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

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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 Planetologieà et Geodynamique,à Faculteà des Sciences et des Techniques, 2 rue de la Houssiniere, 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,à France cDepartementà des Sciences de la Terre, Universiteà 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 pres- sure 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 proba- bility 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.
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