domain: math phys spi

text:
J Gattacceca

A Lamali

P Rochette

M Boustie

L Berthe

The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks

Introduction

The effects of shock waves on the natural remanent magnetization (NRM) and the intrinsic magnetic properties of geological materials remain poorly known. Still, hypervelocity impact phenomena are of primary importance in the evolution of many extraterrestrial bodies and of Earth. Hence the magnetic anomalies associated with impact basins on Mars [START_REF] Hood | Distribution of crustal magnetic fields on Mars: shock effects of basin-forming impacts[END_REF], the Moon [START_REF] Halekas | Magnetic fields of lunar multi-ring impact basins[END_REF] or on Earth [START_REF] Pilkington | The geophysical signature of terrestrial impact craters[END_REF]) cannot be interpreted with certainty. Also, shock-induced changes of rock magnetic properties should be taken into account when studying the magnetic signature of terrestrial impact structures.

Since the 1970's, efforts have been devoted to the experimental study of remagnetization of rocks upon impact, whereas little has been done about the shock-induced modifications of their intrinsic magnetic properties. Different techniques have been used to generate shock waves in a variety of geological materials: air guns accelerating aluminum or copper projectiles [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF][START_REF] Martelli | Hypervelocity cratering and impact magnetisation of basalt[END_REF][START_REF] Cisowski | The effect of shock on the magnetism of terrestrial rocks[END_REF][START_REF] Srnka | Magnetic field and shock effects and remanent magnetization in a hypervelocity impact experiment[END_REF][START_REF] Dickinson | Shock magnetism in fine particle iron[END_REF], explosives [START_REF] Hargraves | Investigations of the effect of shock on natural remanent magnetism[END_REF][START_REF] Pesonen | Magnetic properties of diabase samples shocked experimentally in the 4.5 to 35 GPa range[END_REF], free falling mass [START_REF] Kletetschka | Pressure effects on martian crustal magnetization near large impact basins[END_REF].

Common limitations are the difficulty in calibrating the pressure in the shocked sample and the recovery of intact samples due to brecciation of the target. On the other hand modern mechanical impact experiments using gas guns can recover intact samples with good pressure calibration (e.g. Louzada et al., in press). Recently, the use of laser shocks allowed a good estimate of the demagnetization of saturation isothermal remanent magnetization up to 5 GPa [START_REF] Gattacceca | Investigating impact demagnetization through laser impacts and SQUID microscopy[END_REF], but the pressure gradient was limited to a few millimeters inside the sample, making it impossible to study the changes in intrinsic magnetic properties. Despite these numerous experiments, the effects of shock waves on magnetization and magnetic properties are not clearly understood in particular because of the numerous parameters that may have an influence: shock intensity and duration, ambient field, magnetic mineralogy, rheology, magnetization existing prior to shock, and temperature.

In this paper, we present new experiments in which different geological materials were impacted using a high-order explosive (penthrite). The shock wave was modelled numerically and we studied the effects of shock on the NRM and on the intrinsic magnetic properties of the rocks.

Material and methods

Four different lithologies were studied: a Quaternary alkaline basalt (from the Bas-Vivarais area, France, described in [START_REF] Rochette | La province volcanique Pléistocène supérieur du Bas-Vivarais (Ardèche, France) : propagation de fentes crustales en échelons ?[END_REF], a Tertiary quartzitic microdiorite A c c e p t e d M a n u s c r i p t ("esterellite", from the Estérel range near the southeastern coast of France), a Permian rhyolitic pyroclastic rock from the same area [START_REF] Vlag | Paleomagnetism in the Esterel rocks: a revisit 22 years after the thesis of H. Zijderveld[END_REF], and a Precambrian-Ordovician pyrrhotite-rich metamorphic schist from Wilson Terrane (Northern Victoria Land, Antarctica). This choice was guided by the differences in magnetic mineralogy and magnetic properties among these four lithologies.

The shock wave was driven into the samples using a high-order explosive (penthrite, PETN).

The shocked samples were large blocks in the range 10-20 kg. A flat surface was cut using a circular saw. The sample was then placed in a large (0.3 m 3 ) plastic container half-filled with gravel. A penthrite detonator (0.2 g of penthrite contained in an aluminium cylinder of external diameter 7.3 mm and thickness 0.5 mm) was fixed in direct contact with the flat, locally polished surface of the sample. The container was then filled with gravel. The penthrite was detonated remotely using a non-electric detonating wire. The outdoor experimental setting contained no metallic parts except the aluminium cylinder containing the penthrite, and no electromagnetic signal is expected during the detonation. Therefore we did not use any system of magnetic field control and assume that the magnetic field seen by the sample is the local geomagnetic field (I = 59°, 46 µT). Each sample was oriented so that its original NRM made an angle of about 90° with the local field. After recovery of the shocked samples, we drilled an oriented core (Ø 2.5 cm) perpendicular to the flat surface and centred on the impact. This core was in turn cut in 10 oriented 4 x 4 x 3 mm 3 parallelepipeds with a wire saw (Fig. 1). Note that the upper few millimetres have been lost during the explosion for the basalt (3 mm) and the rhyolite (8 mm). In the following, the sample numbers correspond to the depth (in mm) of the centre of the 3 mm-high parallelepipeds from the original surface.

All magnetic analyses were performed at CEREGE (Aix-en-Provence, France). The magnetization measurements were performed with a 2G Enterprises DC SQUID magnetometer and data processed with Paleomac software [START_REF] Cogné | PaleoMac: a Macintosh™ application for treating paleomagnetic data and making plate reconstructions[END_REF]. Magnetic susceptibility measurements and thermomagnetic analyses were performed with an Agico KLY2-CS2 apparatus. Hysteresis loops were studied with a Princeton Micromag VSM apparatus.

Shock modelling

In order to estimate the stress field induced in the samples by the explosions, a numerical simulation of the experiments was performed. For this purpose, the Radioss code [www.mecalog-group.fr] has been used in a 2D axisymmetric configuration. The explosive PETN has been modelled by a Johnson Wilkins Lee law [START_REF] Wilkins | Computer simulation of dynamic phenomena[END_REF]:

P = A 1- ω R 1 V       exp -R 1 V ( )+ B 1 -ω R 2 V       exp -R 2 V ( )+ ωE V
where P is the pressure, A, B, R1 and R2 are empirical parameters, ω is the Gruneisen coefficient, E is the internal energy and V is the relative volume.

The modelled target material is a basalt described by an elasto-plastic constitutive law coupled to the Mie-Grüneisen equation of state with reference to the Hugoniot through a linear relationship between shock speed D and particle velocity u: D= C o + s . u., where C 0 is the sound speed and s is an empirical parameter. All the parameters used in the simulation are listed in table 1. In the model, the diameter of the basalt has been taken large enough (6 cm)

to avoid lateral reverberations on the free surface during the duration of observation of the phenomena (first pass of the shock).

The modelled evolution of stress versus time at various depths is given in Fig. 2. The shock applied by the explosion has an almost triangular shape, with a peak pressure of 30 GPa and a duration of about 1µs. The peak pressure decays to 5 GPa at only 20 mm. At depths greater than 5 mm, following the compression the material is submitted to a tensile stress, due to the lateral release initiated at the rim of the explosive charge, which generates expansion when crossing behind the main shock.

According to the assumptions made for this simulation (homogeneous, isotropic and non porous rock), and the variability of the intrinsic petrophysical parameters among the four different samples (for instance bulk density is 2270 kg.m -3 for the rhyolite, 2700 kg.m -3 for the microdiorite and the schist, and 3000 kg.m -3 for the basalt), we provide here only an estimate of the stress field into the samples. Based on this estimate, the depth scale for each shocked sample can be converted to a peak pressure scale (Fig. 3).

Thermal modelling

Because of the generation of the shock by a high explosive, an important heat flux is transferred to the target. The temperature profile applied to the target by this explosion has been calculated using the thermomechanical code Carte [START_REF] Auroux | Sensitivity of the EOS of detonation products to the parametrization of the intermolecular potential for pure fluids in thermomechanical calculations[END_REF] from the Commissariat à l'Energie Atomique (CEA, France). A maximum temperature of about 4500°C is applied during about 1 µs. A simulation of the dissipation of this heat into the target has been performed using a heat conduction simulation with FEMLAB 3.1 code (from COMSOL company). Physical properties introduced in the code are given in Table 1. The temperature profile with depth is given in figure 4 and shows that the zone affected by a significant heating (temperature > 50 °C) is restricted to the first upper micrometers. As a consequence, no thermal effect is expected at all on the magnetization and the magnetic properties of the studied samples.

On the other hand, the shock wave itself is accompanied by a transient increase of temperature. For pressure below the elastic limit of the rock (~ 5 GPa for a basalt), this increase is negligible (~10°C). For pressure greater than the elastic limit, the increase in temperature can be estimated to about 50°C at 10 GPa and 100°C at 20 GPa (e.g. Stöffler et al., 1991 and references therein).

Pre-shock magnetization and magnetic properties of the studied materials

Thermomagnetic curves (Fig. 5) allow the determination of the main magnetic carrier in the samples. The basalt has a main Curie temperature (T c ) of 50 °C indicating Ti-rich titanomagnetite of composition Fe 0.25 Ti 0.75 O 4 [START_REF] Dunlop | Rock magnetism: fundamentals and frontiers[END_REF]. A second, less substituted titanomagnetite population is evidenced by the blocking temperature spectrum of thermoremanence that extends up to 350°C interval (Fig. 5). The microdiorite has T c = 575°C

indicating almost pure magnetite. This is confirmed by the observation of a Verwey transition at 114°K. The rhyolite has T c = 650°C indicating titanohematite. The thermomagnetic curve for the schist shows the γ transition (antiferromagnetic to ferrimagnetic) of hexagonal pyrrhotite at 220°C, T c = 280°C of hexagonal pyrrhotite and T c = 320°C of monoclinic pyrrhotite. Hysteresis loops are in agreement with these interpretations (Fig. 6). For the rhyolite, the wasp-waisted hysteresis loop evidences the existence of a minor amount of spinel (titanomagnetite or titanomaghemite) in addition to titanohematite.

In view of the pressure profile in the samples ( §3) and the temperature increase associated to the shock wave ( §4), no thermal effect is expected on the remanent magnetization or the magnetic mineralogy of the studied rocks. Only for the basalt that has the lowest blocking temperatures, a partial TRM acquisition (about 5-10% of the total TRM, see Fig. 5) is possible up to a distance of 10 mm away from the point of explosion, the temperature increase at this distance being ~50 °C.

To study the natural variability of magnetic properties within the studied rocks, we drilled a Ø 2.5 cm core parallel to the direction of the impact and more than 10 cm away from the impact point. This core was cut in smaller samples whose hysteresis properties (B c : coercivity, B cr : coercivity of remanence, M s : saturation magnetization, M rs : remanente magnetization at saturation), magnetic susceptibility, anisotropy of magnetic susceptibility (AMS) and NRM were measured. The results show no significant variation of the NRM intensity and magnetic properties with depth or mass of the sample. The only exception is a 50% increase of magnetic susceptibility in the upper 5 mm of the rhyolite sample. The basalt, the microdiorite and the rhyolite are magnetically homogeneous at the sampling scale (~200 mg). The schist is heterogeneous at scale <1g: although the magnetic carriers have identical hysteresis properties their concentration varies (and hence the magnetic susceptiblity and NRM) due to aggregation of pyrrhotite grains. The pre-shock magnetic properties are given in Table 2. In summary, we studied fours samples with the following dominant magnetic mineralogy: multidomain magnetite (microdiorite), pseudo-monodomain Ti-rich titanomagnetite (basalt), pseudomonodomain monoclinic pyrrhotite (schist) and monodomain titanohematite (rhyolite). The direction of the NRM of each sample was measured on an oriented fragment before the shock. The direction and intensity of the principal axis of magnetic susceptibility (noted K1 and K3 for the maximum and minimum axes, respectively)

were evaluated on the same samples.

Magnetic properties of shocked materials

After measurement of the NRM (see next section), hysteresis parameters of shocked samples were measured (Fig. 6). The plots of the hysteresis properties versus the distance to the impact point show that for the basalt, the microdiorite and the schist, the coercivity and the remanent magnetization at saturation increase close to the impact (Fig. 7). The effect, already observed by [START_REF] Pesonen | Magnetic properties of diabase samples shocked experimentally in the 4.5 to 35 GPa range[END_REF] is stronger for the microdiorite sample, with a fivefold increase of both parameters. In all three cases, the intrinsic magnetic properties of all samples are clearly modified by the shock wave. Various causes could explain the modifications of magnetic properties: change in magnetic grain size, wall displacement in the magnetic grains, shock-induced defects. We observed that the shock-induced changes in hysteresis properties are not removed by stepwise heating up to 580°C. Therefore, these modifications are not attributable to stress whose effects would be annealed at rather low temperature (e.g. [START_REF] Van Velzen | A method to study alterations of magnetic minerals during thermal demagnetization applied to a fine-grained marine marl (Trubi formation, Sicily)[END_REF]. Similarly, application of a strong field (up to 3 T) does not reset the original magnetic properties. Therefore, wall displacements cannot be the cause of the hysteresis modification. The only plausible explanation is a permanent modifications of the crystalline structure of the magnetite grains, namely microfractures, lattice defects or dislocations.

The bulk magnetic susceptibility and the AMS (except for the rhyolite and the schist) were measured after the shock. A slight decrease of magnetic susceptibility is observed for heavily shocked (titano-)magnetite-bearing samples (Fig. 8), as already evidenced in previous works (e.g. [START_REF] Hargraves | Investigations of the effect of shock on natural remanent magnetism[END_REF].

It is noteworthy that for the basalt (with a pre-shock minimum susceptibility axis K3 that is about 30° away from the direction of impact), the heavily shocked samples have a higher AMS degree (Fig. 9a) and their K3 axis is parallel to the direction of impact (Fig. 9b). For the microdiorite (with a pre-shock K3 axis that is perpendicular to the direction of impact), away from the impact point the K3 axes rotate from a direction parallel to the impact towards the pre-impact direction (Fig. 9b). The intensity of the AMS for the microdiorite does not decay away from the impact point as regularly as for the basalt, probably because we observe the progressive superimposition of two different fabrics: the original one and the impact-induced one. These observations show that the impact modified the existing magnetic fabric in the first cm (peak pressure > 10 GPa) of the shocked basalt and microdiorite sample despite the absence of visible macroscopic brecciation. The physical phenomena responsible for the shock-induced magnetic anisotropy may be small-scale fracturing and deformation of magnetite grains. It is unlikely that domain walls displacement by the shock wave is responsible for even a small fraction of the shock-induced magnetic anisotropy. Indeed, the magnetic anisotropy remains unchanged after application of high magnetic fields (3 T) that would reset any domain wall displacement.

Magnetization of shocked materials

Demagnetization data

The NRM of all oriented sub-samples was measured and stepwise demagnetized with alternating field (AF) up to 140 mT (Fig. 10). We also provide demagnetization data for unshocked samples.

Unshocked basalt samples possess a single component of magnetization that is interpreted as the original TRM. All shocked basalt samples posses a high coercivity component with a direction close to the magnetization of the unshocked sample, that represents what is left from the original TRM. The ~20° discrepancy between the pre-and post-shock high coercivity directions is easily explained by summing the orientation uncertainties when drilling the preand post-shock cores and when cutting and orienting the small parallelepipeds out of the postshock core. All shocked samples, even located at 3 cm from the impact (with an estimated peak pressure of 2 GPa), have acquired a secondary component that is completely erased at 5 mT. This component of magnetization may be attributed to the shock or to the sawing process. Basalt samples located close to the impact (< 1 cm, estimated peak pressure > 10 GPa) possess a more stable secondary component isolated below 10 mT. This component may be interpreted as a shock remanent magnetization (SRM) acquired in the A c c e p t e d M a n u s c r i p t ambient magnetic field present during the explosion. However a thermoremanent origin cannot be excluded for this low-coercivity component in view of the low blocking temperatures of the basalt (see §4). Although poorly defined, the low coercivity directions are not closely related to the ambient field at the time of impact (Fig. 11). They lie within the plane defined by the pre-shock NRM and the ambient field.

For the microdiorite, the unshocked sample possesses two components of magnetization: a low coercivity component, isolated below 6 mT, and a high coercivity component that is not fully demagnetized at 150 mT. This latter component is interpreted as the original TRM.

Despite the low bulk coercivity of the micriodiorite (Bc = 2 mT), its natural TRM is carried by a high-coercivity fraction. The shocked samples still possess most of the original TRM.

The shocked samples located close to the impact (< 1.5 cm, peak pressure > 6 GPa) possess a secondary component isolated below 30 mT and is interpreted as a SRM. The SRM directions are scattered.

For the rhyolite, the unshocked sample possesses a single component of magnetization carried by hematite. It is not clear if this original magnetization is a TRM or a chemical remanent magnetization (see discussion in e.g. [START_REF] Vlag | Paleomagnetism in the Esterel rocks: a revisit 22 years after the thesis of H. Zijderveld[END_REF]. All shocked samples possess a high-coercivity component of similar direction than the original magnetization. The shocked samples closest to the impact point (< 1 cm, peak pressure > 10 GPa) also possess a low-coercivity component (SRM) isolated below ~30 mT. The SRM directions are scattered.

The pyrrhotite-bearing schist did not provide stable directions of NRM when demagnetized by alternating field (Fig. 10). Therefore we will not discuss the possible remagnetization in the shocked schist.

Remagnetization and demagnetization by shock

In our experiments, since the directions of the original TRM and the SRM are different we cannot simply compare the intensities of the pre-and post-shock NRM. For the basalt for instance, the intensity of the total post-shock NRM is much lower than the sum of the intensities of the two components of magnetization (e.g. sample B5 of Fig. 10). In figure 12, we plot the scalar sum of the intensities of the stepwise-demagnetized magnetization vectors for basalt and microdiorite samples. The intensities are normalized to the saturation magnetization of each sample to take into account the natural variability in ferromagnetic mineral concentration. After the shock, the sum of the intensities of the different components of magnetization is weaker than before the shock for the basalt, but higher for the microdiorite. The basalt is globally demagnetized whereas the microdiorite is globally A c c e p t e d M a n u s c r i p t

remagnetized by the shock. To our knowledge, this is the first time that shock experiments actually increase the original NRM of a rock. The increase of the magnetization of the microdiorite after the shock does not mean that SRM acquisition is more efficient than TRM acquisition. This is due to the increased capacity of the microdiorite to acquire a remanent magnetization after the shock (i.e. increase of Mr/Ms by a factor up to five) and primarily to the fact that the original remanence was carried almost entirely by the grains with high coercivity so that the shock added a secondary low-coercivity SRM to the original highcoercivity TRM that was not much affected by the shock.

In view of the rather unstable behaviour of the NRM of the microdiorite and the schist under AF demagnetization and the high resistance of the NRM of the rhyolite to AF demagnetization (Fig. 10), only the basalt was suitable for a detailed study of the the ffect of shock on the remanence. For the basalt that has a simple demagnetization behaviour under alternating field and a TRM carried by grains spanning the whole coercivity spectrum, we can compare the magnetization slope (dNRM/dAF) for shocked and unshocked samples as a function of the peak alternating field (Fig. 13). Above 10-15 mT, all shocked samples located more than 15 mm from the impact point (peak pressure < 6 GPa) closely follow the curve for the unshocked basalt. Contrarily, heavily shocked samples (B5 to B14) plot below the unshocked samples between 10 and 40 mT. Above 40 mT all curves are identical. On the interval 10-40 mT, these heavily shocked samples have a magnetization that has the same direction as the original TRM. This means that the original TRM of samples B5 to B14 has been partly demagnetized on the 10-40 mT coercivity window. If a SRM or a TRM has been acquired on the same coercivity window during the shock, it is small enough not to be noticeable on the demagnetization plot, i.e. it is at most a few % of the original TRM. We can quantify the shock demagnetization of the original TRM on the 10-40 mT coercivity interval by comparing the amount of NRM demagnetized between 10 mT and 40 mT for pre-and post-shock samples (fig. 14). Up to a distance of 14 mm from the impact, corresponding to a peak pressure of about 7 GPa (sample B14), the original TRM of shocked samples has been significantly demagnetized. For sample B5 that has suffered peak pressure around 20 GPa, the original TRM has been divided by up to a factor 5. It is noteworthy that attempting a paleointensity measurement on such a shocked sample would be problematic since it is impossible to notice that part of the TRM has been demagnetized by shock. Although it is not clear how this demagnetization is dispatched along the blocking temperature spectrum, the paleointensity experiment would at best provide an underestimated value (up to a factor 5 in the case of sample B5 for instance).

A c c e p t e d M a n u s c r i p t

Generally speaking the effect of the explosive-driven shocks on the NRM of the four studied lithologies appear rather weak compared to a number of previous studies performed on isothermal remanent magnetization (IRM). Complete demagnetization of the IRM of a titano-magnetite bearing basalt shocked with a laser pulse was observed at about 2 GPa [START_REF] Gattacceca | Investigating impact demagnetization through laser impacts and SQUID microscopy[END_REF]. Shock experiments with a gas gun on pyrrhotite-bearing samples showed a 80% demagnetization of IRM at only 0.5 GPa (Louzada et al., in press). The large differences are attributed to the fact that NRM and IRM react differently to shock waves.

Conclusion

Experimental shocks of four rocks with different lithology and magnetic mineralogy show that, in most cases (only the hematite case is not conclusive), the intrinsic magnetic properties of the rock are permanently modified by the shock wave. A remarkable effect, not documented in previous studies, is the capacity of the shock wave to superimpose a new fabric (with a minimum susceptibility axis parallel to the direction of impact) to the original magnetic fabric of the rock. Multidomain magnetite-, pseudo-single domain titanomagnetiteand monoclinic pyrrhotite-bearing rocks show a noticeable increase of their coercivity for pressure above 10 GPa. These changes are not annealed even at high temperature (580 °C).

They are attributed to fracturing and/or dislocations of the ferromagnetic grains. This fracturing is also responsible for the appearance of a shock-induced anisotropy of magnetic susceptibility. These results show that the magnetic properties of meteorites which are commonly shocked to pressures well above 10 GPa (e.g. Martian meteorites, [START_REF] Nyquist | Ages and geologic histories of Martian meteorites[END_REF] may not be representative of the magnetic properties of their parent body.

For (titano)magnetite bearing rocks, we observe both a shock demagnetization of the original TRM for magnetic grains with coercivity up to 40 mT, and a possible shock magnetization for grains with coercivity up to 10 mT. NRM appears to be much more resistant to shock than IRM (probably because they have different coercivity spectra), implying that more work is needed on the effects of shock on natural magnetization. As observed by [START_REF] Cisowski | The effect of shock on the magnetism of terrestrial rocks[END_REF], the demagnetizing effects of the shock wave depend closely on the coercivity spectrum of the grains carrying the original remanence, and the shock-remagnetizing effect depend on the presence (or creation by the impact itself) of low-coercivity magnetic grains.

With an impact occurring in an ambient magnetic field of similar intensity to the original magnetizing field, the post-shock magnetization may be higher or lower than the pre-shock magnetization depending on these two factors.

To summarize, although an impact occurring after dynamo shutdown will indeed demagnetize the crust to a variable extent, an impact occurring while the dynamo is still active may demagnetize the crust almost as efficiently or conversely may lead to the situation where the shocked crust has a stronger magnetization than the surrounding rocks (depending on the efficiency of SRM acquisition, and on the nature of the original NRM). Therefore, it appears difficult to draw conclusions about the dynamo history of a planet by studying the magnetic anomalies above its impact basins, unless the anomalies provide information about the magnetization of the rocks heated during the impacts (if they are preserved). The decisive clue to the presence of an active dynamo at the time of impact is the presence or absence of a thermoremanence carried by the volume of rocks heated above blocking temperatures during the impact. Similarly, it may be difficult to determine which magnetic phase dominates the crust based only on the demagnetization pattern around impact basins.

Figure captions

Figure 1 -Sketch illustrating the different steps of the sampling after explosion. The wire used to saw the parallelepipeds is 220 µm in diameter. Figure 2 -Modelled pressure versus time at various depths in the rock straight below the explosion. The modelling was performed with a Johnson Wilkins Lee law for the explosive and the Radioss code for the shock wave propagation in the sample (see text). Figure 3 -Peak pressure versus depth in the rock straight below the explosion. The pressure values are deduced from the shock wave modelling presented in Fig. 2. The solid line is computed with a density of 2300 kg.m -3 , the dashed line is computed with a density of 3000 kg.m -3 . Figure 4 -Modelled peak temperature versus depth in the sample straight below the explosion, considering the amount of heat transferred to the to by the explosion of the PETN detonator. Dashed line is at 50°C. The modelling was performed using Carte and FEMLAB codes (see text). Figure 5 -Thermomagnetic curves for the four studied lithologies (susceptibility vs. temperature). Empty circles indicate the beginning of the heating curves. Heating = thick lines, cooling = thin lines. For the basalt and the microdiorite, progressive TRM acquisition curves are also plotted (dotted line, with standard deviation when available). Figure 6 -Representative hysteresis loops for shocked and unshocked samples of the four studied lithologies. The loops have been corrected for the paramagnetic slope. Figure 7 -Hysteresis properties vs. depth for the shocked samples (M r : remanent magnetization at saturation, M s : saturation magnetization, B cr : coercivity of remanence, B c : coercivity). Dashed line is the mean value for unshocked samples (grey band = one standard deviation). Figure 8 -Low-field specific magnetic susceptibility of impacted samples. Pre-impact mean are indicated with one standard deviation (grey bands). Figure 9 -a-c) Degree of anisotropy of magnetic susceptibility (Pams = ratio of maximum to minimum principal susceptibility values) vs. distance to the impact. Pre-impact means are indicated (dashed line) with one standard deviation (grey bands). b-d) Lower-hemisphere equal area stereographic projection of minimum axis of magnetic susceptibility K 3 . Figure 10 -Orthogonal demagnetization plots of oriented samples of the shocked rocks. Open and solid symbols represent projections of the magnetization vector on vertical and horizontal planes, respectively. Demagnetization plots for oriented unshocked samples are given for comparison. Demagnetization steps are 5, 10, 15, ..., 50, 60, 70, 80, 100, 120, 140 mT. Figure 11 -Equal-area stereographic projection of the directions of magnetization (0° = North and 90° = East in Fig. 10). Open (solid) dots represent projection onto upper (lower) hemisphere. Open ellipses are the projections of the 95% confidence cones about the directions. Diamond: ambient field during the impact; K 1 (resp. K 3 ) : maximum (resp. minimum) susceptibility principal axis, large labelled circles: low-coercivity components, small circles: high-coercivity components; large labelled star: pre-impact direction of magnetization (determined on a separate core), star: mean direction of the high-coercivity components of shocked samples. Figure 12 -Sum of demagnetized vectors (scalar intensity) normalized by saturation magnetization vs. distance from the impact. The dotted line represents an unshocked sample. Figure 13 -NRM slope (dNRM/dAF) as a function of alternating field for shocked basalt samples. The curve for pre-shock NRM (dashed line) is plotted for comparison. Curves are normalized to saturation magnetization (Ms) to take into account the possible variability in titanomagnetite content. Data for demagnetizing field below 10 mT are not represented A c c e p t e d M a n u s c r i p t because the origin of the low coercivity component is not ascertained for the basalt (see text). Figure 14 -Mean degree of shock demagnetization of the basalt on the 10-40 mT coercivity window as a function of distance to impact. This value is derived from the ratio of the NRM moment demagnetized between 10 mT and 40 mT before and after shock. Tables Table 1 - 1.70 ± 0.22 10 -3 1.71 ± 0.12 10 -4 4.19 ± 0.44 10 -5 6.60 ± 2.84 10 -5

For each magnetic property, the number of measured samples (n) is indicated. * For susceptibility and magnetization of the schist, only samples with mass > 1g have been taken into account due to small-scale heterogeneities in pyrrhotite concentration.

  Figure1

  Physical parameters used in the shock and thermal simulations. : density; D: shock speed; P CJ : Chapman-Jouguet pressure; A, B, R 1 , R 2 : JWL parameters associated to the JWL equation mentioned in the text[START_REF] Wilkins | Computer simulation of dynamic phenomena[END_REF]; ω: Grüneisen coefficient; C o : sound speed; S: empirical parameter; Γ: Grüneisen coefficient; Y o : yield stress; k: thermal conductivity; C: heat capacity.

	Explosive (PETN)	ρ o (g.cm -3 )	D (m.s -1 )	P CJ (GPa)	A (GPa)	B (GPa)	R 1	R 2	ω
		1.77	8300	33.35	617	16.93	4.4	1.2	0.25
	Basalt	ρ o (g.cm -3 )	C o (m.s -1 )	S	Γ	Y o (GPa)	k (W.m -1 .K -1 )	C (J.kg.K -1 )
		2.88	4800	1.34	2	0. 3	1.99	1000
	ρ

o

Table 2 -

 2 Magnetic properties of materials before shock

		Basalt	Microdiorite	Rhyolite	Schist
	Hysteresis Mr (Am 2 kg -1 ) Ms (Am 2 kg -1 ) Mr/Ms	n=10 9.78 ±0.67 10 -2 6.22 ± 0.46 10 -1 1.57 ± 0.03 10 -1	n=12 2.38 ± 0.20 10 -2 1.28 ± 0.14 10 -1 1.39 ± 0.07 10 -2	n=10 2.31 ± 0.22 10 -3 4.91 ± 0.72 10 -3 4.77 ± 0.73 10 -1	n=10 4.48 ± 2.90 10 -2 9.14 ± 6.02 10 -2 4.99 ± 0.28 10 -1
	Bc (mT)	5.19 ± 0.16	1.86 ± 0.08	137 ± 69	23.8 ± 5.9
	Bcr (mT)	18.4 ± 1.1	19.1 ± 0.7	406 ± 35	31.3 ± 11.7
	Bcr/Bc	3.54 ± 0.14	10.3 ± 0.4	3.56 ± 1.47	1.29 ± 0.12
	Susceptibility Susceptibility (m 3 kg -1 )	n=22 1.61 ± 0.03 10 -5	n=28 1.35 ± 0.07 10 -5	n=9 3.31 ± 0.58 10 -8	n=7* 3.19 ± 0.20 10 -7
	AMS	n=8	n=8
	Anisotropy degree	1.029 ± 0.009	1.040 ± 0.008
	Magnetization NRM (Am 2 kg -1 )	n=14	n=13	n=19	n=7*

Acknowledgements

This work was supported by the Programme National de Planétologie (INSU/CNES, France).

We acknowledge very constructive comments by S. T. Stewart-Mukhopadhyay and an anonymous reviewer.

Estimated peak pressure (GPa)


J Gattacceca

L Berthe

M Boustie

F Vadeboin

P Rochette

T De Resseguier

On the efficiency of shock magnetization processes

The acquisition of remanent magnetization caused by hypervelocity impacts may be a major contribution to the remanent magnetization of planetary surfaces and meteorites. In this paper, we investigate the properties of shock remanent magnetization (SRM) and in particular the relative efficiency of this phenomenon with respect to thermoremanent magnetization (TRM), a parameter of interest for the understanding of the magnetic signatures of impact basins on extraterrestrial bodies. We imparted shock remanent magnetization on basalt and microdiorite samples using laser shock in controlled magnetic field. Shock modeling indicates a pressure range of 0.6-1.5 GPa for our experiments. The results confirm that the SRM is parallel to the ambient magnetic field. SRM increases inearly with the ambient field in the 1 µT-2500 µT range. The intensity of SRM is independent of the angle between the shock direction and the direction of the ambient field. The coercivity spectrum of SRM is shifted towards lower values compared to the coercivity spectra of TRM and isothermal remanent magnetization.

For the two studied lithologies, the efficiency of SRM vs TRM acquisition is ≥17% for the basalt and is 36% for the microdiorite. This efficiency depends on the magnetic mineralogy and increases with decreasing coercivity. The rather high efficiency values that we obtained show that a significant remanent magnetization can be acquired by the crust during an hypervelocity impact on a planetary surface in the presence of an ambient field.

Introduction

The effect of shock waves on the remanent magnetization of rocks has implications for the understanding of the magnetic anomalies associated with impact basins on Mars [START_REF] Hood | Distribution of crustal magnetic fields on Mars: shock effects of basin-forming impacts[END_REF], the Moon [START_REF] Halekas | Magnetic fields of lunar multi-ring impact basins[END_REF] or Earth [START_REF] Pilkington | The geophysical signature of terrestrial impact craters[END_REF], and also for the interpretation of the paleomagnetic signal of meteorites and lunar rocks that have all been shocked to a variable degree.

Leaving aside the possible thermoremanent magnetization (TRM) carried by the central volume of rock that was heated above blocking temperatures during the impact (if it is preserved), the magnetic anomalies observed above impact basins are mainly attributed to the A c c e p t e d M a n u s c r i p t much larger volume of surrounding rocks that were affected by relatively low to moderate shock pressures (typically > 1 GPa). The interpretation of this magnetic signature in terms of magnetic mineralogy of the crust or in terms of presence/absence of a magnetic field (global field created by a dynamo or transient field created by the impact) is closely related to the efficiency of shock remanent magnetization (SRM) acquisition. Yet this efficiency has never been determined precisely.

Since the 1970's, a number of studies have dealt with the demagnetization by shock waves of natural (e.g. [START_REF] Cisowski | The effect of shock on the magnetism of terrestrial rocks[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF][START_REF] Hargraves | Investigations of the effect of shock on natural remanent magnetism[END_REF][START_REF] Gattacceca | The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks[END_REF] or artificial (e.g. [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Gattacceca | Investigating impact demagnetization through laser impacts and SQUID microscopy[END_REF], Louzada et al., 2006) remanent magnetization. Much less has been done on the acquisition of remanent magnetization upon shock. Only few papers address this particular issue: [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF] who actually named this type of magnetization "shock remanent magnetization" (SRM), [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] and [START_REF] Nagata | Shock remanent magnetization of meteorites[END_REF]. In these works, demagnetized rock samples were submitted to shock in a controlled magnetic field. Although the work by [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF] was pioneering and set the basis of the understanding of SRM, the maximum shock pressures were in the 45 MPa range, which is about two orders of magnitude lower than the pressures experienced during natural hypervelocity impacts (several GPa). Moreover, no information was provided about the magnetic properties of the target rocks, which are necessary to fully understand the phenomena. [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] conducted experiments on basalt with shock pressures up to 1 GPa but did not discuss the efficiency of the SRM acquisition. In order to determine the efficiency of SRM acquisition, we conducted shock experiments with a pulsed laser in controlled magnetic field on previously demagnetized samples.

Description of the target rocks

Our shock experiments were conducted mostly on a Pleistocene basalt from Chanteuges (Haute-Loire, France) and to a lesser extent on a microdiorite from the Esterel range (France).

The basalt is an alkaline basalt containing less than 5% of phenocrystals (mainly olivine and clinopyroxene in equal proportion and up to 1.5 mm in size, and some rare opaque minerals).

The matrix is finely crystallized with an intergranular texture. It contains clinopyroxene (about 20%), plagioclase, olivine and opaque minerals. The microdiorite has a microgranular matrix composed of plagioclase and quartz. The phenocrystals in the microdiorite consist in large zoned automorphic plagioclase crystals, green hornblende crystals, and a few large opaque crystals.

The magnetic properties of the basalt and the microdiorite are synthetized in Table 1 that also provides some petrophysical parameters of interest for shock wave propagation (density, sound speed, porosity). Based on experimental work and numerical simulations, [START_REF] Berthe | Mechanical characterization of basalt using shock wave induced by laser, Application to planetary hypervelocity impact effect[END_REF] describes the mechanical behaviour of this particular basalt under short (ns) and moderate-pressure (~GPa) shock wave comparable to pressure loadings used in the present paper. The mechanical properties and modeling parameter obtained by [START_REF] Berthe | Mechanical characterization of basalt using shock wave induced by laser, Application to planetary hypervelocity impact effect[END_REF] are given in Table 2.

Hysteresis properties and thermomagnetic analyses indicate that titanomagnetite is the main magnetic mineral in the basalt. The thermomagnetic curves display two Curie temperatures at 60°C and 150°C (Fig. 1). However TRM acquisition experiments show that only 10% of the TRM is acquired below 150°C. The fact that most of the TRM is acquired above the thermomagnetic Curie point, up to 300°C evidences that a minor population of titanomagnetite pseudosingle-domain grains carries the remanence (Fig. 1). The microdiorite is described in details in [START_REF] Gattacceca | The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks[END_REF] and its physical properties are given in Table 1. The main magnetic mineral in the microdiorite is multidomain magnetite. As shown by the small standard deviations in Table 1, these two rocks have homogeneous magnetic properties at the ~50 mg scale. Therefore we can consider that for each rock all samples (~2g) used in the shock experiments have the same magnetic behaviour.

All magnetic measurements have been performed at CEREGE (Aix-en-Provence, France) with a 2G cryogenic magnetometer (remanent magnetization), Micromag Vibrating Sample Magnetometer (hysteresis properties) and a KLY2 Kappabridge (magnetic susceptibility) equipped with a CS2 furnace (thermomagnetic analyses). Thermal demagnetization and acquisition of artificial TRM were performed with a MMTD furnace.

Shock waves induced by laser

Pressure shock waves in the range of 1-5 GPa can be easily produced by laser induced plasma in the well-known water confined regime [START_REF] Anderholm | Laser-generated stresses Waves[END_REF][START_REF] Fabbro | Physical study of laserproduced plasma in confined geometry[END_REF][START_REF] Berthe | Shock waves from a waterconfined laser-generated plasma[END_REF]. It consists in irradiating by a focused and pulsed (ns range) laser (GW.cm-2), the target material covered with few mm of water. The energy of the laser induces material ablation into a high-pressure plasma generating a compressive wave inside the target by the action/reaction principle. The expansion of the plasma, limited by the presence of the confining water, allows the generation of a pressure loading higher and longer than in the direct regime for same laser parameters (peak power density, pulse duration, wavelength).

The maximum pressure generated by laser plasma in the water confinement regime is given by the following relation [START_REF] Fabbro | Physical study of laserproduced plasma in confined geometry[END_REF]) validated experimentally [START_REF] Fabbro | Physical study of laserproduced plasma in confined geometry[END_REF][START_REF] Berthe | Shock waves from a waterconfined laser-generated plasma[END_REF]

: ) . ( ) . . ( 01 . 0 ) ( 2 0 1 2 3      cm GW I s cm g Z GPa P   (1)
where  is the fraction of the internal energy devoted to thermal energy (typically =0.25), I 0 is the incident power density and Z is the reduced shock impedance between the target and the confining water (2/Z=1/Z water +1/Z target ). For basalt target in water confined regime, Z water =0.165 10 6 g.cm -2 .s -1 , Z basalt = 0 C 0 =Z target =1.8 10 -6 g.cm -2 .s -1 and Z=3.04 10 5 g.cm -2 .s -1 .

Equation (1) provides a link between the laser-matter interaction and the pressure loadings induced at the surface of the target material. Pressure increases with power density. At 1 and 2 GW.cm -2 , pressure is 1.5 and 2.2 GPa respectively.

The propagation of shock wave in the target basalt has been simulated using SHYLAC (Shock Hydrodynamic LAgrangian Code), a software developed at LCD (Laboratoire de Combustion et de Détonique, Poitiers, France). A good review on methods used in SHYLAC to simulate shock waves propagation in solids is presented also in [START_REF] Cottet | Spallation study in aluminium targets using shock waves induced by laser irradiation at various pulse durations[END_REF], [START_REF] Antoun | Spall fracture[END_REF] and [START_REF] Zel'dovich | Physics of shock waves and high-temperature hydrodynamic phenomena[END_REF]. SHYLAC is a 1D finite difference code solving hydrodynamics conservative laws including a Mie-Grüneisen equation of state and a perfectly elasto-plastic constitutive law for metallic materials (von mises Criteria and hooke law). Main data required for SHYLAC simulations are: the pressure loading profile (obtained from equation (1) and [START_REF] Fabbro | Physical study of laserproduced plasma in confined geometry[END_REF] and physical and mechanical material properties: density   , yield strength Y 0 , shear modulus G, Mie-Grüneisen coefficient, bulk sound velocity C 0 and material constant S. For the target basalt, these parameters are reported in Table 2. SHYLAC calculates the state of matter as a function of time and location in the target. In particular, pressure attenuation in the basalt can be computed (Fig. 2). The pressure decreases down to a depth for which it becomes constant at 0.6 GPa. This level corresponds to the pressure of the elastic wave propagating without attenuation [START_REF] Berthe | Mechanical characterization of basalt using shock wave induced by laser, Application to planetary hypervelocity impact effect[END_REF]). This depth of elasto-plastic transition depends on the incident loading: it is 8.8 mm at 4 GW.cm -2 (3 GPa) against 0.86 mm at 0.16 GW.cm -2 .

Clearly, the laser beam and high-pressure plasma induce a temperature increase in the material that is negligible in the present case. Indeed, the heated zone consists of a thin layer of only 10-20 µm [START_REF] Peyre | Influence of thermal and mechanical surface modifications induced by laser shock processing on the initiation of corrosion pits in 316L stainless steel[END_REF], to be compared to the thickness of sample (10 mm).

Besides, the shock wave itself induces a temperature increase that is negligible (typically about a few °C) for the pressures encountered in this work (e.g. [START_REF] Stöffler | Shock metamorphism of ordinary chondrites[END_REF].

Experimental protocol

The experimental protocol can be decomposed into two main steps: laser shock treatment in a controlled magnetic field followed by measurement of the remanent magnetization of the shocked sample. Oriented cylindrical samples (10 mm high, 9.5 mm in diameter, mean mass 2.14±0.05 g for the basalt and 1.98±0.01 g for the microdiorite) were subjected to laser shocks in the water-confined regime in a magnetic field controlled by three orthogonal pairs of Helmholtz coils (Fig. 3). The sample is held in place by a plastic device. There are no metallic parts inside the Helmholtz coils system. The experiments have been performed with a Ndglass laser at LCD (Laboratoire de Combustion et de Détonique, Poitiers, France). The pulse duration is 30 ns, the maximum energy is 21.5 J and the spot diameter is 4.25 mm at the surface of the sample. This setting is described in more details in [START_REF] Gattacceca | Investigating impact demagnetization through laser impacts and SQUID microscopy[END_REF]. For each laser shot, the pulse duration and shape and energy are recorded. The energy of the laser at the surface of the sample is adjusted by intercalating along the laser path calibrated neutral densities. Power densities used in this work are in the range 0.1-4 GW.cm -2 .

In order to isolate the shock magnetization process without interference of the original magnetization of the basalt, the samples were fully demagnetized before the experiments and the residual remanent magnetization was measured. The basalt samples were demagnetized using thermal demagnetization at 290°C followed by alternating field (AF) demagnetization at 150 mT. The microdiorite samples were demagnetized using thermal demagnetization at 590°C followed by AF demagnetization at 150 mT. We checked on test samples of basalt and microdiorite that these thermal treatments had no effect on the intrinsic magnetic properties (hysteresis, magnetic susceptibility). The residual remanent magnetization is 5.20 ± 2.16 10 -5 Am 2 kg -1 for the basalt and 7.83 ± 1.13 10 -5 Am 2 kg -1 for the microdiorite. The lower detection limit of the 2G DC SQUID magnetometer is about 10 -11 Am 2 , i.e. 4 orders of magnitude lower than these residual magnetization.

After the shock experiments, the remanent magnetization of the oriented samples was measured. If we suppose that the residual pre-shock magnetization is not affected by the shock (in view of its high coercivity), the vectorial difference between the post-shock magnetization and the pre-shock magnetization provides the SRM moment. The SRM was subsequently stepwise demagnetized with AF fields or thermal treatments.

Results

Although repeated shocks with the same intensity can create an increasing SRM [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF], we performed a single shock experiment on each sample because the goal of this study is to model experimentally single natural impacts.

Pressure and SRM homogeneity in the sample

A first set of 12 basalt samples was submitted to shock of different intensity in a magnetic field of 200 µT oriented parallel to the direction of shock. The intensities of the resulting SRM show that for an energy flux above ~1 GWcm -2 there is no significant increase of the SRM (Fig. 4). As a consequence, we used for all the other shock experiments a laser pulse with a constant energy flux of ~1.9 GWcm -2 , which is enough to impart an almost complete SRM (an analogy for acquisition of TRM would be heating above the maximum blocking temperature). For an energy flux of 1.9 GWcm -2 the pressure in the sample decays from 2 GPa at the surface to 0.6 GPa at the bottom of the sample (Fig. 2).

In order to study the possible decay of SRM with distance to the impact, we cut 1 mm-thick parallelepipedic sub-samples (with mass ~ 20-30 mg) from two shocked basalt samples using a wire saw with a wire diameter of 220 µm. For sub-samples located straight below the impact spot, the intensity of SRM is higher for the first upper mm and is fairly constant from 1 to 10 mm with a mean deviation of 5% around the mean intensity (Fig. 5). Referring to the pressure model of Fig. 2, this indicates that the SRM acquisition is approximately constant for pressures in the range 0.6-1 GPa, whereas it is ~20% higher at 1.7 GPa. The same experiments for the microdiorite show a constant SRM from top to bottom of the shocked sample with a mean deviation of 10% around the mean SRM (Fig. 5), indicating almost complete shock magnetization even at the lower pressure suffered by the bottom of the sample (~0.6 GPa if we consider that the propagation of shock wave in the microdiorite is similar to the propagation in the basalt).

Unexpectedly, the SRM intensities of sub-samples taken directly straight below the laser spot or on the edges of the sample (more than 1 mm away from the loaded spot) show no significant difference (Fig. 5). The diameter of the loaded spot at the surface of the sample is 4.25 mm, so that the volume located straight below the impact spot represents only 20% of the total volume of the sample. The fact that the whole volume of the samples is homogeneously affected by shock magnetization is probably linked to multiple 3D reflections of the elastic compression wave throughout the sample, which could result in a minimum peak pressure of ~0.6 GPa in the whole volume of the sample. Further work has been planned to clarify that point.

In conclusion, with an energy flux of 1.9 GW.cm -2 the SRM acquisition is rather homogeneous in the cylindrical sample, as the whole volume of the sample seems to be affected by a minimum peak pressure of 0.6 GPa. This homogeneity justifies that the SRM intensity can be computed directly as the SRM moment measured on the bulk sample divided by the sample mass. With these shock settings, SRM in the microdiorite samples seems to have reached its maximum value whereas the SRM in the basalt samples is shy by at least 20% from its maximum value.

SRM properties

A second set of 54 basalt samples was submitted to shock with a mean energy flux of 1.89±0.16 GWcm -2 in an ambient field varying in strength between 10 nT and 2.5 mT, and varying in direction between 0° and 90° away from the direction of shock. For a given magnetic field, we do not observe a significantly lower SRM when the ambient field is perpendicular to the direction of propagation of shock than when it is parallel (Fig. 6). [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF] had observed a decrease of SRM by a factor of ~0.75 when the ambient field was perpendicular (for pressures up to 45 MPa). Our results indicate that this observation may be relevant only for low shock pressures (<< 1 GPa).

The SRM increases linearly with the ambient field in the 1 µT-2500 µT range (Fig. 7), confirming previous results [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] and extending them to higher and lower magnetic fields. It is noteworthy that within this field range, isothermal remanent magnetization is about one order of magnitude lower than SRM and does not contribute significantly to the magnetization of the shocked samples. Below 1 µT, the lack of linearity is likely attributable to poor control of the ambient field (see a similar discussion about TRM acquisition in [START_REF] Tauxe | A linear field dependence of thermoremanece in low fields[END_REF] and/or to an increasing relative contribution of a transient field possibly created by the laser shock itself [START_REF] Srnka | Magnetic field and shock effects and remanent magnetization in a hypervelocity impact experiment[END_REF][START_REF] Crawford | Laboratory observations of impact-generated magnetic fields[END_REF]. Also, at low fields the expected SRM becomes lower than the residual magnetization before shock (Fig. 7) so that slight differences in orientation when measuring the residual magnetization and the post-shock magnetization vectors may result in a large error in the SRM computed as the difference between these two vectors. Moreover the subtraction does not take into account a possible shock demagnetization of the residual pre-shock remanence, even though the very high coercivity of the pre-shock remanence probably limits this effect.

Alternating field and thermal stepwise demagnetization show that samples have acquired a single component of magnetization during the shock (Fig. 8). SRM has a coercivity spectrum dominated by coercivities below 20 mT with a median destructive field of 5 mT compared to A c c e p t e d M a n u s c r i p t 11 mT for TRM and 9 mT for saturation isothermal remanent magnetization (sIRM) (Fig. 9).

For a magnetizing field above 1 µT, the direction of the SRM is parallel to the direction of the applied field, with a mean angular departure of 3.8° between the direction of impact and SRM, which is easily explained by the orientation errors during the shock experiments and magnetic measurements. For magnetizing field below 1 µT, the angular departure increases significantly for the above-mentioned reasons (poor field control and/or transient field).

In order to compare SRM acquisition with TRM acquisition, we conducted TRM acquisition experiments on a set of 5 other basalt samples, using fields between 10 µT and 150 µT. The results are plotted in Fig. 7. The same set of experiments was conducted on 6 microdiorite samples. The data for the acquisition of SRM and TRM by the microdiorite are presented in Fig. 10. The AF demagnetization data of SRM, TRM and sIRM for the microdiorite are presented in Fig. 11.

For both the microdiorite and the basalt, the hysteresis properties and magnetic susceptibility show no variation with depth and are identical to the properties of unshocked samples, as expected in the pressure range used in this study (< 2 GPa), and in contrast with the permanent modification of magnetic properties observed for pressures > 10 GPa [START_REF] Gattacceca | The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks[END_REF].

Discussion

The existing works about SRM acquisition [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF][START_REF] Nagata | Shock remanent magnetization of meteorites[END_REF]) allowed the main properties of SRM to be defined. SRM is parallel to the ambient magnetic field present at the time of shock, and its intensity is proportional to the strength of this field. The intensity of SRM increases linearly with pressure below 45 MPa [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Nagata | Shock remanent magnetization of meteorites[END_REF]. For higher pressures, the intensity of SRM still increases with pressure, though with a decreasing rate. This was observed up to 1 GPa [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] and it is probable that above a given pressure the intensity of SRM does not increase any more. Lastly, repeated shocks with the same intensity create higher and higher SRM. This effect is most dramatic at low pressures [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF] but remains visible for pressures up to at least 0.25 GPa [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF].

The relative efficiency of SRM versus TRM acquisition is a valuable parameter for the interpretation of magnetic anomalies observed above impact basins. In the following, we define this efficiency (noted ) as the ratio of SRM intensity to TRM intensity acquired in the same field. The absence of magnetic anomalies above extraterrestrial impact basins are generally interpreted as evidence that the dynamo had shut down at the time of impact (e.g. [START_REF] Acuña | Global distribution of crustal magnetization discovered by the Mars Global Surveyor MAG/ER experiment[END_REF], but this cannot hold if  is << 1. In that case additional information about the magnetization in the rock melted during the impact (if they are preserved) is necessary.

Data on SRM acquisition are scarce and no reliable data is available about the efficiency of SRM acquisition.  has been estimated between 1 and 10% for fine particle iron (Dickinson and Wasilewski, 2000), but [START_REF] Martelli | Hypervelocity cratering and impact magnetisation of basalt[END_REF] have found, by impacting magnetitebearing basalts, that TRM and SRM acquisitions were equally efficient. Data from [START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] on a titanomagnetite-bearing basalt indicate that  increases with pressure (up to 1 GPa) and does not depend on the ambient field, at least between 100 and 700 µT.

The comparison between the SRM and TRM acquisition curves (Fig. 7 and 10) provides a precise estimate of the SRM efficiency  for a shock pressure of ~0.6 GPa (noted  0.6 ). The data show that  0.6 is independent of the magnetic field on the 1-1000 µT range.  0.6 values are 0.14 for the pseudosingle-domain titanomagnetite-bearing basalt, and 0.36 for the multidomain magnetite-bearing microdiorite. As discussed in §5.1, for the basalt  0.6 is shy by at least a factor 1.2 from the true  value that may be reached at higher pressure, whereas for the microdiorite  0.6 is probably close to the true  value. The differences between the values for the microdiorite and the basalt indicate that  is sensitive to the intrinsic magnetic properties of the rock and that no general value can be proposed. For the basalt and the microdiorite, SRM has a coercivity spectrum shifted towards low coercivities with respect to TRM (Fig. 9 and 11). The median destructive field of SRM (resp. TRM) are 5 mT (resp. 11 mT) for the basalt and 7 mT (resp. 10 mT) for the microdiorite. This shift suggests that SRM will be more sensitive to viscous decay than TRM. As a consequence a SRM acquired in and around an impact basin may undergo more viscous relaxation than the surrounding TRM and may be relatively difficult to detect by now for impacts that are several billions years old (see [START_REF] Shahnas | Viscous and impact demagnetization of Martian crust[END_REF] for a quantitative estimate of TRM viscous demagnetization of the Martian crust for instance).

From the SRM and TRM alternating field demagnetization data, the efficiency of SRM versus TRM acquisition can be computed on different coercivity windows as the ratio of the SRM and TRM moments demagnetized over the same coercivity window, noted ' (Fig. 12, following the concept of REM' introduced by [START_REF] Verrier | Estimating peak currents at ground lightning impacts using remanent magnetization[END_REF][START_REF] Verrier | Estimating peak currents at ground lightning impacts using remanent magnetization[END_REF]Gattacceca and[START_REF] Gattacceca | Toward a robust normalized magnetic paleointensity method applied to meteorites[END_REF]. It clearly appears that the acquisition of SRM is more efficient at lower coercivities. The two rocks display contrasting behaviour: for the basalt ' decreases quickly and is below 0.1 at 10 mT whereas for the microdiorite ' almost plateaus around 0.3 between 5 mT and 40 mT. This conclusion is valid for the moderate shock pressures involved here (2 GPa maximum) that do not result in "shock hardening" (shock-induced coercivity increase) as demonstrated in the higher pressure range (10 GPa) used in [START_REF] Gattacceca | The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks[END_REF]. When shock hardening is involved, SRM intensity and coercivity may become similar to the one of TRM [START_REF] Gattacceca | The effects of explosive-driven shocks on the natural remanent magnetization and the magnetic properties of rocks[END_REF]. In any case, even for the pressure range used in this work, it is noteworthy that SRM acquisition may be of the same order of magnitude as TRM acquisition for samples dominated by low-coercivity grains.

Conclusion

We have performed laser shock experiments on igneous rocks in controlled magnetic fields and studied the subsequent acquisition of remanent magnetization (SRM). Shock modeling indicates a pressure range of 0.6-1.5 GPa for our experiments. Our results confirm that the SRM is parallel to the ambient magnetic field. SRM increase linearly with the ambient field in the 1 µT-2500 µT range, confirming previous results [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF][START_REF] Pohl | Shock magnetization and demagnetization of basalt by transient stress up to 10 kbar[END_REF] and extending them to higher and lower magnetic fields. Contrary to previous studies [START_REF] Nagata | Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks[END_REF], we do not observe a lower SRM when the ambient field is perpendicular to the direction of propagation of shock than when it is parallel, which suggests that this observation may be relevant only for low shock pressures (<<1 GPa). The coercivity spectrum of SRM is shifted towards lower values compared to the coercivity spectra of TRM and isothermal remanent magnetization.

Comparison of SRM and TRM acquired in the same magnetic field provides a precise value of the efficiency (noted ) of SRM acquisition with respect to TRM acquisition, a parameter of interest for the understanding of the magnetic signatures of impact basins on extraterrestrial bodies. For the two studied lithologies,  is ≥17% for the basalt and is 36% for the microdiorite.  depends on the magnetic mineralogy and increases when coercivity decreases in agreement with a lower coercivity of SRM versus TRM. The range of observed values shows that a significant remanent magnetization can be acquired by the crust during an hypervelocity impact on a planetary surface in the presence of an ambient field. As a consequence, this magnetizing mechanism must be considered when studying the magnetic signature of planetary surfaces submitted to impacts (on Mars, Earth, the Moon) or the paleomagnetism of meteorites that have almost all been shocked to pressures higher than a few GPa. horizontal planes, respectively. The post-shock magnetic moments are 5.81 10 -6 Am 2 for the basalt sample and 7.56 10 -7 Am 2 for the microdiorite sample.

Captions

Figure 1 -

 1 Figure 1 -Thermomagnetic curve for the basalt (susceptibility vs. temperature). Empty circles indicate the beginning of the heating curves. Heating = thick line, cooling = thin line.Progressive TRM acquisition is also plotted (dotted line, with standard deviation for the 3 measured samples).

Figure 2 -

 2 Figure 2 -Peak pressure in the basalt sample as a function of depth for different energy densities applied by the laser at the sample surface. The pressure values are derived from the experimental calibration of Berthe et al. (2007).

Figure 3 -

 3 Figure 3 -Sketch of the experimental setting used in this work.

Figure 4 -

 4 Figure 4 -Shock remanent magnetization (SRM) acquired by the basalt samples in an ambient field of 200 µT as a function of the energy flux applied by the laser pulse. Standard deviations are plotted when several samples were measured for the same energy flux.

Figure 5 -

 5 Figure 5 -Shock remanent magnetization (SRM) of sub-samples located straight below the impact spot as a function of depth below the surface for a basalt sample (solid line) and a microdiorite sample (dashed line). The horizontal line is the mean value (with s.d.indicated by the grey band) of the sub-samples that are not located straight below the impact spot. The SRM are normalized to the remanence at saturation (Mrs) in order to take into account the natural variability in magnetic mineral content and properties at the scale of the ~20 mg sub-samples.

Figure 6 -

 6 Figure 6 -Shock remanent magnetization (SRM) acquired in an ambient field of 100 µT and a laser energy flux of 1.9 GW.cm -2 as a function of the angular deviation between the direction of shock and the direction of the ambient field. The dashed line is the linear best fit. Several samples have been measured for each orientation and the standard deviations are indicated by the vertical "error bars".

Figure 7 -

 7 Figure 7 -TRM upon heating at 280°C (solid circles, solid line) and SRM upon laser shock with a mean energy density of 1.89 GWcm -2 (open circles, dashed line) acquired by the 54 basalt samples as a function of the ambient magnetic field. Several samples have been studied for each field value and the standard deviations are indicated by the vertical "error bars". The residual remanent magnetization of the samples before the shock experiment is indicated by the thin horizontal line (with standard deviation indicated by the grey band).

Figure 8 -

 8 Figure 8 -Orthogonal projection plots of stepwise demagnetization data of a basalt and a microdiorite cylindrical samples shocked with a laser energy density of ~1.9 GW.cm -2 in a vertical magnetic field of 200 µT. Open and solid symbols are projections on vertical and

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  c c e p t e d M a n u s c r i p t

Figure 9 -

 9 Figure 9 -Alternating field demagnetization data of SRM acquired by the whole cylinder samples of basalt during the shock experiments. The data for saturation IRM (acquired in a 3T field) and artificial TRM (acquired upon heating at 290 °C in a field of 100 µT) are given for comparison.

Figure 10 -

 10 Figure 10 -TRM upon heating at 590°C (solid circles, solid line) and SRM upon laser shock with a mean energy density of 1.81 ± 0.02 GWcm -2 (open circles, dashed line) acquired by the 6 microdiorite samples as a function of the ambient magnetic field. When several samples have been studied for the same field value, the standard deviations are indicated by the vertical "error bars". The residual remanent magnetization of the samples before the shock experiment is indicated by the thin horizontal line (with standard deviation indicated by the grey band).

Figure 11 -

 11 Figure 11 -Alternating field demagnetization data of SRM acquired by the acquired by the whole cylinder samples of microdiorite during the shock experiments. The data for saturation IRM and artificial TRM (acquired upon heating at 590 °C in a field of 100 µT) are given for comparison.

Figure 12 -

 12 Figure 12 -Efficiency of SRM acquisition versus TRM acquisition in a given coercivity window (') for the basalt (solid circles) and the microdiorite (empty circles). The alternating field value is the middle of the coercivity window of interest. The negative ' values are attributable to measurement noise for high AF values. The total  values are indicated by the horizontal solid line (basalt) and the horizontal dotted line (microdiorite).

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  Figure 7

  Figure 8

Acknowledgements

A c c e p t e d M a n u s c r i p t

This manuscript benefited from careful and constructive reviews by Mike Fuller and an anonymous reviewer. We thank D. Hermitte (CEREGE) for sound speed measurements and A. Demant (Université Aix-Marseille 3) for the petrographic description of the target rocks. This work was funded by the French Agence Nationale de la Recherche. When more than one sample has been measured, the number of measured samples is indicated. The anisotropy of magnetic susceptibility is given as the ratio (in %) of maximum to minimum susceptibility. Bulk density was determined by measuring the mass and dimensions of rock cylinders. Porosity was computed using the grain density measured with a Quantachrome helium pycnometer. Sound speed was measured with a Panametrics Epoch III model 2300 ultrasonic flaw detection scope.