Initial observations of low-frequency magnetic fluctuations in the Martian ionosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005je002587, 2006 Initial observations of low-frequency magnetic fluctuations in the Martian ionosphere J. R. Espley, 1,2 G. T. Delory, 3 and P. A. Cloutier 1 Received 2 September 2005; revised 6 April 2006; accepted 12 April 2006; published 22 June [1] Using Mars Global Surveyor magnetometer/electron reflectometer measurements, we report initial observations of low-frequency magnetic fluctuations in the Martian ionosphere. We find that the waves have dominant frequencies between 0.01 and 1 Hz and are observed both close to and far from crustal magnetic fields. These waves are possibly related to magnetosonic perturbations produced at higher altitudes in the Mars solar wind interaction. These fluctuations have implications for understanding the physics of the ionosphere and potentially could also help characterize electromagnetically active atmospheric phenomena such as dust devils and dust storms. The presence of such fluctuations in the Martian ionosphere is also an indication of the plausibility of using lowfrequency electromagnetic methods, such as the magnetotelluric technique, to probe the deep subsurface. One potential result of such an investigation would be the identification of any subsurface liquid water that might be present within the first several hundred meters to the first few kilometers of the subsurface. Citation: Espley, J. R., G. T. Delory, and P. A. Cloutier (2006), Initial observations of low-frequency magnetic fluctuations in the Martian ionosphere, J. Geophys. Res., 111,, doi: /2005je Introduction [2] Because Mars lacks an intrinsic planetary magnetic field, the solar wind interacts directly with the Martian ionosphere. However, patches of the Martian crust are highly magnetized and contribute to standing off the solar wind by the creation of mini-magnetospheres [Acuña et al., 1998]. In the cases of the strongest crustal fields, the minimagnetospheres protrude above the ionopause [Brain et al., 2003] and protect the atmosphere that lies below them just as the Earth s global magnetosphere protects the terrestrial atmosphere from the solar wind. Interactions between the ionosphere, the solar wind, and the mini-magnetospheres produce a great deal of low-frequency plasma fluctuations that have been studied at altitudes greater than 800 km [Bertucci et al., 2004; Espley et al., 2004]. Using data from Mars Global Surveyor s (MGS) magnetometer/electron reflectometer (MAG/ER) experiment, we present here initial observations of low-frequency magnetic oscillations at ionospheric altitudes (approximately <400 km). [3] These fluctuations are interesting for several reasons. By identifying or at least constraining which wave modes are present in a plasma, investigators are able to probe the temperature, density, composition, and pressure of a plasma. The Martian ionosphere has been the subject of several 1 Department of Physics and Astronomy, Rice University, Houston, Texas, USA. 2 Now at NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. 3 Space Sciences Laboratory, University of California Berkeley, Berkeley, California, USA. Copyright 2006 by the American Geophysical Union /06/2005JE recent studies [Shinagawa, 2000; Trotignon et al., 2000; Mitchell et al., 2001; Nagy et al., 2004; Lundin et al., 2004] but further observations would be helpful. Such observations may be especially useful in understanding the ionospheric properties adjacent to and within the minimagnetospheres. Furthermore, a wide variety of atmospheric phenomena, including dust storms and dust devils, are likely to produce low-frequency electromagnetic signals which could potentially be fruitfully studied via in situ magnetic field observations [Farrell et al., 1999]. Lastly, an important geophysical exploration method, passive low-frequency electromagnetic sounding, relies upon the existence of naturally occurring low-frequency magnetic fluctuations. Specific varieties of this technique include the magnetotelluric technique [Vozoff, 1991] and magnetic gradiometry [Pincon et al., 2000]. We focus here on the magnetotelluric technique as an example of these methods. Demonstrating the plausibility of these techniques for use at Mars (perhaps in a manner complementary to many of the other techniques detailed in this special issue [Heggy et al., 2006]) is one of the primary goals of this report. [4] The magnetotelluric technique (MT) is a passive electromagnetic sounding technique that has been used to great effect on Earth for geophysical exploration. Measuring the horizontal electric (E x ) and magnetic fields (H y ) (where the x and y subscripts simply indicate perpendicular cartesian coordinates) at the surface and taking their ratio indicates the conductivity structure of the subsurface, via the relation for r the apparent subsurface resistivity [cf. Vozoff, 1991, equation (8)]: rðf Þ / 1 f 2 E x H y ð1þ 1of7

2 [5] As the wave frequency f decreases, the electromagnetic skin depth (the penetration of the wave into the subsurface) increases; hence a measurement of the horizontal components E x and H y yields the resistivity as a function of f, which can then be inverted into resistivity vs. depth. Highly conductive features such as liquid water stand out from more insulating host materials by at least several orders of magnitude. Note that water ice is significantly more resistive than liquid water and hence would be rather difficult to distinguish from the surrounding rock. Therefore any use of MT at Mars will need be accompanied by other techniques if a full subsurface characterization is to be accomplished. Figure 1 shows a schematic diagram illustrating the technique. Grimm [2002] laid out much of the theoretical framework necessary to use MT for subsurface sounding on Mars. As he noted, the small payload mass and power requirements for MT (its reliance on naturally occurring magnetic fluctuations means that it does not require powered transmitters) and its depth of penetration (several hundreds of meters or greater) make it an important potential exploratory tool on Mars. It could provide useful data regarding the distribution of subsurface liquid water which would have implications for the topic of climate change at Mars, for the possibility of current or past Martian life, and for resource location for future human exploration. 2. Data Set and Analysis Techniques [6] MGS arrived at Mars in 1997 and since that time the MAG/ER investigation has been returning a steady flow of data [Acuña et al., 2001]. During the pre-mapping phases of the mission (from September 1997 to March 1999) the spacecraft was in a highly elliptical orbit with periapses of km [Albee et al., 2001]. These low-altitude passes provide in situ observations of the magnetic fluctuations present in the Martian ionosphere, providing a unique opportunity to probe the low-frequency electromagnetic environment of the Martian atmosphere. Observations from the mapping orbits (from March 1999 to the present) provide additional observations at altitudes near 400 km. We focus here on data from the periapses of the premapping orbits since they provide data in the altitude range we are most interested. [7] The MAG instrument returns high time resolution vector magnetic field data at a rate of 8, 16, or 32 samples per second. However, better calibrated lower time resolution data are available with a time resolution of 1/24th of the high time resolution data. These low time resolution data record the absolute data value rather than simply the difference between measurements recorded by the high time resolution data [Acuña et al., 2001]. Therefore, for calculations that require accurate absolute measurements, we use the lower time resolution data and for calculations that require only relative measurements (e.g., frequency analyses and deviations from the mean magnetic field) we use the high time resolution data. As one further check, we examine the low time resolution data to assure ourselves that broad features observed in the high time resolution data are qualitatively reproduced in the low time resolution data. We find this to be the case. [8] The ER instrument measures electron fluxes every 2 to 48 secs across 30 energy channels ranging from 10 ev to Figure 1. A schematic illustration of the magnetotelluric method. By measuring the ratio of the electric and magnetic field components of an EM wave at the surface, the subsurface conductivity can be determined. This occurs due to the finite skin depth of low-frequency waves in a typical subsurface, which will dissipate energy from the incident waves via direct currents. The ratio of E/H is known as the apparent impedance and when measured as a function of frequency can be used to determine the depth and thickness of electrically conductive features such as liquid water. Natural EM emissions from the atmosphere and ionosphere are commonly used in this technique on Earth. 20 kev in 16 geometrically separate sectors. Because we are interested primarily in the relative densities of electrons in order to compare them to the fluctuations in the magnetic field, we generally use the omni-directional flux of the electrons in just one of the energy bins (the 191 ev bin) with the highest time resolution. The 191 ev electrons are also of high enough energy to be subject to attenuation at the photo-electron boundary [Mitchell et al., 2001] and hence can be used as marker of when MGS is likely within the ionosphere. [9] The MGS data used in the study are given (prior to the data processing described below) in the Sun-state (SS) Cartesian coordinate system. In this system, the Mars-Sun line is defined as the +x direction, the orbital motion of Mars is the y direction, and the +z axis completes the orthogonal set (and is roughly northward on Mars). This system could also be called the Mars solar orbital (MSO) system since it is comparable to the geocentric solar ecliptic (GSE) and the Venus solar orbital (VSO) coordinate systems. [10] Previous work describes in detail our analysis methods [Espley et al., 2004, 2005; Espley, 2005]. Here we give a condensed version of our methods. First, we cubicly detrend the data and we find the mean magnetic field for a given interval. We then calculate the magnetic components perpendicular (B?1 and B?2 ) and parallel (B k ) to that field and find the sense of polarization of B?. B?1 is defined as perpendicular to B k and to the z direction in SS 2of7

3 Figure 2. The magnetic fluctuations observed during a 105 second interval on the second periapsis of 28 July 1998 (decimal day 209). The top two panels show the magnetic field magnitude and 191 ev electron flux for the entire pass, whereas the bottom five panels show, for the selected interval, the parallel (B k ) component, perpendicular (B?1 and B?2 ) components, the relative electron flux, and the rotation angle (q) ofb?. The upper right panel shows, in SS coordinates, a plus sign indicating the MGS location during the interval along with the best fit locations of the magnetic pileup boundary and bow shock. Negative values on the y axis indicate locations in the negative z hemisphere. The lower right panel shows, for a 20 second subinterval near decimal day , the magnetic field components in the directions of the maximum and intermediate eigenvalues of the variance. coordinates, B?2 is perpendicular to both B?1 and B k, and B? is the vector sum of B?1 and B?2. Using minimum variance analysis (MVA) [Song and Russell, 1999] we can calculate the directions of maximum, intermediate, and minimum variance and using these directions find the ellipticity of the magnetic components in the maximum and intermediate variance directions. We also use MVA to calculate the direction of the wave vector (i.e., the direction of propagation for most wave modes) provided that the ratio of the intermediate to minimum eigenvalues is greater than three [Knetter et al., 2003; Hausman et al., 2004] and provided that we assume the waves are planar and that one wave mode dominates such that the direction calculated is that of the mode. In order to study the frequency domain of the oscillations, we use wavelet analysis [Torrence and Compo, 1998]. We use the Morlet wavelet with a wave number of six because its shape represents a good compromise between time and frequency localization and we calculate where the spectral power becomes statistically significant. Details on the methodology of these calculations are given by Torrence and Compo [1998]. We use a high pass filter to reduce the spectral power due to fluctuations that do not complete at least 3 periods during the analyzed interval. Using the wavelet power spectra we are able to calculate the total power for the interval in the B?1, B?2, and B k components. Finally, comparing the ER and MAG data for the interval we are able to calculate the Spearman rank correlation coefficients to see how well correlated the time series are. 3. Results [11] We present here results from two different intervals. A systematic investigation of similar such intervals throughout the entire data set is under way and should yield results that allow for detailed statistics on the nature of the oscillations with respect to altitude, proximity to crustal sources, solar wind strength, and the diurnal cycle. [12] Figure 2 shows an example from the second periapsis of 28 July 1998 (decimal day 209). The top two panels 3of7

4 Figure 3. A wavelet analysis of the components (Bk, B?1, and B?2) shown in Figure 2. The wavelet power spectra show frequency versus time with the color scale indicating wavelet variance, and the global wavelet spectra (time averaged) are shown in the lower right panel. Superimposed on all panels are the local proton, helium, and oxygen gyrofrequencies. Numerical edge effects are obvious at higher frequencies near the start and end of the power spectra. show jbj and the 191 ev electron flux for the entire pass with dotted lines indicating the interval analyzed. The five panels below show, respectively, the Bk component, B?1 component, B?2 component, the relative electron flux, and the clock angle (q) of the rotation of B? from some arbitrary starting point. The upper right panel shows the location of MGS in SS coordinates (the starting and stopping locations nearly overlap on this scale and are marked by plus signs) during the interval analyzed. Negative values on the y axis indicate locations in the negative z (i.e., southern) hemisphere. Also shown are the best fit locations of the bow shock and magnetic pileup boundary [Vignes et al., 2000]. The panel in the lower right shows the magnetic field components in the directions of maximum and intermediate variance for a subinterval of 20 seconds starting at or about 20:42:55 UT. Figure 3 shows wavelet analyses of the same interval for the Bk, B?1, and B?2 components. Also shown are the global (time averaged) power spectra including B? which is calculated as the vector sum of B?1 and B?2. The local proton, helium, and oxygen gyrofrequencies are also marked on both the power spectra and the global spectra. Note that we show the wavelet variance which has units of nt2 instead of the spectral power used by other some workers which has units of nt2/ Hz and hence a linear dependence on frequency. [13] Since contextual ER data show (at approximately decimal day and ) the dropoff in flux characteristic of the photo-electron boundary that has been associated with the ionopause [Mitchell et al., 2001], it is reasonable that the analyzed interval is within the ionosphere. The interval spans altitudes from 219 to 287 km and easily discernible fluctuations are clearly seen in the parallel component and to a lesser extent in the perpendicular component. These observations were made at a solar zenith angle of approximately 90 while MGS passed over the region approximately 160 east longitude and 81 north latitude, a region far from any of the significant crustal fields [Connerney et al., 2001]. At most frequencies the Bk component shows more power than the B? components with the largest amplitude of the fluctuations approaching 1 nt while the background magnetic field is 106 nt. Correlation analysis shows nearly no correlation between the ER data and the MAG data (correlation coefficients of 0.01 and 0.14 respectively for the Bk and B? components) which is easily confirmed by a visual comparison of the data sparse ER time series and the MAG components. 4 of 7

5 Figure 4. The same as Figure 2 but for a 452 second interval during the first periapsis of 16 December 1998 (decimal day 350). The hodogram shows results for a 38 second subinterval starting at [14] A hodogram for the entire interval (not shown) reveals a complex structure and indicates that a mix of several wave modes is likely to be present. However, selected subintervals have characteristics suggestive of semi-monochromatic wave modes. One such subinterval starts at (about 20:42:55 UT) and goes for 20 seconds where a discernible wave form appears in B k and B?2. The hodogram for this subinterval (the lower right panel of Figure 2) shows a fairly elliptical shape (ellipticity of 0.6) and the waves are mostly right handedly polarized (relative polarization of 0.2). The wave vector for this subinterval is 81 with the ratio of the intermediate to minimum eigenvalues being 4.8. [15] Figure 3 shows that the most clearly evident oscillations in the time series have spectral power between 0.08 and 0.7 Hz with significant and relatively long-lived periods of power at 0.1 Hz and 0.5 Hz. These peaks are near the local oxygen and helium gyrofrequencies, respectively, which is interesting since they appear most prominently in the parallel power. The large spectral power at frequencies as low as 0.03 Hz is reflective of the relatively large amplitude fluctuations evident in the time series that just barely make 3 oscillations. [16] Figures 4 and 5 show another example, this time from 16 December 1998 (decimal day 350). In this case, MGS was passing over 340 east longitude and 40 north latitude which is just north of a significant crustal field. Because of the large amplitude signal from the crustal field (seen from approximately decimal day to ) obvious fluctuations are difficult to discern while MGS was directly over the crustal field. However, the interval just after the closest approach to the crustal field does show significant oscillations. Unfortunately, this is one of the orbits during which the ER instrument was turned off during closest approach due to safety concerns [Mitchell et al., 2001], but nonetheless, we can see that at the end of our interval the ER flux greatly increases indicating MGS s passage through the photo-electron boundary. [17] In the third, fourth, and fifth panels of Figure 4 we see fairly large amplitude, easily discernible oscillations in the directions both parallel and perpendicular to the mean magnetic field. Observations of these fluctuations start at an altitude of 209 km and continue past the photo-electron boundary (520 km) well up into the magnetic pileup region. The average jbj is 58 nt and most of the fluctuations are of order 1 nt. A 38 second subinterval starting at decimal day (4:5:43 UT) is shown in the hodogram. The subinterval s fluctuations are fairly elliptical (0.5 ellipticity), are mostly left handed (0.17 relative polarization), and have a wave vector of 80 with an eigenvalue ratio of 6.7. Figure 5 shows that the spectral power is larger in B k for almost all frequencies and times. The only exceptions are at the lowest frequencies (<0.04 Hz) and at the low altitudes (<400 km) where some short lived, large 5of7

6 Figure 5. The same as Figure 3 but for the same interval as Figure 4. scale features are obvious in the time series data (Figure 4). Otherwise, most of the fluctuations occur in the 0.05 to 0.3 Hz range. No significant ER-MAG correlation can be observed due to the lack of ER data for the majority of the interval. 4. Discussion [18] Several important inferences can be drawn even from these initial observations. We have qualitatively examined many other intervals besides the ones shown here and these intervals do not seem abnormal. A more detailed statistical study is underway. [19] First, there is significant spectral power at low altitude at frequencies of order 0.01 to 1 Hz. These are viable frequency regimes for MT methods. Secondly, significant oscillations have been identified both close to and far from crustal field sources. Further study is needed to determine any systematic differences, if any, between oscillations near to and far from the crustal fields. However, the current observations indicate, at least, the plausibility of using MT methods across the entire planet and not just near crustal fields (which are clustered predominantly in the cratered southern highlands). We also note that the lower frequency limit reported here is basically at the realistic lower limit of observation given our moving observation platform. The upper limit appears to be physical. [20] Identifying the various waves modes present would assist us in understanding the physical origin of the waves observed and in understanding how the plasma parameters (such as density and b, the ratio of plasma pressure to magnetic pressure) vary with altitude. Unfortunately, a wide variety of waves modes is likely to be present with some waves originating in the ionospheric plasma and some propagating from the solar wind into the ionosphere thus making a precise identification in terms of theoretical modes difficult. Nonetheless, the waves shown in our two examples have properties consistent with the obliquely propagating (wave vectors >60 ) magnetosonic wave identified theoretically by Gary [1993]. This mode is calculated using Vlasov theory for a uniform plasma and is found to be lightly damped for both low and high b for the lowest frequencies. As the frequency of the mode increases to frequencies at and just below the proton gyrofrequency, the damping decreases for b < 4 [see Gary, 1993, section 6.2]. Our observations show that the predominant waves are obliquely propagating, compressional, and (assuming negligible Doppler shift from the relatively slow moving ionospheric plasma) are observed in approximately the plasma frame with frequencies that are below but within an order of magnitude of the local proton gyrofrequency. [21] The kinetic magnetosonic wave mode also has the fastest phase speed of the modes identified using Vlasov theory and therefore is associated with the MHD fast mode 6 of 7

7 identified using fluid theory [Krauss-Varban et al., 1994]. Such fast mode waves have been identified as one of the primary mechanisms for producing the low-frequency magnetic fluctuations used for MT methods on Earth. Solar wind fluctuations couple with the Earth s planetary magnetic field to produce what are termed cavity modes [Kivelson and Southwood, 1988]. Unaltered, this physical model will not correctly explain the propagation of lowfrequency waves at Mars since it depends on the terrestrial global magnetic field. However, fast mode waves have been identified at Mars by Bertucci et al. [2004] just downstream of the magnetic pileup boundary which has an approximate altitude of 700 km. Furthermore, work has been done trying to understand the propagation of low-frequency waves through the terrestrial ionosphere to the ground [Hughes and Southwood, 1976]. Such work may be applicable to Mars. A fully developed model for the production and propagation of such waves is left for future work. This current report serves to identify such waves and to point out the plausibility of their use in a magnetotelluric survey of the Martian subsurface. [22] Acknowledgments. We are grateful for useful discussions with R. Grimm and J. Connerney. The wavelet analysis software used in this work was based on software provided by C. Torrence and G. Compo and is available at We are sincerely grateful for the helpful comments of the reviewers. This research was supported by the NASA GSRP program under grant NGT5-156 and the NASA Postdoctoral Program at Goddard Space Flight Center. References Acuña, M. H., et al. (1998), Magnetic field and plasma observations at Mars: Initial results from the Mars Global Surveyor Mission, Science, 279, Acuña, M. H., et al. (2001), Magnetic field of Mars: Summary of results from the aerobraking and mapping orbits, J. Geophys. Res., 106, 23,403 23,417. Albee, A. L., R. E. Arvidson, F. Palluconi, and T. Thorpe (2001), Overview of the Mars Global Surveyor mission, J. Geophys. Res., 106, 23,291 23,316. Bertucci, C., C. Mazelle, D. H. Crider, D. L. Mitchell, K. Sauer, M. H. Acuña, J. E. P. Connerney, R. P. Lin, N. F. Ness, and D. Winterhalter (2004), MGS MAG/ER observations at the magnetic pileup boundary of Mars: Draping enhancement and low frequency waves, Adv. Space Res., 33, Brain, D. A., F. Bagenal, M. H. Acuña, and J. E. P. Connerney (2003), Martian magnetic morphology: Contributions from the solar wind and crust, J. Geophys. Res., 108(A12), 1424, doi: /2002ja Connerney, J. E. P., M. H. Acuña, P. J. Wasilewski, G. Kletetschka, N. F. Ness, H. Reme, R. P. Lin, and D. L. Mitchell (2001), The global magnetic field of Mars and implications for crustal evolution, Geophys. Res. Lett., 28, Espley, J. R. (2005), Low frequency plasma waves at Mars, Ph.D. thesis, 107 pp., Rice Univ., Houston, Tex, Nov. Espley, J. R., P. A. Cloutier, D. A. Brain, D. H. Crider, and M. H. Acuña (2004), Observations of low-frequency magnetic oscillations in the Martian magnetosheath, magnetic pileup region, and tail, J. Geophys. Res., 109, A07213, doi: /2003ja Espley, J. R., P. A. Cloutier, D. H. Crider, D. A. Brain, and M. H. Acuña (2005), Low-frequency plasma oscillations at Mars during the October 2003 solar storm, J. Geophys. Res., 110, A09S33, doi: / 2004JA Farrell, W. M., M. L. Kaiser, M. D. Desch, J. G. Houser, S. A. Cummer, D. M. Wilt, and G. A. Landis (1999), Detecting electrical activity from Martian dust storms, J. Geophys. Res., 104(E2), Gary, S. P. (1993), Theory of Space Plasma Microinstabilities, Cambridge Univ. Press, New York. Grimm, R. E. (2002), Low-frequency electromagnetic exploration for groundwater on Mars, J. Geophys. Res., 107(E2), 5006, doi: / 2001JE Hausman, B. A., F. C. Michel, J. R. Espley, and P. A. Cloutier (2004), On determining the nature and orientation of magnetic directional discontinuities: Problems with the minimum variance method, J. Geophys. Res., 109, A11102, doi: /2004ja Heggy, E., S. M. Clifford, T. G. Farr, C. L. Dinwiddie, and R. E. Grimm (2006), Radar investigations of planetary and terrestrial environments, J. Geophys. Res., doi: /2006je002729, in press. Hughes, W. J., and D. J. Southwood (1976), The screening of micropulsation signals by the atmosphere and ionosphere, J. Geophys. Res., 81(19), Kivelson, M. G., and D. J. Southwood (1988), Hydromagnetic waves and the ionosphere, Geophys. Res. Lett., 15, Knetter, T., F. M. Neubauer, T. Horbury, and A. Balogh (2003), Discontinuity observations with Cluster, Adv. Space Res., 32, 543. Krauss-Varban, D., N. Omidi, and K. B. Quest (1994), Mode properties of low-frequency waves: Kinetic theory versus Hall-MHD, J. Geophys. Res., 99, Lundin, R., et al. (2004), Solar wind-induced atmospheric erosion at Mars: First results from ASPERA-3 on Mars Express, Science, 305, Mitchell, D. L., R. P. Lin, C. Mazelle, H. Rème, P. A. Cloutier, J. E. P. Connerney, M. H. Acuña, and N. F. Ness (2001), Probing Mars crustal magnetic field and ionosphere with the MGS Electron Reflectometer, J. Geophys. Res., 106, 23,419 23,427. Nagy, A. F., et al. (2004), The plasma environment of Mars, Space Sci. Rev., 111, Pincon, J. L., M. Menvielle, and L. Szarka (2000), Geomagnetic induction study using the NetLander network of magnetometers, Planet. Space Sci., 48, Shinagawa, H. (2000), Our current understanding of the ionosphere of Mars, Adv. Space Res., 26, Song, P., and C. T. Russell (1999), Time series data analyses in space physics, Space Sci. Rev., 87, Torrence, C., and G. P. Compo (1998), A practical guide to wavelet analysis, Bull. Am. Meteorol. Soc., 79, Trotignon, J. G., M. Parrot, J. C. Cerisier, M. Menvielle, W. I. Axford, M. Paetzold, R. Warnant, and A. W. Wernik (2000), The plasma environment of Mars: From the shocked solar wind down to the ionosphere, Planet. Space Sci., 48, Vignes, D., C. Mazelle, H. Reme, M. H. Acuña, J. E. P. Connerney, R. P. Lin, D. L. Mitchell, P. A. Cloutier, D. H. Crider, and N. F. Ness (2000), The solar wind interaction with Mars: Locations and shapes of the bow shock and magnetic pile-up boundary from the observations of the MAG/ER experiment onboard Mars Global Surveyor, Geophys. Res. Lett., 27, Vozoff, K. (1991), The magnetotelluric method, in Electromagnetic Methods in Applied Geophysics, vol. 2, Application, edited by M. N. Nabighian, pp , Soc. of Explor. Geophys., Tulsa, Okla. P. A. Cloutier, Department of Physics and Astronomy, Rice University, MS-108, Houston, TX 77005, USA. (pac@spacibm.rice.edu) G. T. Delory, Space Sciences Laboratory, University of California Berkeley, 7 Gauss Way, Berkeley, CA , USA. (gdelory@ssl. berkeley.edu) J. R. Espley, NASA Goddard Space Flight Center, MS 695.0, Greenbelt, MD 20701, USA. (jared.espley@gsfc.nasa.gov) 7of7