Complementarity of Seismological and Electromagnetic Sounding Methods for Constraining the Structure of the Martian Mantle Antoine Mocqueta;∗ , Michel Menvielleb;C

Planetary and Space Science 48 (2000) 1249–1260 www.elsevier.nl/locate/planspasci

Complementarity of seismological and electromagnetic sounding methods for constraining the structure of the Martian mantle Antoine Mocqueta;∗ , Michel Menvielleb;c

aUMR-CNRS 6112 Laboratoire de PlanetologieÃ et Geodynamique,Ã FaculteÃ des Sciences et des Techniques, 2 rue de la Houssiniere,Â BP 92208, 44322 Nantes Cedex 3, France bCETP, UMR CNRS=UVSQ 8639-Observatoire de Saint-Maur, 4 Avenue de Neptune, 94107 Saint-Maur-des-Fosses,Ã France cDepartementÃ des Sciences de la Terre, UniversiteÃ Paris-Sud, France

Received 31 May 1999; received in revised form 17 December 1999; accepted 12 April 2000

Abstract The complementarity of seismological and electromagnetic sounding methods for the thermodynamical characterization of the Martian mantle is discussed by illustrating the observational constraints and limitations of both methods. The increase of temperature within a few hundreds of kilometers thick Martian outer lid with conductive heat transfer should induce the presence of a seismic low-velocity zone, due to the relatively small increase of pressure within Mars. The depth of minimum velocity will help to constrain the thickness and mean thermal gradient of the lid. These parameters will be strongly constrained by electromagnetic sounding methods. At greater depths, temperature variations of the order of 400 K will be detectable if seismic velocities can be determined with an accuracy better than 2%. An extrapolation of presently available laboratory data to the pressure range of Mars’ mantle predicts that the deep mantle electrical conductivity will be accessible if Mars’ mantle is cold, and mineralogically similar to the Earth’s. On the other hand, the high temperature and=or the high conductivity of garnet might impede an interpretation of electromagnetic sounding data at depths greater than 300 km for a nominal duration of the NetLander mission of the order of one Martian year. If the mantle is olivine-rich, the phase transitions of olivine should translate into ÿrst-order seismic and electromagnetic discontinuities, eventually smoothed if the iron content of Mars’ mantle is about twice the Earth’s one. The depth of occurrence of the exothermic olivine to waldsleyite and ringwoodite transitions will provide information on the temperature of the mantle. A pyroxene-rich mantle should instead be characterized by a constant increase of seismic velocities in the depth range 800–1200 km. This seismic gradient would be generated by the progressive increase of the garnet content at the expense of pyroxenes in solid solutions of non-olivine minerals. c 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction magnetic sounding methods in the particular case of Mars’ mantle. In the frame of the 2005 joint CNES-NASA mission to After describing the theoretical approach, the advantages Mars, a set of 4 NetLanders developed by an European and limitations of both methods in providing useful in- consortium is expected to land on the planet in mid-2006 formation on the thermodynamical state and mineralogi- (Harri et al., 1999). Among other instruments, the geo- cal composition of the mantle are discussed. The latter pa- physical package of each lander will include a seismometer rameters are only studied brie y from the seismological (LognonnÃe et al., 2000), and a magnetometer (Menvielle point of view, since this has already been explicitly ad- et al., 2000). Following Shankland (1981), who pointed dressed in previous works (e.g. Vacher, 1995; Mocquet out that ‘electromagnetic methods and seismology share the et al., 1996; Bertka and Fei, 1997; Sohl and Spohn, 1997; fact that they geophysically probe the physical properties Sanloup et al., 1999). of a planet in the present instant of geological times’, we illustrate the complementarity of seismological and electro- 2. Theoretical considerations ∗ Corresponding author. Tel.: +33-0-2-51-12-54-68; fax: +33-0-2-51- 12-52-68. E-mail addresses: [email protected] (A. Moc- The seismological and electromagnetic signatures of quet), [email protected] (M. Menvielle). models of the Martian mantle temperature are investi-

0032-0633/00/$ - see front matter c 2000 Elsevier Science Ltd. All rights reserved. PII: S 0032-0633(00)00107-0 1250 A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260 gated by simply transposing the terrestrial 3SMAC (three- 2.2. Electromagnetic modeling dimensional seismological model a priori constrained; Nataf and Ricard, 1996), and by adjusting the values of With some rare exceptions, electrical conduction in geo- the Earth’s mantle electrical conductivity (Xu et al., 1998) logical minerals is a thermally activated process and is well to the pressure range of the Martian mantle. These crude represented by an equation of the form but still realistic approximations are considered in order to −(E∗+PV ) deal to some extent with the present-day large uncertain- = 0 e kT ; (6) ties about the physical properties of high-pressure mineral where E∗ is the activation energy, V is an activa- phases when measured in the laboratory, and to separate tion volume, and k is the Boltzmann constant. The pre- as much as possible the contributions of temperature and exponential factor 0, in general, contains a relatively mineralogy to the elastic structure of the Martian mantle. weak temperature dependence which is usually ignored. The latter is divided into two main regions correspond- In the case of geological materials which are expected to ing to the stability ÿelds of olivine, because the olivine to be present in the mantle of terrestrial planets, the activa- waldsleyite phase transition is now widely accepted to be tion volume is generally found to be very small, if not on mainly responsible for the 4% seismic discontinuity (e.g. the order of the experimental uncertainty, thus indicating Du y et al., 1995), and two-orders of magnitude increase a weak dependence on pressure of the electrical conduc- of electrical conductivity (Xu et al., 1998) which occur at tivity (e.g. Duba et al., 1974; Parkhomenko, 1982; Xu a depth of 410 km within the Earth’s upper mantle. et al., 1998). As a result of this, the pressure dependence is often disregarded, and so do we in the following. 2.1. Seismological modeling When dealing with multicomponent materials, either mineralogical and=or melted phases, we assume that the Following Nataf and Ricard (1996), the values of P- and mixture is made up of fully connected constituents, and S-velocity are considered to depend upon temperature and we describe it in terms of a set of conductors wired up in pressure according to parallel. The resistivity and volume of the conductors are those of the constituents. Then, the bulk conductivity ∗ is X (T; z)=[X0 + Xzz][1 + XT (T − Tref )]; (1) the weighted average of the conductivities i of the con- where X stands either for P-velocity VP, or S-velocity VS, T stituent, the weighting factors being their proportion fi in is the temperature, and z is the depth. The depth derivative Xz the mixture is isentropic, and the logarithmic temperature derivative X X T ∗ = f : (7) is only used when T di ers from the adiabatic temperature i i constituents T evaluated at depth z. ref The resistivity distribution within Mars will be deduced The isentropic depth derivatives Xz are scaled to the pressure range of Mars’ mantle according to from the magnetic ÿeld variations simultaneously recorded at the NetLander stations. Assuming that the resistivity only E E Xz = Xz (dP=dz)=(dP=dz) ; (2) varies with depth, the inductive behaviour of the planet is described by means of a complex scalar transfer function, where P is the pressure, and the superscript E indicates the so-called impedance Z(!) where ! is the frequency. In Earth’s values. Taking the values practice, we will use the apparent resistivity E −1 (dP=dz) ∼ 0:035 GPa km (3) 2 a(!)=|Z(!)| =!; (8) (Dziewonski and Anderson; 1981); and where is the magnetic permeability of the medium, equal to that of vacuum for most of geological materi- (dP=dz) ∼ 0:012 GPa km−1 (4) als on the Earth. The apparent resistivity is deduced from for Mars (e:g: Mocquet et al:; 1996) leads to the the frequency-wave vector (also called wave number vec- scaling relation tor) spectrum of the electromagnetic ÿeld variations. This spectrum will be estimated using a high-resolution method X ∼ 0:34X E: (5) directly derived from that developed in the frame of the z z future multisatellite space mission Cluster (Pincon and The logarithmic temperature derivatives XT are the val- Lefeuvre, 1991, 1992; Motschmann et al., 1996). An ex- ues estimated at seismic frequencies (1 Hz) by Nataf and tensive presentation of this method is given in Pincon Ricard (1996) after the experimental works of Berckhe- et al. (2000). mer et al. (1982), Gueguen et al. (1989), and Jackson The resistivity proÿle is deduced from the variation et al. (1992). On the average, a decrease (increase) of with frequency of the apparent resistivity a(!). The most 100 K with respect to the reference temperature trans- likely resistivity proÿle (z), and its conÿdence inter- lates into a 1% increase (decrease) of either P- or S-wave val are estimated using inverse methods based upon the velocity. Bayesian technique. This approach is well suited for solving A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260 1251 an inverse problem when a priori information is available. 3. Constraints on the temperature of the mantle The solution is expressed in terms of a posteriori probability distribution function (pdf) of the model parameters, Thermal evolution models of Mars predict a present- the a priori information being expressed as the a priori day value of the mean temperature which ranges from pdf of the parameters. The Bayesian inverse problem is 1400 K (Mocquet et al., 1996) up to 2000 K (Grasset and solved using Markov chains. For each cell, the a priori Parmentier, 1998) in the deep mantle. This large range of and a posteriori pdf are digitized with a limited number M uncertainty re ects the lack of information concerning the of possible values for the parameter [m;m=1;:::;M]. distribution and amount of radioactive elements in the man- The Markov chain relies on updating the model parame- tle and in the crust of Mars. It is also due to the di erent ters during successive scanning of the domain under study. rheology and boundary conditions which are used in the For each step of the scanning, one parameter is updated numerical experiments. given the actual value of the other parameters. Thus we de- Crustal di erentiation and the removal of radioactive signed an ergodic Markov chain, the invariant distribution elements from the mantle have been studied by Spohn of which is the a posteriori distribution of the parame- (1991) and Schubert et al. (1992). Following the conclu- ters, provided the forward problem is completely solved sions of Jagoutz (1991) concerning the isotope character- at each step (Menvielle and Roussignol, 1995; Grandis istics of SNC meteorites, Breuer et al. (1993) proposed et al., 1999). that the ancient crust in the southern hemisphere of Mars We use in the following numerical experiments the is an enriched reservoir of radioactive elements, and that Monte Carlo Markov Chain (MCMC) method proposed by the mantle is severely depleted. They subsequently as- Grandis et al. (1999). The model consists of a stack of L thin sumed that the main contribution of the mantle to the homogeneous layers with ÿxed thicknesses, the distribution present surface heat ow is secular cooling, and that only of the depths zl of the interfaces between two consecutive a smaller part is due to radioactivity. The cooling histo- layers being a logarithmic one. The parameters are then the ries calculated from these models are characterized by resistivity of the layers. The set of possible values is the an early stage of rapid cooling which is followed by a same for all the parameters. The a priori distribution g() period of gradual, and slow cooling, leading to present- favours smooth models. It is deÿned by day values of mean mantle temperature in the range 1600–1800 K (Spohn et al., 1998). This type of model is LY−1 hereafter referred as Model 1. g(%)= (l) h(%i;%j) The latter parameterized models of thermal evolution k=1 are based on the assumption that the boundary between LY−1 2 the thermally conductive lid and the convective region of = (l) C(%i)exp{− ÿ[log(%i) − log(%j)] }; (9) the mantle can be deÿned by an isotherm below which k=1 viscosity is inÿnite on geological timescales. This as- where is a tuning parameter, which governs the degree of sumption has recently been reexamined by Grasset and smoothness on the model: the higher , the smoother the Parmentier (1998) on the basis of laboratory experiments model. The normalization factor ÿ ensures that the meaning of transient cooling performed by Davaille and Jaupart of , in terms of an a priori degree of smoothness, does not (1993). By investigating both the deÿnition of the thermal lid-convecting mantle boundary, and the power law depend on the choice of the parameters of the model. C(i) is a normalization constant such that for each , relation describing convecting heat transfer, Grasset and i Parmentier (1998) showed that the viscosity contrast in the XM convecting mantle remains constant, but not the temper- h(%i;%j) = 1 (10) ature at the bottom of the lid. This result, obtained for a j=1 volumetrically heated uid with strongly temperature- dependent viscosity, leads to a much slower decrease of and is the normalized left eigenvector of the matrix h as- mantle temperature than in Model 1, and to a present-day sociated with the eigenvalue 1. The deÿnition of ensures value of mean temperature of about 2000 K. The latter type that the distribution g is homogeneous with respect to the of model is herafter referred as Model 2. layers. This implies, in particular, that all the marginal dis- Apart from the mean temperature of the mantle, Mod- tributions of g are equal to (Robert, 1996). In the follow- els 1 and 2 also di er by the predicted thickness of the ing, the data are the classical apparent resistivities deÿned stagnant lid overlying the convecting mantle, and by the in Eq. (8). They are estimated at a set of nF frequencies !i, value of the thermal gradient within this lid. In Model i=1;:::;nF, which can be considered as a realization of a set 1, the values of lid thickness can range from 100 up to of nF independent random real scalar variables with centred 400 km, the latter value being obtained when magmatic heat Gaussian noise. The a posteriori distributions are described transfer and=or di erentiation of radioactive elements from in terms of marginal laws digitized over the possible values the mantle into the crust are taken into account (Breuer for the resistivities, [m;m=1;:::;M]. et al., 1993; Spohn et al., 1998). The minimum value of 1252 A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260

Table 1 End-member models of mantle temperature for Marsa

Characteristics Model 1 Model 2

abab

Lithospheric thickness (km) 200 300 200 300 Thermal lithospheric gradient (K km−1) 6.75 4.5 6.75 4.5 Tref (z = 0) (K) 1580 1570 1965 1955 Thermal boundary layer no no yes yes Partial melting (%) 0 0 10 0

aModel 1 after Breuer et al. (1993) and Spohn et al. (1998), Model 2 after Grasset and Parmentier (1998). Tref (z = 0) is the temperature at the foot of the adiabat. The thermal adiabatic gradient is set to a value equal to 0:1Kkm−1 in the deep mantle.

Fig. 1, the maximum degree of melting is about 20%, under the assumption that the amount of melting per degree of temperature increase above the solidus is constant. Geo- dynamical and geophysical considerations related to this potentially melted zone are discussed in Section 5.

3.1. Seismological constraints

In 3SMAC (Nataf and Ricard, 1996), the temperature of the adiabat, extrapolated at surface pressure, is set equal to 1623 K. The values corresponding to Models 1 and 2 are listed in Table 2. The computed values of VP and VS are plotted as a function of depth in Fig. 2. In all models, the linear increase of temperature within the outer thermally conductive lid, together with the small increase of pressure Fig. 1. End-member Marstherms: Model 1 after Breuer et al. (1993) with depth, translate into the development of a signiÿcant and Spohn et al. (1998) (broken curve), Model 2 after Grasset and low-velocity zone, in agreement with previous calculations Parmentier (1998) (solid curve). The liquidus (white dots) and solidus by Mocquet et al. (1996). On the average, the decrease of (black dots) curves of anhydrous peridotite are plotted after Zhang and −1 Herzberg (1994). The thickness of the outermost thermally conductive seismic velocities is of the order of 0:5 0:1kms for lid is either set equal to 200 km (light gray area), or 300 km (dark gray both P- and S-waves, and seismic models of types ‘a’ and area) in both models. The thermal adiabatic gradient is set to a value ‘b’ are clearly distinguishable. In the deep mantle, Models 1 equal to 0:1Kkm−1 in the deep mantle. and 2 di er by more than 3.5 and 2%, above and below the olivine phase transition, respectively. An error lower than 2% will thus be required in the construction of seismic mod- lid thickness provided by Model 2 is about 200 km. In any els in order to estimate the temperature of the mantle with case, the determination of the thickness, and the depth of an accuracy better than 400 K. This goal can be achieved if isotherms are key parameters for estimating the present-day teleseismic epicentral distances can be determined with an temperature of Mars’ mantle. error lower than about 50 km. We thus deÿne two end-member models of temperature distribution (Fig. 1). Model 1 corresponds to a ‘cold’ 3.2. Electromagnetic constraints and depleted mantle (1600 K) while Model 2 corresponds to a ‘hot’ (2000 K) mantle. In both models, the thermal Here, we address the question of the ability of elec- gradient within the lid is either set to a value equal to tromagnetic soundings to determine the thickness of the 6.75 or 4:5Kkm−1. These values deÿne a 200, and 300 stagnant lid with conductive heat transfer, and its tempera- km thick lid, respectively (Table 1). The former case is ture gradient, and the conductivity in the uppermost hun- subsequently labelled ‘a’, and the latter case is labelled dreds of kilometres of the convective mantle. The ‘b’. In Model 2a, the hot Marstherm crosses the solidus electrical conductivity of the melt phase at temperatures of anhydrous peridotite (Zhang and Herzberg, 1994) at around 2000 K is in the range 10–100 S m−1 (e.g. Shank- the base of the stagnant lid, thus allowing for partial land, 1981). The waldsleyite and ringwoodite conductivities melting in the depth range 200–400 km. According to are similar (Xu et al., 1998). They are computed using the A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260 1253

Table 2 Physical parameters transposed from 3SMAC (Nataf and Ricard, 1996) to the pressure range of Mars’ mantlea

Model 1 Model 2

VP VS VP VS

Olivine X0 7.465 4.17 7.205 4.0 −3 −3 −3 −3 Xz 1:32 × 10 0:6 × 10 1:32 × 10 0:6 × 10 −4 −4 −4 −4 XT −0:9 × 10 −1:1 × 10 −0:9 × 10 −1:1 × 10

Waldsleyite and Ringwoodite X0 8.0 4.22 7.85 4.1 −3 −3 −3 −3 Xz 1:14 × 10 0:72 × 10 1:14 × 10 0:72 × 10 a −1 −1 −1 The units are km s ,s , and K , for X0, Xz, and XT , respectively. The olivine-mantle thickness is 1100 and 1200 km for models 1 and 2, respectively. For both models, the values of the parameters do not vary signiÿcantly between sub-models ‘a’ and ‘b’ (Table 1).

Table 3 Range of experimental determination of pre-exponential factor 0 and activation energy E∗ values for olivine, waldsleyite and ringwoodite, pyroxenes and garnetsa

−1 ∗ 0(S m ) E =k(K) Minimum Maximum Minimum Maximum

Olivine 355 708 17960 18880 Waldsleyite and 355 708 11052 11973 Ringwoodite Pyroxenes 4.5 21 11250 11250 Garnets 500 1500 5000 7500

aThe values are compiled after Duba et al. (1974), Huebner et al. (1979), Hinze et al. (1981), Li and Jeanloz (1991), Kavner et al. (1995), and Xu et al. (1998). k is the Boltzmann’s constant.

frequencies down to a cpd allows to estimate the thickness of the resistive cold lithosphere, and to get relevant estimates of the conductivity in the upper part of the Mar- tian mantle. In the case of a ‘cold’ mantle (Fig. 3), the Fig. 2. P- and S-wave velocities corresponding to the temperature proÿles deÿned in Fig. 1 and Table 1. data can bear information on the resistivity down to depths larger than 1000 kilometres provided the frequency range is extended down to 0.1 cpd (see Section 4). In the case maximum values of pre-exponential and activation energy of a ‘hot’ mantle (Model 2), the observed a posteriori given in Table 3. distributions clearly indicate that the data bear no infor- The a posteriori pdf are estimated for the four tempera- mation on the resistivity at depths greater than 300 or ture models, for apparent resistivities computed at frequen- 500 km (Fig. 4) for Models 2a and 2b, respectively. These cies evenly distributed on a logarithmic scale (10 points results show that the critical depth zc topping the regions per decade) over the range 0.1–0.0001 Hz, plus 1–5 cycles inaccessible to magnetotelluric soundings (Parker, 1982) is −1 day (cpd) (nF = 36). Such a set of apparent resistivity de- of the order of a few hundreds of kilometres in the case of terminations corresponds to a very conservative hypothesis an electrically conductive mantle for a frequency spectrum on the results that could be derived from one Martian year limited to 1 cpd on the low-frequency side. We therefore of permanent magnetic recordings at the NetLander stations. get in this case information on the conductivity of the Mar- In all cases, adding 16% Gaussian noise corresponds to a tian mantle just below the resistive lid, i.e. the layer with pessimistic estimate of the precision in the impedance deter- partial melting (Fig. 4a), or the upper part of the adiabatic mination from the network electromagnetic measurements. mantle (Fig. 4b). In any case, the interpretation of the data The results are presented in Figs. 3 and 4 for Models will need information from both the seismological Net- 1 and 2, respectively. They make clear that knowing the Lander experiment on Mars and laboratory measurements apparent resistivities within a precision of about 16% for on terrestrial geological materials. 1254 A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260

Fig. 3. A posteriori distributions of the parameters for (a) Model 1a, and (b) Model 1b. In both cases, the data sets consist of apparent resistivities computed at frequencies evenly distributed on a logarithmic scale (10 points per decade) over the range 0.1–0.0001 Hz, plus 1–5 cycles day−1 (cpd) (nF = 36). In each case, a 16% Gaussian noise is added. For all the models, the a priori distribution and the marginal a posteriori distributions are digitized over a set of 71 possible resistivities evenly distributed on a logarithmic scale as 10 values per decade over the 0.001 to 10000 m interval. The level of grey of the (m; l) pixels corresponds to the value of the marginal a posteriori distribution of the parameter Xl for Xl = m: the darker the pixel, the higher the marginal a posteriori probability. On each image, the expected values (dashed curves) of the resistivities, and the resistivity proÿle of the model used to compute the apparent resistivities (solid curves), are also plotted.

Fig. 4. Same as Fig. 3 for (a) Model 2a, and (b) Model 2b.

4. Mantle mineralogy MPa K−1 (Bina and Hellfrich, 1994), the 400 K di erence between Models 1 and 2 is expected to translate into a 1.2 Mineralogical models available to date advocate either GPa di erence for the pressure value at which the transition an olivine-rich and, possibly, iron-rich Martian mantle (e.g. occurs. In the pressure range of Mars’ mantle, the transi- Dreibus and Wanke, 1985; Longhi et al., 1992), or for a tion is thus expected to occur at depthps equal to 1100, and pyroxene and garnet-rich mantle (Sanloup et al., 1999). 1200 km for Models 1 and 2, respectively. The detection of High-pressure experiments performed in the laboratory pre- a seismic discontinuity in this depth range will thus be an dict that an olivine-rich mantle should be characterized by indirect way of constraining the temperature of the mantle. the phase transitions of olivine into waldsleyite and=or ring- Presently available models of Martian structure cannot woodite, depending upon the iron content of the mantle. As deÿnitely argue the presence or absence of a perovskite shown in the previous section, the phase transition of olivine layer at the base of the mantle. Spohn et al. (1998) re- into waldsleyite should be clearly visible if the composition viewed three possible scenarios of thermal evolution, where of the Martian mantle is similar to the Earth’s one. Since the ringwoodite–perovskite transformation is either absent this transition is exothermic, with a Clapeyron slope of 3 or present during the whole mantle evolution, or where a A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260 1255 perovskite layer gradually disappears due to the cooling of conditions. Since pyroxenes progressively transform to gar- the deep mantle or due to some secular growth of the core. net with increasing pressure and temperature, pyroxene and The detection of a perovskite layer would be a strong con- garnet solid solutions should also induce smooth seismic straint on the thermal state and thermal history of the planet, velocity gradients at great depth. The absence of seismic because it would imply that temperatures in the deep mantle discontinuities in the deep mantle of Mars might thus be have always been in excess of about 2100 K (Spohn et al., interpreted in two di erent ways: either by an iron-rich 1998). Within the Earth, the ringwoodite–perovskite trans- predominantly olivine composition, or by a pyroxene and formation translates into jumps of P- and S-wave velocities garnet-rich composition. We know from the experience of about 5.5 and 6.5%, respectively. It can thus be conÿ- acquired with terrestrial data that an interpretation which dently expected that such large seismic discontinuities, if would only be based on seismic data is not unique. Other present, will be detectable. On the other hand, a nominal constraints, such as laboratory experiments, numerical ex- mission duration of one Martian year might be too short to periments, and additional geophysical observations are characterize the electrical conductivity of the mantle down necessary. The following paragraph will show how electro- to the core-mantle boundary, and we restrict the scope of magnetic data can usefully provide additional constraints this study to the depth range which should be reachable by on the mineralogical composition of the Martian mantle. electromagnetic sounding methods during one Martian year.

4.2. Electromagnetic signature of mantle mineralogy 4.1. Seismological signature of the mineralogy The electrical conductivity of di erent geological materi- It is widely accepted (e.g. Ringwood, 1979; McSween, als can di er by many orders of magnitude. In the case of 1985; Dreibus and Wanke, 1985; Longhi et al., 1992) that mixtures of materials with di erent conductivities, the ac- even though the mantle of Mars could be olivine-rich, it tual conductivity of the mixture may be controlled by the might di er from the Earth’s mantle composition by a presence of a small amount of a material with a very large higher content of iron. Theoretical calculations (Vacher, conductivity compared to that of the other constituents. The 1995; Mocquet et al., 1996) showed that this increase of bulk conductivity of such a mixture actually depends on the the iron content should: conÿguration of the minor conductive constituent. The question has been addressed by many authors, and many di er- • increase the density, and decrease seismic velocities by ent, more or less empirical, formulas have been proposed more than 2% with respect to the values expected within (e.g. Parkinson and Hutton, 1989). The results obtained us- the Earth at similar thermodynamical conditions; ing di erent formulas, however, di er from each other by • smooth out the seismic discontinuities associated less than the current uncertainties in the determination of with the phase transition of olivine over a thickness the conductivity of geological materials, and the choice of of 100–200 km. the formula is therefore not a key point. Furthermore, al- The latter e ect would be due to the coexistence of olivine most all the sophisticated formulas yet published deal with and ringwoodite over an extended domain of pressures, 2-constituent mixtures, while we would have to consider around 2 GPa wide. This theoretical result was conÿrmed mixtures with up to at least 4 constituents (i.e. olivine, wald- by the experimental work of Berka and Fei (1997) for sam- sleyite and=or ringwoodite, pyroxenes, and garnet solid so- ples with the chemical composition as proposed by Dreibus lutions) in order to address the problem of mantle mineral- and Wanke (1985) after the study of SNC (Shergotittes, ogy. This is the reason why we prefer here to use the very Nakhlites, Chassigny) meteorites. According to Vacher simple formula (7), derived by assuming that the mixture is (1995), the smoothing process of the seismic discontinu- made up with fully connected constituents, and describing ities should induce a focusing of seismic rays in the midst it in terms of a set of conductors wired up in parallel. of the Martian mantle, and reduce the importance of body Our current knowledge about the electrical conductivity wave triplications. The high sensitivity of the very broad of individual minerals at temperatures relevant to the man- band seismometers embarked on NetLander (LognonnÃeet tle are summarized in Fig. 5, and the conductivity of the al., 2000) will permit to sample the mantle of Mars in this considered mixtures are shown in Fig. 6. It is emphasized depth range, using Marsquakes with equivalent terrestrial that most of the current experiments are performed at rel- magnitudes larger than 3 (Mocquet, 1999). According to the atively low temperature, and that the minimum and maxi- estimates of Phillips (1991) and Golombek et al. (1992), mum trends shown in Fig. 5 are extrapolated using Eq. (6). more than a hundred of such seismic events are expected It is nowadays impossible to di erenciate olivine and py- per martian year. roxene phases from the values of their individual conductiv- An alternative to the olivine-rich model is the pyroxene ities. Conversely, waldsleyite and ringwoodite on one hand, and garnet-rich model recently proposed by Sanloup et al. and garnet solid solutions on another hand, display signif- (1999) in which orthopyroxenes might account for more icantly di erent values. At a temperature equal to 1500 K, than 60 wt% of the Martian mantle mineralogy at ambient the value of garnet conductivity is one to two orders of 1256 A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260

Fig. 5. Minimum (white symbols) and maximum (black symbols) values of electrical conductivity of major mantle minerals. The values are extrapolated at high temperature after the experimental data of Duba et al. (1974), Huebner et al. (1979), Hinze et al. (1981), Li and Jeanloz (1991), Kavner et al. (1995), and Xu et al. (1998) using Eq. (6). The generic term ‘spinelle’ is used for both waldsleyite and ringwoodite, since these phases display similar values of electrical conductivity (Xu et al., 1998). Fig. 6. Examples of candidate electrical conductivity proÿles for the Martian mantle. The minimum (white symbols) and maximum (black symbols) values are computed using Eq. (7), and the individual values magnitude larger than the value of waldsleyite and ring- of electrical conductivity displayed in Fig. 5. woodite (Fig. 5). However, the very large uncertainties on the electrical conductivity of individual minerals translate into one order of magnitude uncertainty on the electrical con- laboratory measurements of electrical conductivities at high ductivity of the mixtures, whatever the temperature proÿle pressure in order to narrow the domain of possible interpre- or the mineralogical composition of the mantle (Fig. 6). It tations. is thus obvious that further improvements in the experimen- An improvement of the inversion procedure is presently tal determination of electrical conductivities are required in under study. The present state of the art of electromagnetic order to interpret electromagnetic sounding data in terms of sounding interpretations translates sharp variations of elec- mineralogy. trical conductivity into smooth gradients (e.g. Fig. 7b). The Now, if the mantle is ‘cold’ and olivine-rich, can electro- next step to improve the inversion scheme will be to allow magnetic soundings provide information on the phase tran- a discrimination between sharp discontinuities, and smooth sitions present in the mantle of Mars? In Fig. 7, we consider gradients in electrical conductivity proÿles (Menvielle et al., a pure olivine mantle, with an olivine to waldsleyite transi- 1999). tion at a depth of 1100 km. When extending the frequency range of the data set down to 0.1 cpd, the transition is clearly visible on the a posteriori pdf if the inversion is performed 5. Partial melting and the water content of the mantle with a smoothing parameter in Eq. (9) which is set to a low value. A cold and olivine-rich Martian mantle might Let us ÿrst discuss the possible existence of water in thus be the best candidate if the average conductivity of the the mantle of Mars, and its geophysical and geodynamical mantle is low enough for the electromagnetic soundings to consequences. The presence of volatile elements in the man- probe down to depths of the order of 1200 km. On the con- tle of a planet depends on its primordial accretional his- trary, if the high conductivity of garnet predominates, or if tory, and on its subsequent thermal and tectonic evolutions. the mantle of Mars is very hot, the maximum depth of elec- In particular, it is now widely accepted that plate tectonics tromagnetic soundings will hardly reach 500 km (Fig. 4). In contributes signiÿcantly to the exchange cycles of volatile any case, there is a need for signiÿcant improvements in the elements within the Earth, where volatiles are extracted at A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260 1257

Fig. 7. Same as Fig. 3 for a ‘cold’ (Model 1a) and pure olivine mantle, and for two di erent values of the smoothing parameter (Eq. (9). (a) =5; (b) =1.

oceanic accretion centers, hot spots, and volcanic arcs (e.g. non-unique, working hypothesis. An estimate of the amount Gillet, 1995). The crustal part of the oceanic lithosphere of volatile elements presently existing in the mantle of Mars which is created at accretion centres is altered by water, and would shed light on the validity of this hypothesis, and more recycled into the deep mantle at subduction zones. In the generally on the thermal and tectonic history of the planet. absence of plate tectonics, the amount of volatile elements If water were present in the mantle of Mars, it might be depends only on the primordial global accretion history of hosted by oxides and hydrated ferromagnesian silicates. Ac- the planet, and on its subsequent thermal history. cording to Gillet (1995), and Inoue et al. (1995), at least Until recently, it was generally admitted that Mars had nine hydrated mineralogical phases have been experimen- always been a one plate planet without plate tectonics (e.g. tally identiÿed at high pressure in the system MgO–FeO– Wilhelms and Squyres, 1984; Strom et al., 1992). However, SiO2–H2O, in thermodynamical conditions which are rele- the intriguing possibility of sea- oor spreading in the early vant to the Earth’s transition zone, and hence to the deep history of Mars has been recently renewed by Connerney mantle of Mars. The presence of these hydrated mineralog- et al. (1999) to explain the groups of quasi-parallel linear ical phases would have important consequences: features of alternating magnetic polarity evidenced in the most ancient Martian highlands by the Mars Global Surveyor • it would a ect the location at depth and abruptness of seis- spacecraft (Acu˜na et al., 1999). These magnetic lineations mic discontinuities associated with the phase transitions are reminiscent of similar magnetic features on Earth, but of olivine (Inoue et al., 1995); they di er in the value of crustal remanent magnetization, • the temperatures of the solidus and liquidus would be about one order of magnitude larger than terrestrial values, lowered by several hundreds of degrees (Inoue and and in the much larger spatial scale. Sleep (1994) had al- Sawamoto, 1992); ready proposed that plate tectonics might have created the • the di usivity of chemical elements, and the associated northern Martian lowlands, and accounted for the formation mechanical weakening of mantle rocks would increase, of the Martian dichotomy. In his model, subduction pro- thus favouring creep mechanisms and convection (e.g. cesses would have buried volatile elements at greater depth Sato, 1992); than within the Earth, because the small Martian gravity • the initial stratiÿcation of the mantle might have been would have allowed for fast plate velocities, of the order signiÿcantly di erent from the one expected in anhy- of8cmyr−1, and for large thicknesses of crust altered by drous conditions, because, if large amounts of water hydrothermal phenomena, of the order of 5 km instead of had been dissolved in the primitive magma ocean at 2 km in the Earth’s case (Sleep, 1994). The link between depths corresponding to pressures of the order of 5–8 Sleep’s (1999), and Connerney and co-workers’ plate tec- GPa (i.e. 500–700 km within Mars), the ÿrst mineral to tonic interpretations is far from being straightforward. To crystallize would have been orthopyroxene or pyrope, our knowledge, remanent magnetic signals are suspicously instead of olivine, and the higher density contrast be- lacking in the northern lowlands, and no large-scale exten- tween the melted phase and pyrope would have permitted sional or compressive tectonic structures have been reported the solid phase to sink down to the base of the magma in the ancient southern highlands. In our view, Martian ocean (Inoue and Sawamoto, 1992). The latter scenario plate tectonics must only be regarded as an intriguing, and would lead to a deep mantle composition close to the 1258 A. Mocquet, M. Menvielle / Planetary and Space Science 48 (2000) 1249–1260

mineralogical composition proposed by Sanloup et al. presence, and to slight variations in their amount. Since the (1999), without advocating for an initial chemical com- conductivity of melt phases is higher by one or two orders position very di erent from the Earth’s mantle one. of magnitude than that of the solid ones, these conductivities would allow to determine whether there is or not partial However, the interpretation of the chemical analysis of melting on top of the convective mantle, thus allowing to SNC (Shergotty, Nakhla, Chassigny) meteorites yields a discriminate between di erent possible models of Mars present water content of the Martian mantle equal to 36 ppm mantle behaviour. The inversion test already presented in (Wanke and Dreibus, 1988; Wanke, 1991). This value only Fig. 4a actually shows that the strong increase of conduc- amounts to 4% of the terrestrial mantle contribution to the tivity in the depth range 200–300 km, which is associated water inventory of the bulk silicate Earth (BSE), and to 14% with the presence of a 10% melted region beneath the lid of the water content of the primitive depleted mantle (DPM) in Model 2a, can be recovered. from which terrestrial mid-oceanic ridge basalts (MORB) are extracted (O’Neill and Palme, 1998). If SNC meteorites are indeed igneous crustal rocks from Mars, the mantle of 6. Conclusion the planet should thus be much drier than the Earth’s. A geophysical conÿrmation of this geochemical result would With the current knowledge about the physical proper- help to understand why either Mars has always been a one ties of mantle minerals, we can already state that one the plate planet, or why plate tectonic processes ceased rapidly major contributions brought by a comparison of seismolog- due to the dehydration of the mantle. ical and electromagnetic sounding data will be to bring con- The detection of partial melting will be hardly possible straints on the temperature of the Martian mantle by evaluat- using only seismological methods. A seismic low-velocity ing the thickness and mean thermal gradient of the outer lid zone in the uppermost mantle of Mars should rather be asso- of the planet. These contributions will complement the pri- ciated with the stronger increase of temperature with depth mary objectives of seismology and electromagnetism sum- relative to pressure, than to the presence of a small amount of marized in this issue by LognonnÃe et al., and Menvielle et melt. Karato and Jung (1998) showed that mineral physics al., respectively. The variations of seismic velocities with and terrestrial seismological observations do not support the respect to an Earth’s like model can be interpreted either in interpretation of the Earth’s seismic low velocity and high terms of temperature, or mineralogy. For instance a 2% de- attenuation zone as being caused by partial melting, but on crease of seismic velocities in the deep mantle can be either the contrary that low velocities and high seismic attenuation due to an increase of temperature of the order of 400 K, or are best explained by the presence of volatile elements. The to an increase of the iron content of the mantle. Similarly, dependence of seismic wave velocities with respect to par- smooth gradients in the midst of the mantle can be due to tial melting is governed by the thermal proÿle, the amount this increase of the iron content, but also to the progres- of water which is contained in the rocks, the mode of partial sive transformations in pyroxene and garnet solid solutions, melting (either batch or fractional melting), and the geom- even though the latter transformations are expected to spread etry of upwelling ow (either passive ow of dynamic up- over a 400 km depth range, instead of 100 km in the former welling). The main di erences between Mars and the solid case. Now, if the electrical conductivity of mantle rocks is Earth are that the latter is presently a ected by plate tecton- low enough to permit soundings deeper than 1200 K, a cold ics, volcanic activity and overlain by liquid water. Current and olivine-rich mantle will be a good candidate, because observations do not support the existence of such processes current experimental studies predict that either a hot and=or on Mars. These di erences have two main consequences. garnet-rich mantle should be too conductive to be sounded First, it is quite realistic to suppose that dynamics upwelling at depths greater than 300 km. best applies to Mars’ interior. Second, recycling processes Similarly to the Earth’s case, the interpretation of the seis- between the inner and outer Mars are likely to be presently mic and electromagnetic e ects associated with a few tens absent. of kilometers thick thermal boundary layer at the base of the We are thus lead to two possibilities: either Mars vol- lid might not be unique, because both partial melting and=or canic activity ceased because of a complete dehydration rock hydration might be advocated to interpret the observa- of mantle rocks, or water is still present in the mantle of tions. Unfortunately, laboratory measurements on the geo- Mars, but partial melting occurs only as batch melting. In physical properties of hydrated mantle minerals are very both cases, partial melting is not expected to have a sig- few, and it has still not been possible to determine precisely niÿcant in uence on seismic wave velocities (Karato and the amount of volatile elements within the Earth’s man- Jung, 1998). tle after seismic proÿling and=or electromagnetic sounding From the electromagnetic point of view, melt phases and methods. interstitial water are minor very conductive constituents Indeed, the data provided by a single geophysical commonly encountered in mixtures of the geological mate- technique cannot be uniquely interpreted in terms of mantle rials which are present in the crust and mantle of terrestrial thermodynamics, chemistry and mineralogy. The geody- planets. Electrical conductivity is very sensitive to their namical interpretations always require a strong collabora- A. Mocquet, M. 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