reads

t ∂ ∂t v(x, t) + t 1 2 |∇ x v(x, t)| c v •, t 2 L ∞ (Q) ( 14
)
for all t, 0 < t 1. From ( 11) and ( 14) it follows that

∂ ∂t v(x, t) ct -1-d 2q F L q (Q) , (15)
∂ ∂x v(x, t) ct -1 2 -d 2q F L q (Q) , (16)
for all t 1. Finally, we use the interpolation inequality

1 v C θ 2 v 1-θ L ∞ v θ C 1
to derive ( 6), [START_REF] Da Prato | Stochastic Equations in Infinite Dimensions[END_REF], and (8), ( 9) from ( 11), (15), and (16). For large t the required estimates follow from the exponential decay of the Green function. This completes the proof of the lemma.

For operators A with measurable coefficients we have the following result.

Lemma 2.2. Let A be a divergence form uniformly elliptic operator with bounded coefficients. Then there exists α > 0 depending only on the ellipticity constants of A and on the domain Q, such that for any θ < α a solution v of problem (5) admits all the estimates of Lemma 2.1.

Proof. The proof is rather similar to that of the preceding lemma and we outline it briefly. According to [START_REF] Aronson | Bounds for the fundamental solution of a parabolic equation[END_REF] the inequality (10) (and thus (11)) is still valid. The bound (13) is not valid any more but instead we can use the Nash-type estimates for the Hölder norms of the solution V (x, t) (see [START_REF] Gilbarg | Elliptic Partial Differential Equations of Second-Order[END_REF], [START_REF] Ladyzenskaja | Linear and Quasilinear Equations of Parabolic Type[END_REF]) to get that

V C α (Qγ ×[1,2]) c V •, 1 2 L ∞ (Q)
for some α > 0 and c independent of γ. The rest of the proof is the same as in the previous lemma. Now we proceed with problem (1) in a "smooth" case. Its solution does exist, is unique, and can be written in the form (see [START_REF] Da Prato | Stochastic Equations in Infinite Dimensions[END_REF]Chapter 5] and [START_REF] Krylov | On L p -theory of stochastic partial differential equations in the whole space[END_REF]) The last formula is, in fact, the definition of a mild solution. Clearly it is sufficient to consider one element of the sum above. In what follows the summation sign and the index j will be omitted. We begin by obtaining point-wise estimates of increments of the solution in x variables. To this end we denote [S t-τ f (x 1 , τ ) -S t-τ f (x 2 , τ )] by g(t, τ ) and introduce a random variable

u(t) = t 0 N j=1 S t-τ f j (x, τ )dw τ . 1 Denoting v L ∞
U = u(t, x 1 ) -u(t, x 2 ) = t 0 g(t, τ )dw τ .
The quadratic characteristics of the stochastic integral is given by X(t) = t 0 g 2 (t, τ )dτ . From Lemma 2.1 we derive the estimate

X(t) M 2 c(θ)|x1 -x2| 2θ t 0 t -θ exp(-2ct) dt M 2 c (θ)|x 1 -x 2 | 2θ ,
valid for any θ < 1. Thus, by the Burkholder-Davis-Gundy inequality we have

|U | p c 1 (p)E(X p/2 ) c(p, θ)M p |x 1 -x 2 | pθ , θ < 1. ( 17
)
Similarly, for a time increment we define

R = u(x, t + δ) -u(x, t) = t+δ t S t+δ-τ f (x, τ )dw τ + t 0 S t+δ-τ f (x, τ ) -S t-τ f (x, τ ) dw τ = I 1 + I 2 .
The first integral I 1 can be estimated as follows:

E|I 1 | p cδ p/2 M p . (18)
Indeed, if we denote S t+δ-τ f (x, τ ) by h 1 (t, τ ), then

t+δ t h 2 1 (t, τ )τ M 2 δ,
and required estimate (18) is a direct consequence of the Burkholder-Davis-Gundy inequality.

In order to estimate I 2 , we define

h 2 (t, τ ) = S t+δ-τ f (x, τ ) -S t-τ f (x, τ ).
By Lemma 2.1 we have

|h 2 (t, τ )| c(θ)M (t -τ ) -θ δ θ exp -c(t -τ )
for any θ < 1 2 . Thus,

t 0 h 2 2 (t, τ )dτ M 2 δ 2θ t 0 (t -τ ) -2θ exp -2c(t -τ ) dτ c(θ)M 2 δ 2θ
and by the Burkholder-Davis-Gundy inequality we have

E|I 2 | p c(θ)δ θp M p , θ < 1 2 . (19)
Combining ( 17), (18), and (19), we obtain

E |u(x 1 , t 1 ) -u(x 2 , t 2 )| p c(θ) |t 1 -t 2 | + |x 1 -x 2 | θp (20)
for any p > 1 and any θ < 1 2 .

3

Boundedness and Hölder-continuity of the solution; higher momenta.

This section deals with the estimation of L ∞ and C θ norms of the solution of problem [START_REF] Krylov | On L p -theory of stochastic partial differential equations in the whole space[END_REF]. The first statement here is given by the following lemma.

Lemma 3.1. Let the functions f j (x, t) satisfy condition B ∞ of the preceding section. Then (a) there is a.s. a continuous version of the solution u(x, t) of problem (1);

(b) under this choice of u(x, t), for any T 0 and any p 1, we have

E u p L ∞ (Q×[T,T +1]) c(p) < ∞.
Proof. The first statement follows immediately from (20) by the Kolmogorov theorem; it just suffices to choose a sufficiently large p.

To prove the second one we consider a cylinder Q T = Q × [T, T + 1] and define a sequence of sets

K n = {k ∈ Z d+1 k2 -n ∈ Q T }, n = 1, 2, . . . .
For an arbitrary vector e ∈ Z d+1 such that

|e| 1 ∼ max 1 j d+1 |e j | = 1, we then set ξ n,e k = |u((k + e)2 -n ) -u(k2 -n )|. By Lemma 2.1 we have E|ξ n,e k | p c(θ)2 -npθ , 0 < θ < 1 2 , (21)
for any p 1. Let us introduce the events

A n,e k,q = ω ∈ Ω | ξ n,e k Kq n .
From (21) by the Chebyshev inequality we get

P(A n,e k,q ) E|ξ n,e k | p K p q np c(θ) 2 -npθ K p q np .
For each n the total number of the events A n,e k,q is not greater than 2 c(d,Q)n . Thus the probability of the union A n q = k∈K |e| 1 =1 A n,e k,q satisfies the estimate

P(A n q ) c(θ)K -p q -pn 2 c(d,Q)n-θpn = c(θ)K -p α n ,
where α = 2 c(d,Q) /(2 θ q) p . If we set θ = 1 3 , q = 2 -1/6 , then α = 2c(d, Q)/2 p/6 . Finally, taking p > 6c(d, Q) + 1, we have α < 1 2 . Hence, for the probability of the event A = n>1 A n q the following estimate holds true:

P(A) c(θ)K -p . ( 22
)
From now on we assume without loss of generality that Q is a d-dimensional cube (0, 1) d . Indeed, to reduce the case of a general domain to that of a cube it suffices to extend the function u(x, t) in the exterior of Q as zero and to rescale the arguments if necessary.

Next, any point of Q can be represented in the form

x = ∞ j=1 e(j)2 -j , |e(j)| 1 1.
Let us denote x(m) = m j=1 e(j)2 -j (as usual, x(0) = 0). Clearly, u(x(0), t) = 0. Then, by the definition of the set A n,e k,q , for any ω ∈ A we have

u(x(m), t) -u(x(m + 1), t) Kq m = K2 -m/6 . Therefore, |u(x, t)| K ∞ m=1 2 -m/6 = K2 1/6 (2 1/6 -1). ( 23
)
It now follows from ( 22) and ( 23) that

P u L ∞ (Q T ) K c p (K + 1) -p for any p > c(d, Q). Finally, denoting U T = u L ∞ (Q T ) , we find that EU s T = ∞ 0 x s dP{U t x} = s ∞ 0 x s-1 P{U t x}dx sc p ∞ 0 x s-1 (x + 1) -p dx < ∞ if p > s + 1.
The lemma is proved.

In order to estimate the Hölder norms of u(x, t), let us first formulate the following simple assertion.

Lemma 3.2. Let a function g(y) satisfy the estimate

osc J g(•) γ n ( 24
)
in any small cube J which is a mesh of the grid 2 -n Z d+1 , i.e., in any J = 2 -n j + [0, 2 -n ] d+1 , where j ∈ Z d+1 . Then, for any ∆ ∈ R d+1 , one has

g(y + ∆) -g(y) 2γ [log 2 (1/|∆|)] ,
where [•] stands for the integer part.

Proof. For n = [log 2 (1/|∆|)] let us consider the family of closed cubes defined above. Clearly, both y and y + ∆ either belong to the same cube or they are situated in adjacent cubes having at least one point in common. So the statement of the lemma follows.

Next, for a solution of (1) and for any ω ∈ A, inequality (24) holds with γ n = Kq n . Thus, u((x, t) + ∆) -u(x, t) 2Kq [log 2 (1/|∆|)] 2Kq log 2 (1/|∆|)-1 = 2Kq -1 2 log 2 (q) log 2 (1/|∆|) = 2Kq -1 |∆| log 2 (1/q) .

If we put q = 2 -θ 1 with θ 1 < θ < 1 2 , then log 2 (1/q) = θ 1 , and the above inequality implies u((x, t) + ∆) -u(x, t)

2K2 θ 1 |∆| θ 1 4K|∆| θ 1 .
Therefore, for all ω ∈ A,

u C θ 1 (Q T ) 4K.
Taking into account (22) we derive from the last estimate that

P u C θ 1 (Q T ) > K c(p, θ 1 )K -p
for all p > 1. Finally, for any θ 1 < 1 2 and any m 1 the bound

E u m C θ 1 (Q T )
c(m, θ 1 ) can be proved in the usual way, and we arrive at the following assertion.

Theorem 2 . 2 .Remark 1 .

 221 If B p holds for some p > d, then (a) for any k 0 and any T 0, a solution of problem (1) satisfies the estimate (2); (b) the solution u(x, t) is Hölder-continuous a.s., and for any T 0, k 0, and 0 < θ < 1/2 -d/(2p) the upper bound (3) holds. If the zero-order term c(x) of the operator A is non-positive, then the exponential factor disappears in all the estimates (2)-(3) above.

  by γ0 and v C 1 by γ1, we have |v(x + y) -v(x)| 2γ0 and |v(x + y) -v(x)| 2γ1|y|. Raising these inequalities to the degrees (1 -θ) and θ, respectively, and multiplying the new ones, we get that |v(x + y) -v(x)| 2 1-θ γ 1-θ 0 γ θ 1 |y| θ . This relation implies the required inequality.

Lemma 3 . 3 .

 33 For any θ < 1 2 a solution u(x, t) of problem (1) is a.s. a C θ -function. Moreover, for any cylinder Q T and any m 1, the inequalityE u m C θ (Q T ) c(m, θ) holds.Now, to complete the proof of Theorem 2.1 it is merely sufficient to refer to Lemmas 3.1 and 3.3. Other statements of this work can be justified in the same way.


Upper Rhine Graben (France) with electromagnetic methods

HAL is

Introduction

Electricity and heat production using Enhanced Geothermal System (EGS) technology rely on our knowledge and prediction capacity of hydrothermal fluid property, mainly temperature and flow rate. Most of hydrothermal fluid properties are obtained from post-drilling phases, whereas proxy information is hard to access in an economically viable way. The main challenge is then to develop methods to access these properties at the early stage of the exploration phase.

Deep fractured reservoirs are usually characterized by non-destructive geophysical methods (seismic, gravity, etc.). However, these techniques have a low sensitivity to geothermal fluids and so, do not predict accurately the geothermal resource, and more particularly the flowrate, before drilling operation.

Due to their sensitivity to fluids and particularly brine water in rocks [START_REF] Archie | The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics[END_REF], passive electromagnetic (EM) techniques (e.g. Magnetotellurics or MT) or active (Controlled-Source Electromagnetic or CSEM) have been traditionally used to investigate the subsurface conductivity. EM methods have shown to be effective to characterize geothermal reservoir geometry in volcanic area [START_REF] Munoz | Exploring for geothermal resources with electromagnetic methods[END_REF], hydrocarbon reservoir geometry in offshore sedimentary area or onshore mineral exploration. Nevertheless, the ability of EM methods to image targets with high geothermal potential in deep fractured reservoir and in a high man-made noise environment still need to be demonstrated. Indeed, CSEM sources must compete with high noise levels and a conductive sedimentary cover resulting in low signal to noise ratio. In the framework of DEEP-EM project, we propose to adapt EM methods layout and imaging techniques to overcome these constraints and so reduce the risk of EGS projects exploration.

The benefit of the developed method will not be limited to deep fractured reservoirs but could be adapted to different settings like shallow geothermal reservoirs (e.g. Dogger layer in Paris Basin) and used to characterize other kinds of fluid content (e.g. CO2 storage).

Design of the CSEM exploration campaign using electrical resistivity logs

For about thirty years, the Upper Rhine Graben (UGR) has been a main target for research on geothermal exploration in deep fractured formations. Favorable targets are mainly deep and fractured hard rocks. In the last twenty years, geothermal activity in the Upper Rhine Graben has been on-going with several French (Soultz-sous-Forêts, Rittershoffen, Vendenheim, Illkirch), German (Landau, Insheim, Bruchsal, Bruhl) and Swiss (Riehen, Basel) deep geothermal sites which are active from exploration to exploitation. All these projects deal with deep fractured geothermal reservoirs located within Triassicsediments and/or crystalline basement [START_REF] Aichholzer | New stratigraphic interpretation of the Soultzsous-Forêts 30-year-old geothermal wells calibrated on the recent one from Rittershoffen (Upper Rhine Graben, France)[END_REF].

Predictive modelling suggests that CSEM anomalies in sedimentary basins are controlled at first order by the sedimentary cover resistivity (layer geometry and resistivity variation between and within the layers) and in a second order by hydrothermal fluid circulations. Hence, the knowledge of resistivity variations in the sedimentary cover is required to properly image deep fluid flow with high accuracy.

The Soultz-sous-Forêts and Rittershoffen (Alsace, France) geothermal wells data have provided electrical resistivity logs to study the electrical signature of deep fluid circulations. Preliminary results show a conductive trend for hydrothermally altered fractured zones and a highly resistive trend for unaltered facies (Figure 1) and hence a strong link between conductivity and permeable zones. These results will help to design an appropriated acquisition campaign, since investigation and resolution depth in EM measurements mainly depend on formation resistivity and on the transmitted frequency (Zonge and Hughes,1991).

Figure 1 GPK1 resistivity laterolog in granite (geothermal well from Soultz-sous-Forêts) linked with cuttings observation. Red arrows correspond to the position of the main permeable fracture zones [START_REF] Genter | Synthesis of geological and geophysical data at Soultz-sous-Forêts (France)[END_REF]. Red and yellow line correspond to resistivity average for unaltered facies and green and purple to altered facies. GRAN: Biotite porphyritic standard granite. PROP: Propylitised biotite porphyritic granite. MELA: Biotite-rich granite. LEG1: Leucogranite 1. LEG2: Leucogranite 2. HEMA: Hematitised biotite porphyritic granite. HMOD: Moderately altered granite. HHIG: Highly altered granite. HEXT: Extremely altered granite [START_REF] Traineau | Petrography of the granite massif from drill cutting analysis and well log interpretation in the HDR borehole GPK1 (Soultz, Alsace, France)[END_REF].

Field trial and exploration campaign

In July 2019, a CSEM/MT field trial (12 receivers (RX) installed every kilometre between Soultz-sous-Forêts and Rittershoffen plants) performed to validate the design of a large-scale exploration campaign. The main goal of this test was to prove that despite the anthropogenic noise in the area, the CSEM setup was appropriate to image resistivity variations in the deep fractured granitic basement. In particular, the distance (~3km) between electrodes transmitter (TX) was increased that resulted in an amplification of the dipole moment (product of dipole length by an inject current intensity) and allowed to obtain a good signal to noise ratio more than 10km away from the TX. CSEM data were inverted with MARE2DEM software [START_REF] Key | MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data[END_REF] and inversion results showed that the signal to noise ratio was sufficiently low to image resistivity variations within the basement. During the inversion process, the basement/sediments interface defined by seismic imaging was used to constrain the subsurface geometry to improve the vertical resolution of resistivity. Interestingly, inverted resistivity shows a good match with electrical resistivity logs within the sedimentary cover and granitic basement (Figure 2). (Soultz-sous-Forêts) and GRT-1 (Rittershoffen) geothermal wells are located on the W-E profile (Figure 3). Electrical resistivity logs from GPK-1 show a good match with the inverted resistivity.

Several geothermal power plants projects consisting of quadruplets (2 injection wells and 2 production wells) are planned in Northern Alsace with the aim to reach temperatures over 150°C and flow rate over 250 m3/h per well. The results of this field trial have been used to define the acquisition parameters of a large-scale exploration campaign (6 transmitters and 100 receivers spread on 150km², Figure 3) carried out in October 2020 and that covered the whole exploration license and aims at providing additional subsurface information to prioritize the geothermal areas of interest. Results from the 3D inversion of this dataset will be available by the time of the conference.

Figure 2

 2 Figure2CSEM/MT results from 2019 acquisition linked with the main formation isohypses. GPK-1 (Soultz-sous-Forêts) and GRT-1 (Rittershoffen) geothermal wells are located on the W-E profile (Figure3). Electrical resistivity logs from GPK-1 show a good match with the inverted resistivity.

Figure 3

 3 Figure 3 3D CSEM/MT exploration campaign planned in October 2020 and location of 2019 acquisition campaign.

Acknowledgements

The authors wish to thank the ADEME (French Agency of Energy and Environment) in the framework of the DEEP-EM project. The authors acknowledge the GEIE EMC and ECOGI for their grateful help in this project.

Conclusions

EM methods have been traditionally used to characterize shallow geothermal targets in volcanic context. The aim of DEEP-EM project is to develop these methods in order to use them for deep geothermal targets in sedimentary basins. Preliminary EM results showed the ability of resistivity measurements to provide information on deep fluid circulations at two different scales (borehole and reservoir). Electrical resistivity logs reveal a clear separation between altered/unaltered facies and furthermore a link between conductivity and permeable zones. At the reservoir scale, a CSEM field trial demonstrated the ability of the technique to image resistivity variations underneath a thick sedimentary cover (>1.4 km). These results have been used to design the acquisition of a large-scale EM exploration campaign in 2020 and provide additional subsurface information to prioritize the geothermal areas of interest.


V Mavromatis
email: vasileios.mavromatis@get.omp.eu

I M M Power

A L L Harrison

A Beinlich

G M M Dipple

P Bénézeth

Β Μαυρομάτης

Mechanisms controlling the Mg isotope composition of hydromagnesite-magnesite playas near Atlin, British Columbia, Canada

Introduction

Engineered carbon storage in the form of carbonate minerals has been proposed as a climate change mitigation strategy [START_REF] Lackner | Carbon dioxide disposal[END_REF][START_REF] Wilson | Offsetting of CO2 emissions by air capture in mine tailings at the Mount Keith Nickel Mine, Western Australia: Rates, controls and prospects for carbon neutral mining[END_REF][START_REF] Harrison | Accelerated Carbonation of Brucite in Mine Tailings for Carbon Sequestration[END_REF]Kelemen et al., 2011;[START_REF] Matter | Permanent storage of carbon dioxide in geological reservoirs by mineral carbonation[END_REF][START_REF] Matter | Rapid carbon mineralization for permanent disposal of anthropogenic carbon dioxide emissions[END_REF][START_REF] Power | Carbon Mineralization: From Natural Analogues to Engineered Systems[END_REF]. In this respect, the formation of Mg-bearing carbonates is of great interest because Mg is an abundant element in Earth's crust and a major constituent of seawater. Indeed, ultramafic settings have a high potential for CO2 uptake via the carbonation of Mg-silicate minerals. Despite the high concentration of Mg in aquatic environments and in silicate rocks, the formation of the thermodynamically most stable Mg-carbonate mineral, magnesite (MgCO3), is unlikely to occur at temperatures below 60 °C within timescales that would allow for its use as a CO2 storage medium [START_REF] Hänchen | Precipitation in the Mgcarbonate system--effects of temperature and CO2 pressure[END_REF][START_REF] Saldi | Magnesite growth rates as a function of temperature and saturation state[END_REF]2012[START_REF] Power | Room Temperature Magnesite Precipitation[END_REF]. This limitation is due to the very slow exchange of water molecules between the hydration sphere of the aqueous Mg ion and bulk water, which kinetically inhibits magnesite formation [START_REF] Bénézeth | Experimental determination of the solubility product of magnesite at 50 to 200°C[END_REF]2013). In low temperature environments the formation of hydrous Mg-carbonates such as lansfordite (MgCO3•5H2O), nesquehonite (MgCO3•3H2O) and hydromagnesite (Mg5(CO3)4(OH)2•4H2O) may occur and is often driven by evaporation [START_REF] Hopkinson | The Transformation of Nesquehonite to Hydromagnesite in the System CaO-MgO-H2O-CO2: An Experimental Spectroscopic Study[END_REF]2012;[START_REF] Beinlich | In situ sequestration of atmospheric CO2 at low temperature and surface cracking of serpentinized peridotite in mine shafts[END_REF][START_REF] Harrison | Accelerated Carbonation of Brucite in Mine Tailings for Carbon Sequestration[END_REF]2015;2016;[START_REF] Teng | Magnesium isotope geochemistry[END_REF][START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF][START_REF] Teng | Magnesium isotope geochemistry[END_REF][START_REF] Wilson | Carbon Dioxide Fixation within Mine Wastes of Ultramafic-Hosted Ore Deposits: Examples from the Clinton Creek and Cassiar Chrysotile Deposits[END_REF]2014;[START_REF] Assima | Impact of temperature and oxygen availability on the dynamics of ambient CO2 mineral sequestration by nickel mining residues[END_REF][START_REF] Oskierski | Chemical and isotopic signatures of waters associated with the carbonation of ultramafic mine tailings, Woodsreef Asbestos Mine, Australia[END_REF][START_REF] Mccutcheon | Microbially accelerated carbonate mineral precipitation as a strategy for in situ carbon sequestration and rehabilitation of asbestos mine sites[END_REF][START_REF] Teng | Magnesium isotope geochemistry[END_REF][START_REF] Turvey | Hydrotalcites and hydrated Mg-carbonates as carbon sinks in serpentinite mineral wastes from the Woodsreef chrysotile mine, New South Wales, Australia: Controls on carbonate mineralogy and efficiency of CO2 air capture in mine tailings[END_REF].

Owing to the measurable fractionation of Mg isotopes among natural waters, rocks, and plants (e.g., [START_REF] Young | The isotope geochemistry and cosmochemistry of magnesium[END_REF], this isotopic tool has been proven to be a powerful tracer of low-temperature biogeochemical processes such as plant growth, weathering and soil formation (e.g., [START_REF] Black | Magnesium-isotope Fractionation During Plant Growth[END_REF][START_REF] Pogge Von Strandmann | The influence of weathering processes on riverine magnesium isotopes in a basaltic terrain[END_REF][START_REF] Bolou-Bi | Experimental determination of magnesium isotope fractionation during higher plant growth[END_REF]Illina et al., 2013;[START_REF] Opfergelt | Magnesium retention on the soil exchange complex controlling Mg isotope variations in soils, soil solutions and vegetation in volcanic soils, Iceland[END_REF][START_REF] Oelkers | The efficient long-term inhibition of forsterite dissolution by common soil bacteria and fungi at Earth surface conditions[END_REF][START_REF] Mavromatis | The effect of permafrost, vegetation, and lithology on Mg and Si isotope composition of the Yenisey River and its tributaries at the end of the spring flood[END_REF][START_REF] Kimmig | Biogeochemical cycling of Mg and its isotopes in a sugar maple forest in Québec[END_REF]. The large isotope fractionation between solid and fluid has also been used to trace Mg isotope composition of oceanic water in the geological past [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF] as well as to constrain mineral formation temperature [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF]. The Mg isotope composition of Mg-bearing carbonate minerals has been shown to be distinctly enriched in the lighter 24 Mg isotope compared to silicate phases (e.g. [START_REF] Teng | Magnesium isotope geochemistry[END_REF], which has helped to decipher the Mg cycle [START_REF] Tipper | The magnesium isotope budget of the modem ocean: Constraints from riverine magnesium isotope ratios[END_REF]. Recently, the potential application of Mg isotopes to trace engineered CO2 storage has been explored [START_REF] Oelkers | Using stable Mg isotope signatures to assess the fate of magnesium during the in situ mineralisation of CO2 and H2S at the CarbFix site in SW-Iceland[END_REF][START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF].

The interpretation of the fractionation of Mg upon incorporation into carbonate minerals, however, is not always straightforward and may depend on mineral growth rate and formation pathway (Mavromatis et al., 2017b). For example, the incorporation of Mg in calcite is strongly affected by mineral growth rate effects [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF], whereas this growth-induced signature is rapidly erased in the case of Mg-calcite formation via an amorphous precursor (Mavromatis et al., 2017b). Although growth kinetic effects have been shown to affect the isotopic composition of Mg-bearing carbonates, which has direct implications for the interpretation of geological archives, growth rate effects have yet to be observed during the formation of hydrous Mg-carbonates. Indeed, the Mg isotope composition of nesquehonite and dypingite precipitated in laboratory experiments has been shown to be independent of growth kinetic effects and to be better described as a continuous exchange closed system process occurring at equilibrium conditions [START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF]. The same has been argued for the formation of hydromagnesite stromatolites in Lake Salda in Turkey [START_REF] Shirokova | Using Mg Isotopes to Trace Cyanobacterially Mediated Magnesium Carbonate Precipitation in Alkaline Lakes[END_REF]. However, the experimental studies comprise examples of hydrous Mg-carbonate formation in conditions with low solid to fluid ratios. In contrast, geological settings such as the hydromagnesite-magnesite playas near Atlin, British Columbia, Canada are dominated by the solid phase. Differences in solid to fluid ratios impact the extent to which exchange between fluid and solid affect the isotopic composition of solids, therefore studies in the field where solid:fluid ratios are high, provide additional insights into Mg isotope behavior between fluids and solids.

As described by [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF] based on field observations and mineralogical data, the precipitation of hydromagnesite in Atlin is interpreted to be limited by the transport of Mg-rich waters through evaporation above the water table. In contrast, waters throughout the sediment profiles (saturated and unsaturated zones) are supersaturated with respect to magnesite and its precipitation is interpreted to be reaction-controlled (i.e., controlled by precipitation kinetics; [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. Therefore, this site offers the opportunity to contrast the impact of different formation processes on Mg isotope compositions of low temperature Mg-carbonate minerals. In this study, we examine the Mg isotope composition of the Mg-carbonate sediments in three depth profiles recovered from this unique and wellcharacterized environment. These profiles exhibit differences in abundance of magnesite and water table depth, resulting in different vertical Mg isotope composition of the solid phase.

Our findings provide insight into Mg isotope fractionation behavior in Mg-carbonate minerals and the use of Mg-isotopes to trace the fate of carbon in CO2 storage scenarios.

Geologic setting and playa genesis

Hydromagnesite-magnesite playas lie adjacent to the town of Atlin, British Columbia, Canada (Fig. 1a; 59°34' N, 133°42' W). A playa depositional model [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF] and investigation of magnesium carbonate formation [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF] are summarized here as background information for this study. The reader is referred to these previous studies for the data from which the playa genesis model was derived. The ultramafic bedrock in the Atlin region consists of a tectonically emplaced upper mantle section of oceanic lithosphere that is mainly composed of variably serpentinized harzburgite and minor dunite together with localized zones of hydrothermal quartz-magnesite alteration (listvenite) (Ash and Arksey, 1990a;[START_REF] Hansen | Carbonated serpentinite (listwanite) at Atlin, British Columbia: a geological analogue to carbon dioxide sequestration[END_REF]. The weathering of this bedrock produces alkaline Mg-HCO3 - groundwater that discharges topographic lows where the playas lie [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF][START_REF] Power | The hydromagnesite playas of Atlin, British Columbia, Canada: A biogeochemical model for CO2 sequestration[END_REF]. There are two groups of playas (total area ≈ 0.2 km 2 ); a northern group and a southern group with the latter having water bodies and grassland areas in addition to Mgcarbonate mounds (Fig. 1).

The playas consist of three sedimentary units: Mg-carbonate sediments at the surface underlain by Ca-Mg-carbonate sediments, and then glaciolacustrine mud [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF].

Glaciolacustrine mud was first deposited in glacial lakes and mainly contains silicate minerals (e.g., quartz, feldspars, micas). Over time, carbonate deposition overtook siliciclastic deposition as surface runoff declined and alkaline Mg-HCO3 -groundwater became the dominant water source (Fig. 2a). Modern groundwater near the playas is supersaturated with respect to anhydrous Ca-and Mg-carbonate minerals including aragonite (CaCO3) and magnesite (MgCO3). Subaqueous carbonate deposition fills ponds with mainly aragonite, and through diagenesis a Ca-Mg-carbonate unit comprised of aragonite, ankerite (Ca(Fe,Mg,Mn)(CO3)2), and disordered dolomite (CaMg(CO3)2) formed overlying the glaciolacustrine deposit. A transition from subaqueous to subaerial sediment deposition is indicated by buried vegetation near the top of this Ca-Mg-carbonate unit (Fig. 2b).

Radiocarbon dating of this vegetation indicates that the overlying Mg-carbonate unit began forming at most 8000 cal yr BP [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF]. Hydrated Mg-carbonate precipitation is driven by the evaporation of Mg-HCO3 -waters that are drawn to the surface by capillary action. This process manifests itself as mounds of sediments (10s cm high) that are dominated by hydromagnesite (Fig. 2c-2d). The average deposition rate for the Mg-carbonate unit is ~0.4 mm/yr and its overlying weight results in subsidence, thus the boundary between this unit and the underlying Ca-Mg-carbonate unit now lies well below the water table.

The depositional model constrains magnesite formation to the Holocene and Earth's surface temperature. Sediment temperature in the present-day playas ranges from 3 °C at depth (10s cm below water table) to 14 °C at the surface in the summer. For comparison, clumped isotope geothermometry of magnesite collected from the surface of profile 4 gave a formation temperature in the range of 1-11 °C [START_REF] Falk | Geochemistry and petrology of listvenite in the Samail ophiolite, Sultanate of Oman: Complete carbonation of peridotite during ophiolite emplacement[END_REF].

Sampling and analytical techniques

Sample collection

Hand specimens of harzburgite, partially serpentinized harzburgite, serpentinite, and listvenite (quartz-carbonate altered serpentinite) were collected from the Atlin area (Fig. 1; Table 1). Sediments composed of hydromagnesite and magnesite were collected from three depth profiles in the southeastern (profiles 4 and 6) and northern playas (profile N. playa) (Figs. 1 and3; see [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF] for details on sampling). Depth sampling was carried out using an auger with sediments being collected in plastic bags and later dried at room temperature. Waters in the Atlin area included pond water atop Monarch Mountain, spring water collected at its base (~3.5 km to the southeast of the playas), groundwaters from private wells near Monarch Mountain and near the southern playas, surface waters from the northern and southeastern playas, and from the water table within the hydromagnesite-magnesite sediments (Fig. 1; Table 1). The wells were flushed a minimum of three times to obtain representative groundwater. All water samples were filtered (0.22 μm) into TraceClean TM 40 mL amber borosilicate vials with a fluoropolymer resin/silicone septum and no headspace.

Samples were stored at 4 °C before analysis. Presence of carbonate solids was not observed in these samples, which is consistent with the inability of magnesite to form at low and ambient temperatures. Selected samples from profile 4 were imaged using scanning electron microscopy as described by [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF].

Isotope analyses

The magnesium isotope composition of solid and fluid samples was determined following the method described in Mavromatis et al. (2014b). Hydromagnesite was removed from one sample, 11AT1-J, to determine the composition of magnesite alone.

Hydromagnesite was removed by reacting the bulk sediment with diluted acetic acid (10 vol. %) for ~30 min. After this treatment the mineralogic composition of the solid was characterized using X-ray diffraction analysis to assess whether hydromagnesite was removed. All solids were then digested in concentrated HNO3 and/or HF. Digested solids and acidified liquid samples were evaporated to dryness and re-dissolved in 1N HNO3. About 15 μg of Mg was used for column chemistry in 10 mL Bio-Rad Poly-prep columns containing AG-50W-X12 cation exchange resin for Mg separation from matrix elements. The yields after chromatographic separation were better than 99% of the total Mg loaded in the columns.

Magnesium isotopic compositions were measured using a Thermo-Finnigan "Neptune" Multi Collector Inductively Coupled Plasma Mass Spectrometer (MC-ICP-MS) at Géosciences Environnement Toulouse (GET) laboratory (France). All samples were prepared in 0.35 N HNO3 and introduced into the Ar plasma with a large Stable Introduction System spray chamber (double Scott Cyclonic spray chamber). Instrumental mass fractionation effects were corrected using sample-standard bracketing, and all data are presented as δ x Mg with respect to DSM3 reference material (δ x Mg=(( x Mg/ 24 Mg)sample/( x Mg/ 24 Mg)DSM3-1) × 1000) where x refers to the Mg mass of interest. All sample analyses were run in triplicate with the mean value presented in Table 1. The reproducibility of the δ 26 Mg analyses was determined using replicate analyses of the DSM3, CAM-1 and OUMg monoelemental Mg reference standards and was typically better than 0.08‰. The reproducibility of the measurements is in agreement with previously published values from the same laboratory [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]2014a;[START_REF] Beinlich | Inter-mineral Mg isotope fractionation during hydrothermal ultramafic rock alteration -Implications for the global Mg-cycle[END_REF]2018;), as well as from other laboratories [START_REF] Bolou-Bi | Magnesium Isotope Compositions of Natural Reference Materials[END_REF][START_REF] Wombacher | Separation of Mg, Ca and Fe from geological reference materials for stable isotope ratio analyses by MC-ICP-MS and double-spike TIMS[END_REF][START_REF] Geske | The magnesium isotope (δ 26 Mg) signature of dolomites[END_REF][START_REF] Riechelmann | Impact of diagenetic alteration on brachiopod shell magnesium isotope (δ 26 Mg) signatures: Experimental versus field data[END_REF]2018;Mavromatis et al., 2017a;2017c;[START_REF] Shalev | Mg Isotope Interlaboratory Comparison of Reference Materials from Earth-Surface Low-Temperature Environments[END_REF]. The reproducibility of chromatographic separation was assessed by repeated analyses of selected samples and the JDo-1 (dolomite) and IAPSO seawater as shown in Table 1, and was better than 0.08 ‰.

Results

Isotopic composition of country rock, waters, and carbonate sediments

The Mg isotope composition of the five rock samples (AT03-42, AT04-3, 04AT4, 01AT5-2, AT03-20-PC2) representing various lithologies in the region exhibit a narrow range in δ 26 Mg with an average of -0.36±0.07‰ (Fig. 4 and Table 1). These samples consist of ultramafic rocks including harzburgite, serpentinite, and listvenite, and have Mg isotope compositions similar to that of the bulk Earth (i.e., δ 26 Mg = -0.25±0.07‰; [START_REF] Teng | Magnesium isotope geochemistry[END_REF]. In contrast, the Mg isotope composition of the three water samples (16AT-water1; 16AT-water3; 16AT-water6) that were in contact with these country rocks are enriched in 24 Mg compared to the composition of the rocks and exhibit δ 26 Mg values that range from -1.20 to -0.97‰ (Table 1).

Magnesite and hydromagnesite are the two major Mg-carbonate phases in the playa sediments and their abundance varies significantly between the two depth profiles of the south playa (Fig. 3). The upper 280 cm of sediments in profile 6 contain less than 10 wt.% magnesite (Fig. 3; Table1), whereas in profile 4 the abundance of this mineral phases is as high as 96 wt.%. The samples where magnesite is the predominant phase are significantly enriched in 24 Mg compared to all the other materials analyzed in this study exhibiting δ 26 Mg compositions in a range between -2.11 and -2.95‰ (Fig. 4). For instance, sample 11AT1-J (96 wt.% mgs) has an isotopic composition of -2.63‰ and after hydromagnesite removal by acid washing, its isotopic composition decreases to -2.95‰ (Table 1). Note here that massbalance to determine the Mg isotope composition of the initial hydromagnesite in sample 11AT1-J yields a δ 26 Mg composition >5.0‰ which is unlikely to be realistic. There are several potential explanations for this such as mineralogical and isotopic inhomogeneity in the solids or presence of X-ray amorphous material in the initial sample that is unaccounted for by the mass balance calculation. In most of the carbonate sediments the anhydrous Mgcarbonate mineral is magnesite; however, in samples 11AT1-L and 12AT1-8E the abundance of magnesite is as low as 15-17 wt.% and other anhydrous Mg-bearing carbonates such as disordered dolomite [CaMg(CO3)2] and ankerite have been identified. Their relative abundances are listed in Table 1. Hydromagnesite-dominated sediments have higher δ 26 Mg values compared to those dominated by magnesite and mixed anhydrous carbonates. The Mg isotope compositions of hydromagnesite-dominated samples span a wide range with δ 26 Mg values from -0.92 to 1.14‰. Interestingly, the Mg isotope composition of hydromagnesite and, to a lesser extent magnesite, in all the sediment profiles, exhibits significant variation of δ 26 Mg values with depth with the most 24 Mg depleted samples near the surface (e.g., Fig. 5).

Finally, the five water samples collected from the playa sediment water tables (n=2), the wetlands adjacent to the playas (n=2), and a well next the southern playa (n=1) exhibit a wide range of δ 26 Mg values between -0.36 and 0.60‰ (Table 1).

Discussion

Formation of hydromagnesite

Previous results indicate that the formation of hydromagnesite in the Atlin playas proceeds through transformation of more hydrated phases as well as by direct precipitation in the unsaturated zone of the Mg-carbonate unit. Details on the genesis model of hydromagnesite/magnesite playas in Atlin can be found in [START_REF] Power | The hydromagnesite playas of Atlin, British Columbia, Canada: A biogeochemical model for CO2 sequestration[END_REF]2014). Waters at the water table are saturated with respect to hydromagnesite and lansfordite, the latter cementing sediments to form a hardpan. Evaporation draws water from the water table upwards, and evapo-concentration causes precipitation of mainly hydromagnesite throughout the unsaturated zone. This upward water movement is evidenced by stable isotope data that shows enrichment in 13 C and 18 O of the bulk sediments (mgs + hmg) towards the surface (see Fig. 10 in [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF]. These enrichments are consistent with evaporation of water and degassing of CO2-rich fluids. Selective analysis of only the hydromagnesite also showed enrichment in 13 C and 18 O towards the surface (see Fig. 8 in [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. At the scale of the playas, hydromagnesite formation is limited by these physical processes (capillary rise and evaporation) and is thus effectively transport-controlled [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF].

The formation of hydromagnesite due to the vertical transport of water from the water table upwards results in depletion of 24 Mg of the sediments which obtain δ 26 Mg values as high as 1.14‰ (profile 6; near-surface sample 05AT1-8A; Fig. 5; Table 1). Note here that this sample contains ~7 wt. % magnesite, which suggests that the δ 26 Mg value of pure hydromagnesite may be even higher. This isotopic composition of the hydromagnesitedominated sediments is the highest δ 26 Mg value recorded in the literature for carbonate minerals, to the best of our knowledge. In contrast to the highly depleted 24 Mg composition of the sediments in Atlin, experimental studies have demonstrated that both hydrous and anhydrous Mg-bearing carbonate minerals tend to preferentially take up the lighter, 24 Mg isotope (e.g. [START_REF] Saulnier | Mg isotope fractionation during calcite precipitation: An experimental study[END_REF]Mavromatis et al., 2017a). For example, the study of hydromagnesite stromatolites in Lake Salda (SW Turkey) by [START_REF] Shirokova | Can Mg isotopes be used to trace cyanobacteria mediated magnesium carbonate precipitation in alkaline lakes[END_REF]2013) revealed that Mg isotope fractionation between solids and bulk fluid is equal to -1.0±0.2‰. This fractionation factor is in excellent agreement with that reported by [START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF] who conducted dissolution/precipitation experiments of hydromagnesite under laboratory conditions. If the same fractionation factor were applicable to the Atlin hydromagnesite, the due to capillary rise could result in vertical variations in its isotopic composition related to mass transfer of Mg to the solid phase. Moreover, it has been observed in experiments that both Mg and C atoms in hydrated carbonate minerals undergo exchange with the fluid during mineral phase transformations. This exchange results in the isotopic composition being reset within a time frame of days to weeks [START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF]. This would make the Mg isotope compositions of the carbonate sediments sensitive to the contemporary fluid composition, even if they precipitated from an older fluid of different Mg isotope composition. The hydromagnesite-magnesite playas grow by precipitation throughout the sediment profile; therefore, the youngest sediments are not necessarily at the surface. Thus, the Mg-isotopic composition of the sediments that transformed post-deposition may reflect the composition of the fluid at depth different than their original precipitation. For instance, if lansfordite originally precipitated at the water table but later transformed to hydromagnesite above the water table, its composition would reflect exchange with the fluid above the water table. Unlike the experiments conducted by [START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF] however, where excess fluid was available for exchange, the Atlin sediments are dominated by solids, with a relatively small volume of fluid. Thus, the Mg budget and isotope composition at Atlin is effectively mineral buffered, limiting the extent to which isotopic exchange would "reset" isotopic compositions compared to fluid-rich experiments. The limited exchange is also supported by the co-variation of δ 26 Mg and δ 13 C values of the sediments (R 2 = 0.72; p<0.05; Fig. 6). Indeed, the increasing δ 13 C and δ 18 Ο values of surface sediments are indicative of degassing and evaporation suggesting reducing fluid contents in the pore space closer to the surface. At the same time, an increasing enrichment of 26 Mg of the sediments is consistent with limited exchange of Mg between solid and fluid. Interestingly, higher δ 26 Mg and δ 13 C values are observed in the near surface sediments of profile 6 compared to profile 4 (Figs. 5 and6), which we interpret to reflect the greater distance from the water table to the surface, i.e., greater thickness of the unsaturated zone, in profile 6 compared to profile 4. This observation further supports the role of upward fluid migration on Mg, C, and O isotope composition of the forming solids.

If the precipitation of hydromagnesite-dominated sediments is envisioned as occurring along a 1-dimensional vertical flow path that is progressively depleted in 24 Mg as Mgcarbonate minerals precipitate, then the isotopic composition of the Mg-carbonate minerals along the flow path may be explained as a distillation process. A 1-dimensional vertical flow path is assumed due to primarily vertical fluid transport in the unsaturated zone. As the precipitation of hydromagnesite is expected to be transport-controlled [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF], a Rayleigh-type distillation process may in part explain the observed trend in Mg isotope composition. Here we focus our discussion primarily on the South playa profiles, 4 and 6, due to a higher sample density, but the North playa samples exhibit similar trends.

The direct application of a Rayleigh-type equation in the hydromagnesite-dominated sediments of profiles 4 and 6 (Fig. 3) for the estimation of the amount of Mg removed from the fluid due to mineral formation is not straightforward. The Rayleigh equation is based on the assumption that the isotope fractionation factor is constant along the whole migration pathway of the fluid from the water table up to the surface, which in reality may not be true, as the abundances of magnesite and hydromagnesite vary above the water table between the two profiles (see Fig. 3). Note here that the same limitations exist for the N.playa profile, where the near surface sediment samples (n=2) are composed of ~80 wt. % hydromagnesite (Table 1). In addition, the precipitation of Mg-carbonate in the playa sediments only affects the isotope ratio but does not significantly lower the total concentration of dissolved Mg which is driven by evaporation, thereby allowing Mg-carbonates to maintain (super)saturation. It is also worth noting that the Rayleigh calculation refers to isotopic composition of the bulk fluid, although changes in chemical speciation due to precipitation most likely affect the isotopic composition of the Mg 2+ (aq) ion [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF] 1), so the prevalence of Rayleigh processes in the saturated zone cannot be determined.

The large difference in the isotopic composition of the sediments between the two south playa profiles can be assigned to two parameters. In profile 4, the water table occurs at ~90 cm below the surface, whereas in profile 6 it occurs at ~120 cm (Fig. 3). This longer pathway along which the Mg-bearing fluid has to move above the water table coincides with an increase of its Mg isotope ratio, consistent with a greater extent of hydromagnesite formation along the longer flow path. In addition to the difference in the water table depth between the two profiles, the presence of higher abundances of magnesite (see Fig. 3) in the sediments of profile 4 may affect the isotopic composition of the bulk sediments. Based on our observations of the magnesite-rich sediments, and the observations of [START_REF] Oskierski | Mg isotope fractionation during continental weathering and low temperature carbonation of ultramafic rocks[END_REF], magnesite preferentially uptakes the lighter 24 Mg isotope compared to hydromagnesite formed at the same temperature.

Overall, the vertical distribution of Mg isotope composition of hydromagnesite sediments is broadly consistent with a Rayleigh distillation process along the flow path (Fig. 5). This process points towards a precipitation reaction without significant post-depositional exchange of isotopes between fluid and solid. It also implies that in cases where Mg isotopes are used for mass-balance calculations and/or to distinguish precipitation of carbonates versus silicates, the potential for Rayleigh fractionation may complicate interpretations in Mg supply-limited environments.

Formation of magnesite

The Atlin playas are one of the most well-characterized sites for magnesite formation at Earth's surface conditions (Power et al., 2007;2009;2014;2019). Textural and stable carbon and oxygen isotope data demonstrate that magnesite precipitates from pore waters as opposed to forming through transformation of hydromagnesite [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. Magnesite grains exhibit crystal growth features including submicrometer cone-like terraced morphologies above the water table and smooth crystal faces below the water table (Fig. 2e-f). This implies there may be variable crystal growth mechanisms and precipitation rates with depth. Fluids in both the saturated and unsaturated zones are highly supersaturated with respect to magnesite, implying its formation is reaction-controlled. Magnesite formation is likely nucleationlimited with long induction times and slow precipitation rates, whereas hydromagnesite can form more readily at low-temperature. Thus, these minerals are spatially, but not entirely temporally associated with one another, and the predominant fluids that have formed these two minerals may differ.

The rates of magnesite formation (nucleation + crystal growth) were estimated to lay in the range of 10 -13 to 10 -12 mol/m 2 /s with magnesite abundance increasing exponentially over time [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. Playa surface sediments exhibit variable magnesite abundances ranging from <1 to ~40 wt.% (see Figure 5 in [START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF]. This variability is likely a result of the heterogeneity of the playas, with Mg carbonate mounds being adjacent to grassland areas that are adjacent to ponds in a relatively small area (Fig. 1b). With this heterogeneity in mind and the expectation that magnesite abundance increases exponentially with time [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF], the greater abundance of magnesite in profile 4 compared to profile 6, may be due to these sediments being modestly older, or potentially due to differences in vertical fluid flow.

The δ 26 Mg composition of magnesite-bearing sediments in Atlin is significantly lower than those dominated by hydromagnesite (Fig. 4). Hence, if hydromagnesite is the precursor phase of magnesite in this environment, the transformation can only occur via a dissolution/re-precipitation process, as this would change the Mg isotope composition [START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF]. A solid-state transformation from hydromagnesite to magnesite can therefore be excluded. This observation clearly suggests that magnesite formation in low temperature environments like the Atlin playas is not taking place by solid-state transformation of a hydromagnesite precursor but by direct precipitation from the fluid phase.

This argument is further supported by textural observations as well as stable carbon and oxygen isotope compositions of the two phases previously reported by [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF].

For example, textures such as spiral crystal growth seen in magnesite from above the water table most likely result from direct precipitation and growth rather than transformation from hydromagnesite (Fig. 2f). Furthermore, stable carbon and oxygen isotope analyses of magnesite and hydromagnesite showed that these minerals have distinct isotopic compositions with the former likely being precipitated from waters with similar isotopic compositions to that of groundwater, and the latter forming from waters with compositions similar to that of surface waters (see Figure 9 in [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. This isotopic evidence supports hydromagnesite formation being driven by evaporation in the unsaturated zone towards the surface and magnesite forming initially at depth from pore waters with a more groundwater-like composition. Magnesium isotopes cannot be used in the same way as C and O isotopes to distinguish surface water vs groundwater, as the source of Mg is the same in both (i.e., groundwater).

The Mg isotope composition of magnesite-bearing sediments in Atlin provides a unique opportunity to directly constrain the Mg isotope fractionation factor between magnesite and forming fluid at ~10 °C. However, it should be noted here that an estimation of the Mg isotope fractionation factor between magnesite and fluid is not straightforward.

The isotopic composition of the fluid (i.e., pore fluid) is uncertain and likely variable, and a number of other parameters may influence the Mg isotope fractionation including speciation of Mg in solution and formation of other Mg-bearing carbonate phases such as hydromagnesite, disordered dolomite, and ankerite. The abundance of magnesite in the sediment profiles is significantly higher below the water table, including a few samples that contain almost exclusively magnesite that can be seen in Fig. 3 and in Table 1. Starting with the working hypothesis that the isotopic composition of the forming fluid of magnesite below the water table was constant over the last 8000 years and similar to that of the weathering fluid (i.e. ~-1.1±0.1‰) and taking into account that the magnesite growth rate is significantly slow as to not be affected by growth kinetics, a first estimation of the equilibrium Mg isotope fractionation factor between magnesite and fluid can be made. Note here that according to [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF] the δ 13 C and δ 18 O values of magnesite precipitated from groundwater denote formation under isotope equilibrium conditions. Sample 11AT1-J after the removal of hydromagnesite was used for calculation of the Δ 26 Mgmgs-fluid as it was the only sample without other mineral phases. However, all magnesite-rich samples had similar δ 26 Mg values (Fig. 4, Table 1), including those in both the South and North playa despite being several hundred metres apart. Based on the isotopic composition of magnesite sample 11AT1-J after the removal of hydromagnesite (i.e., -2.95‰, Table 1) the Δ 26 Mgmgs-fluid value is equal to -1.85±0.1‰. It should be noted that this is an apparent fractionation factor, with uncertainty arising from the use of an estimated fluid composition and potential isotopic heterogeneity of the solid.

Nevertheless, the estimated fractionation factor of -1.85±0.1‰ is within a similar range to the value proposed by [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF] who estimate a fractionation factor of ~-2.3 ‰ at 25 °C (Fig. 7) based on extrapolation of hydrothermal experiments at 150 and 200 °C. In addition, this value lays within the range of published theoretical calculations that span from -0.7‰ [START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg 2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF] to -4.7‰ [START_REF] Schauble | First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals[END_REF] at 10 °C (Fig. 7). Note that these fractionation factors were derived from theoretical calculations that consider the isotopic composition of free Mg 2+ (aq) ion in their calculations, whereas the values plotted for Atlin playa samples represent fractionation between bulk Mg(aq) and magnesite. Considering that magnesite growth proceeds via the standard ion-by-ion addition of Mg 2+ on the growing mineral surface [START_REF] Burton | The Growth of Crystals and the Equilibrium Structure of their Surfaces[END_REF], the isotopic composition of the Mg 2+ (aq) ions is likely to be affected by the formation of Mg-carbonate aquo complexes such as MgHCO3 + and MgCO3 0 depending on their abundance in the fluid phase. The formation of these complexes is accompanied by a reduction from 6 water molecules in the inner hydration sphere of Mg 2+ (aq) ion to 5 or 4 in the carbonate-bearing complexes MgCO3 0 and MgHCO3 + (Schott et al., 2016;Stefánsson et al., 2017). Speciation calculations of the pore fluid from profile 6 using the data provided by [START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF] suggesting that the Mg isotope fractionation between magnesite and aqueous Mg is small and about -0.7±0.1‰ in excellent agreement with the value proposed by [START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg 2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF].

Overall, the major limitation for the estimation of the Mg isotope fractionation between magnesite and fluid in Atlin is the formation of other Mg-bearing carbonate phases such as hydromagnesite and uncertainty regarding the isotopic composition of the fluid. The differences in the fractionation factors between the two mineral phases and the forming fluid, and the differences in the rates of formation and transformation of these phases makes a direct estimate of the magnesite fractionation factor challenging. Nevertheless, the magnesite-rich samples are consistently enriched in the isotope of lower mass, 24 Mg, relative to hydromagnesite samples at ~10 °C (Fig. 4). This is consistent with observations at higher temperature in laboratory experiments [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Perez-Fernandez | Ca and Mg isotope fractionation during the stoichiometric dissolution of dolomite at 51 to 126 o C and 5 bars CO2 pressure[END_REF].

Implications for CO2 storage in hydrous Mg-carbonates

Given the unusual fluid source composition that would need to exist to generate the Magnesium isotope compositions of solids and fluids have recently been applied as tracers of engineered CO2 storage and can be used to distinguish precipitation of Mgcarbonates, that store CO2, and Mg-silicates, that do not store CO2 [START_REF] Oelkers | Using stable Mg isotope signatures to assess the fate of magnesium during the in situ mineralisation of CO2 and H2S at the CarbFix site in SW-Iceland[END_REF]. This relies on the fact that secondary Mg-silicates tend to favour 26 Mg relative to the fluid, whereas anhydrous Mg-carbonates tend to favour 24 Mg relative to the fluid as has been observed previously in both high and low temperature systems [START_REF] Beinlich | Inter-mineral Mg isotope fractionation during hydrothermal ultramafic rock alteration -Implications for the global Mg-cycle[END_REF][START_REF] Oskierski | Mg isotope fractionation during continental weathering and low temperature carbonation of ultramafic rocks[END_REF]. Our observations at Atlin suggest that consideration of a distillation process, when applicable, may help refine such interpretations. For example, Mg-carbonate precipitation in ultramafic mine tailings is often driven by evaporation and may be subject to a similar distillation process [START_REF] Wilson | Carbon Dioxide Fixation within Mine Wastes of Ultramafic-Hosted Ore Deposits: Examples from the Clinton Creek and Cassiar Chrysotile Deposits[END_REF].

The anhydrous Mg-carbonate mineral magnesite is the ideal carbon sink in terms of thermodynamic stability compared to hydrous carbonates [START_REF] Power | Carbon Mineralization: From Natural Analogues to Engineered Systems[END_REF]. However, its formation in low temperature environments is unlikely to occur on short timescales (Hänchen et al., 2008;[START_REF] Saldi | An experimental study of magnesite precipitation rates at neutral to alkaline conditions and 100-200°C as a function of pH, aqueous solution composition and chemical affinity[END_REF], thus making the hydrated Mg-carbonates the targets for CO2 storage at near Earth's surface temperatures. Although hydromagnesite, dypingite and nesquehonite are common products of ultramafic rock weathering [START_REF] Assima | Impact of temperature and oxygen availability on the dynamics of ambient CO2 mineral sequestration by nickel mining residues[END_REF][START_REF] Bea | Reactive Transport Modeling of Natural Carbon Sequestration in Ultramafic Mine Tailings[END_REF][START_REF] Boschi | Enhanced CO2-mineral sequestration by cyclic hydraulic fracturing and Si-rich fluid infiltration into serpentinites at Malentrata (Tuscany, Italy)[END_REF][START_REF] Chaka | Ab initio thermodynamics of magnesium carbonates and hydrates in water-saturated supercritical CO2 and CO2-rich regions[END_REF][START_REF] Felmy | Reaction of water-saturated supercritical CO2 with forsterite: Evidence for magnesite formation at low temperatures[END_REF]Garcia del Real et al., 2016;[START_REF] Gras | Isotopic evidence of passive mineral carbonation in mine wastes from the Dumont Nickel Project (Abitibi, Quebec)[END_REF][START_REF] Highfield | Lowtemperature gas-solid carbonation of magnesia and magnesium hydroxide promoted by non-immersive contact with water[END_REF]Hövelmann et al., 2012;[START_REF] Kristova | Carbonate mineral paragenesis and reaction kinetics in the system MgO-CaO-CO2-H2O in presence of chloride or nitrate ions at near surface ambient temperatures[END_REF][START_REF] Loring | In situ infrared spectroscopic study of brucite carbonation in dry to water-saturated supercritical carbon dioxide[END_REF][START_REF] Montes-Hernandez | Rapid precipitation of magnesite microcrystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-aging step (from similar to 20 to 90 o C)[END_REF][START_REF] Pronost | Carbon sequestration kinetic and storage capacity of ultramafic mining waste[END_REF][START_REF] Schaef | Brucite [Mg(OH)2] carbonation in wet supercritical CO2: An in situ high pressure X-ray diffraction study[END_REF]2013;[START_REF] Zhao | Aqueous carbonation of natural brucite: Relevance to CO2 sequestration[END_REF], previous studies on their formation that used Mg isotope systematics suggested a continuous exchange of Mg isotopes between the solid and the fluid phase at ~25 o C (e.g., [START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF][START_REF] Shirokova | Using Mg Isotopes to Trace Cyanobacterially Mediated Magnesium Carbonate Precipitation in Alkaline Lakes[END_REF]. Similar observations were made based on the δ 13 C value of the solid and the dissolved inorganic carbon composition of the forming fluid [START_REF] Mavromatis | The continuous re-equilibration of carbon isotope compositions of hydrous Mg carbonates in the presence of cyanobacteria[END_REF] and likely reflect the high reactivity of these

Conclusions

The Mg isotope composition of the hydromagnesite and magnesite sediments of the alkaline playas near Atlin, British Columbia, Canada, provide significant information regarding the formation conditions of these phases in low temperature environments.

Hydromagnesite formation above the water table occurs via transport and evaporation of Mgrich water, which imparts a 24 Mg depleted isotope composition that is uncommon for Mgbearing carbonate minerals. This depletion of 24 Mg in hydromagnesite is interpreted to reflect a distillation process occurring during the migration of Mg-rich fluids towards the surface.

This process has to be taken into consideration when interpreting Mg isotope composition of carbonate minerals formed where Mg transport may be the limiting factor. Several instances of Mg-carbonate mineral formation in near-surface environments are driven by evaporation (e.g., mine wastes; [START_REF] Wilson | Carbon Dioxide Fixation within Mine Wastes of Ultramafic-Hosted Ore Deposits: Examples from the Clinton Creek and Cassiar Chrysotile Deposits[END_REF], therefore the impact of distillation on Mg isotope signatures may be important to the interpretation of Mg-isotope signatures in numerous natural and engineered environments where hydrous Mg-carbonates precipitate.

The Mg isotope compositions of co-existing hydromagnesite and magnesite are distinct, suggesting that the formation of magnesite does not occur via solid-state transformation of pre-existing hydromagnesite, but rather proceeds via direct precipitation from the fluid phase or dissolution-reprecipitation. The first estimates for the Mg isotope fractionation during magnesite formation between 3 and 14 o C (average ~10 o C) are reported.

The estimated fractionation factor of -1.8±0.1‰ is within the range of published theoretical calculations; however, if aqueous Mg speciation and associated isotope fractionation among aqueous species is considered, this value becomes -0.7±0.1‰ suggesting speciation may be of major significance during Mg-carbonate mineral formation in environments with high alkalinity.

Ank (6.1), Hun (5.7), Amor.

(30.5)

  abnormally high δ26 Mg values observed at the playa surface through equilibrium Mg isotope fractionation, it is likely that the observed trends in Mg isotope composition above the water table are due to a distillation process along an upward, evaporation-driven flow path. The Mg isotope compositions therefore provide insight into the mechanism of playa formation. The depositional model proposed by[START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF] based on mineralogical evidence, field observations, and C and O isotopic data suggested that the precipitation of hydromagnesite occurred in the unsaturated zone and proceeded by a combination of transformation of more hydrated phases and precipitation from evaporation-influenced pore fluids. Further insight provided in[START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF] suggested that hydromagnesite precipitation was transportcontrolled, in the sense that it (or a more hydrated phase) precipitates quickly upon reaching saturation as Mg-rich waters are transported from the water table and evaporate. This is consistent with the observed trend in Mg isotopes, which may reflect continuous enrichment of the fluid in 26 Mg along the evaporation-driven flow path, as24 Mg is removed by carbonate precipitation.

  phases. However,[START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF] observed a lack of fluid-solid isotopic exchange between nesquehonite and fluid at 5 °C suggesting that lower temperatures may reduce the rate of isotope exchange. The apparent lack of post-depositional isotope exchange in the Atlin playas, as evidenced by the relative consistency with a distillation process which implies long-term stability of isotopic compositions of the formed minerals.[START_REF] Harrison | Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations Geochim[END_REF] observed that the Mg isotope composition of hydrated carbonate minerals is substantially reset during transformation to less hydrated phases. However, the relatively small reservoir of dissolved Mg in the playa sediments relative to the amount of Mg in the solid likely limited the extent of this isotopic resetting even during lansfordite transformation to hydromagnesite. As, even if the fluid changed isotopic composition, the much larger reservoir of Mg in the solid would limit the extent to which bulk solid composition would change, unless a long-term, relatively high-volume flux of fluid with substantially different isotopic composition were present. This could in part explain the preservation of the strongly exchange with the fluid. The preservation of these isotopic signatures also suggest that once incorporated into the mineral, the Mg and C are likely stored for at least the 8,000-year time scale of the playa's existence. These findings are evidence of the long-term stability of CO2 storage by hydrous Mg-carbonate at low temperature in both hydrous Mg-carbonates and anhydrous magnesite.

  . An additional challenge in applying a Rayleigh model is that the initial Mg isotope composition of the forming fluid cannot be precisely constrained. Due to a lack of sufficient fluid volume to analyze in the near-surface sediments, the corresponding increase in δ 26 Mg values in the fluid could not be measured. Notably, the δ 26 Mg values of the fluid at the watertable in the profiles are the highest of all measured fluids, consistent with enrichment in 26 Mg due to carbonate precipitation. Furthermore, all water samples collected in Atlin playas are enriched in 26 Mg compared to weathering water/runoff samples (Table 1). Although the greatest change in δ 26 Mg values of hydromagnesite sediments occurs between samples near the water table and those at or near the surface, the minor enrichment in 26 Mg between samples just below and just above the water table indicate a Rayleigh process may begin to occur below the water table. However, the majority of samples analyzed below the water table were comprised mainly of anhydrous carbonates (Table

Although the exact extent of Mg removal from the pore fluid cannot be estimated, the similarities in the mineralogical and isotopic composition of the bulk sediments below and directly above the water table and their further enrichment in 26 Mg towards the surface suggest a unidirectional transport process occurring during sediment formation. For example, in profile 4, the δ 26 Mg composition of samples 05AT1-6I (below water table) and 05AT1-6D (directly above water table) is very similar at -1.09‰ and -0.92‰, respectively, whereas that of the near surface sample 05AT1-6A is significantly higher (-0.62‰). Similarly, in profile 6 samples 05AT1-8P (below water table) and 05AT1-8G (directly above water table) have similar compositions (i.e. -0.41 and -0.21‰, respectively) compared to the near surface sample in this profile which has a δ 26 Mg value of 1.14‰.

  number in parenthesis denotes wt % of phase abundance according to XRD analyses.

						Ara (54.8),
						Ank (10.7),
						Dol (7.3),
						Hun (2.5),
	12AT1-8E	Sediment	362-368		15	Cal (0.3)	-1.14	0.03	-2.22	0.00
	Solids-N.playa
	Profile
	12AT-NA	Sediment	0-5	81	19		0.31	0.01	0.61	0.01
	12AT-NB	Sediment	30-46	76	24		0.12	0.02	0.23	0.02
	12AT-NC	Sediment	56-75	6	94		-1.08	0.03	-2.11	0.04
	12AT-ND	Sediment	89-99	2-4	96-98		-1.29	0.02	-2.47	0.08
	Fluids
	16AT-water1	Water					-0.51	0.04	-0.97	0.06	Pond on Monarch Mountain
	16AT-water2	Water	30				0.31	0.01	0.60	0.01	Southeastern playa water table
										122 m deep well water near Monarch
	16AT-water3	Water					-0.63	0.04	-1.20	0.03	Mountain
	16AT-water4	Water					-0.17	0.04	-0.36	0.05	North playa wetland
	16AT-water5	Water					0.12	0.05	0.25	0.06	Southeastern playa main wetland
	16AT-water6	Water					-0.55	0.03	-1.07	0.03	Spring at base of Monarch Mountain
	12AT-Norm	Water					0.14	0.02	0.28	0.03	35m deep well water near southeastern playa
	12AT-Nplaya	Water	50				0.07	0.02	0.14	0.03	North playa water table
	Reference
	materials
	DSM3						0.00	0.03	0.00	0.04	Monoelemental reference material
	CAM-1						-1.34	0.03	-2.65	0.07	Monoelemental reference material
	OUMg						-1.46	0.07	-2.82	0.06	Monoelemental reference material
	IAPSO						-0.43	0.03	-0.83	0.08	Certified seawater
	JDo-1						-1.26	0.07	-2.43	0.08	Certified dolomite reference material

*

Mg-depleted hydromagnesite-dominated sediment sample near the surface of profile 6 (sample 05AT1-8A; Fig.5) must be the result of mineral precipitation from a fluid with a δ 26 Mg of +2.2‰. Such Mg isotope fluid compositions would be unusual, considering that the majority of water bodies at the Earth's surface exhibit δ 26 Mg values below 0.5‰[START_REF] Teng | Magnesium isotope geochemistry[END_REF] and the most enriched solids measured record δ 26 Mg values of ~ 1.8‰[START_REF] Liu | Massive magnesium depletion and isotope fractionation in weathered basalts[END_REF]. Note here that the bedrock samples in this area (i.e. harzburgite, serpentinite, listvenite) generate an average δ 26 Mg value of -0.36±0.07‰ or ~ 1.5‰ lower than that of hydromagnesite. Moreover, all of the water samples analyzed from Atlin have δ 26 Mg values of < 0.6‰ (see Table1), although fluids from the unsaturated zone could not be sampled due to low water contents of the sediments. Together, these data suggest that the high δ 26 Mg values of hydromagnesite in the near-surface sediments are unlikely to reflect equilibrium fractionation during mineral formation from an infinite aqueous Mg reservoir, as it requires an unfeasibly high δ 26 Mg composition of the fluid.Likely these elevated δ 26 Mg values are the result of the precipitation of Mg-bearing carbonate minerals during the upward migration of Mg-rich water from the water table, generating a Rayleigh-type distillation effect. This is consistent with the previously postulated formation pathway for hydromagnesite in the Atlin playas, which stated that hydromagnesite precipitation is effectively transport-limited and depends on the replenishment of Mg-rich waters from depth[START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF] 2019). The formation of hydromagnesite is driven by CO2 degassing and evaporation, and may also occur by transformation of more hydrated phases such as lansfordite. This formation model for hydromagnesite in the playas, derived from field observations, mineralogical data, and other isotopic results[START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF] 2019), suggests that the unusually high δ 26 Mg values of the Mg-carbonate sediments likely reflects a combination of phase transformation and transport effects in a water-limited system. The upward migration of the Mg-bearing fluid

Acknowledgments

We are grateful to Jérôme Chmeleff for his support with MC-ICP-MS analyses. We thank Masako Tominaga and Jenine McCutcheon for assistance in the field. This study benefited from the financial support of the ISIFoR Carnot institute (Institute for the Sustainable Engineering of Fossil Resources) under the project SERP-CARB AAP-2016 and by the French national programme LEFE/INSU.