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Lunar and Planetary Science XXXVI (2005) 


Joint Inversion and Forward Modeling of Gravity and Magnetic Data in the Ismenius Region of 
Mars. C.A. Milbury', C.A. Raymond^ J.B. JewelP, S.E. Smrekar^ and G. Schubert''\ 'University of California, 
Los Angeles, Department of Earth and Space Sciences, 595 Charles Young Drive East, Box 951567, Los Angeles, 
CA 90095-1567;; ^Jet Propulsion Lab, California Institute of Technology, M.S. 183-501, 
4800 Oak Grove Dr., Pasadena, CA 91109; Institute of Geophysics and Planetary Physics, University of California, 
Los Angeles, CA 90095-1567. 

Introduction: The unexpected discovery of 
remanent crustal magnetism on Mars was one of the 
most intriguing results from the Mars Global 
Surveyor mission. The origin of the pattern of 
magnetization remains elusive. Correlations with 
gravity and geology have been examined to better 
understand the nature of the magnetic anomalies. In 
the area of the Martian dichotomy between 50 and 90 
degrees E (here referred to as the Ismenius Area), we 
find that both the Bouguer and the isostatic gravity 
anomalies appear to correlate with the magnetic 
anomalies and a buried fault, and allow for a better 
constraint on the magnetized crust [1]. 

Ismenius Area: The highlands in this area are 
separated from the lowlands by a topographic bench. 
We interpret the bench as a down-faulted highlands 
block based on both age constraints and evidence for 
faults on either side [2]. Topographic knobs cover the 
bench, but disappear abruptly to the north under 
plains fill. This transition is parallel to graben along 
the dichotomy boundary and is interpreted as a 
cryptic normal fault [2]. 

In order to gain more insight into the geologic 
evolution and subsurface structure in this area, we 
perform an inversion of the gravity and magnetic 
anomaly data, focusing on two major anomalies on 
either side of the mapped buried fault, using the fault 
to guide the placement of the source array. The 
magnetic field changes polarity across the fault, 
which is indicative of some type of edge effect in the 
subsurface magnetized material. A large positive 
gravity anomaly occurs northeast of the fault, in the 
same general area as the magnetic anomaly. 
Southeast of the fault, a small negative gravity 
anomaly is aligned with the magnetic anomaly. 

An initial examination of possible correlation 
between the gravity and magnetic anomaly sources 
explored different hypotheses by modeling a 1-D 
profile across the dichotomy boundary, the buried 
fault, and the 2 gravity and magnetic anomalies 
described above [2]. We tested two types of models. 
In the first model the sources for the magnetic and 
gravity anomalies are the same and are therefore 
correlated. For this model, the correlations between 
the magnetic anomalies and positive density 
variations are most likely to be a result of subsurface 
magmatic intrusions. The second model assumes that 
the bodies are anticorrelated. This model has gaps in 
the magnetization (relative to the highlands source 

layer) that are approximately aligned with the 
isostatic gravity anomalies. These gaps are consistent 
with discrete, high density intrusions causing 
demagnetization of the crust. Paleopole estimates for 
Mars which have been previously derived place both 
normal and reversed polarity poles in a region 
centered at 230E, 25N [3], or in a region centered at 
225 W, 50N [4]. The uncertainties on the paleopole 
estimates allow a wide range of possible inclinations 
for the study area, but exclude steep paleofield 
inclinations (>+60°). The estimated range of 
paleolatitudes expected across the sampled profile for 
is 10°-30° + 30° [3] or 25° to 40° [4]. Given this large 
range of paleopole position, it was not possible to 
distinguish between the two models on the basis of 2- 
D forward modeling. 

Gravity and Magnetic Field Data: Both the 
free air and Bouguer gravity fields exhibit anomalies 
with a similar wavelength and amplitude variation as 
the magnetic field anomalies. We use the isostatic 
anomaly, which removes the gravity signature of a 
subsurface crustal layer from the Bouguer gravity, 
assuming that the layer provides isostatic 
compensation of the topography. For the magnetic 
data we take advantage of the full resolution 
available in the 3-component magnetic measurements 
of the MGS orbiter. Individual profiles are selected 
and the data are then processed. This includes 
selecting high and low altitude data and eliminating 
noisy data via a combination of visual inspection, 
track-to-track comparison, and examination of the 
power spectrum for effects of aliasing. 

Inversion: We base the 3D joint inversion 
method on the approach developed by [5] and 
references therein. This approach is one of the few 
that allow a full 3-D joint inversion, the subsurface is 
represented as a series of rectangular prisms. The 
inversion solves for susceptibility, remanent 
magnetization, paleopole inclination, density, and 
depths to the top and bottom of the prisms [5]. Our 
approach modifies the method of [5] in several ways. 
We have eliminated the calculation of the induced 
magnetic field and inversion for susceptibility from 
the original code to reflect the lack of an active field 
on Mars. The new code is based in Martian 
coordinates. In addition, the steepest descent inverse 
approach has also been replaced by a Bayesian 
approach, motivated primarily by the non-uniqueness 
of models that fit the data (as observed for ID models 

Lunar and Planetary Science XXXVI (2005) 


in [1]). The Bayesian figure of merit for various 
models is the posterior probability, given in terms of 
prior probabilities for the models (chosen to reflect 
physical constraints on the models) and the likelihood 
of observing the data in the context of a given model. 
The likelihood of observing the data in the context of 
a model is determined by the instrument noise - it is 
the negative log-likelihood, also known as x""chi- 
squared" (for the case of Gaussian noise) which is 
typically minimized in traditional approaches to the 
inverse problem (usually through steepest descent, or 
other optimization algorithms). Our emphasis has 
shifted from finding a single "best" model to 
quantifying the collection of models with similar 
values of the Bayesian posterior probability - 
providing a generalization of the notion of "error 
bars". While more expensive than steepest decent, a 
Bayesian approach provides a more complete picture 
of what has been learned from the data, and allows 
the quantification of our uncertainty (through 
samples from the Bayesian posterior). 







V XI- 

" T 









Figure 1 . Location of model prisms, buried fault 
and model inversion results for magnetization 
intensity (A/m). 

Source prisms are defined as 4 different types. 
Prisms that allow for inversion of: 1) remnant 
magnetization only, 2) density only, 3) magnetization 
and density, or 4) magnetization or density. Figure 1 
below shows an example inversion of magnetization 
intensities obtained assuming a paleopole at 230E, 
25N [3], for a set of prisms where all prisms are 
inverted for magnetization and density. Densities are 
not shown. The scale bar is magnetization in A/m, 
and the mapped buried fault is the black curve. In 
separate forward modeling trials, prisms closer to the 
fault match the magnetic field data better than those 
that are farther away, and the prisms farther from the 
fault better fit the gravity data. In this inversion, 
prisms located closer to the fault exhibit higher 

magnetization values than those that are further from 
the fault, consistent with the intrusion model 
mentioned previously. 

This same set of prisms was inverted with the far 
group of prisms being selected as density only 
prisms, and the near group selected as magnetic only 
prisms. This resulted in a posterior probability lower 
than the first. This shows that a better fit is obtained 
allowing all prisms to have magnetic and density 
variations, even if they are relatively low. 

Future Work: We find the best fitting solutions 
for source dimension, density and paleopole based on 
assumption that gravity and magnetic anomalies are 
caused by the same sources (prisms). Initial prism 
locations will be defined based on the location of the 
isostatic anomalies. To test for anticorrelation, we 
will constrain the solution such that those prisms 
defined by the isostatic anomalies will have 
magnetization set to 0, and the magnetic prisms will 
have density set to 0. Additional prisms will be added 
in which the magnetization can vary. To test if the 
sources are largely uncorrected, we will blanket the 
region with small prisms and let the density and 
magnetization vary within reasonable bounds. We 
will compare the best-fit solutions to determine 
which hypothesis provides the best, and most 
reasonable, fit. A key aspect of the study will be an 
examination of how the inversion changes with 
paleopole location. As discussed in the context of ID 
models, determining whether or not the gravity and 
magnetic source regions are correlated or 
anticorrelated has important implications for the local 
history of the crust. If magnetic and gravity 
anomalies here and elsewhere can be correlated, it 
will be possible to better constrain paleopole 

References: [1] Smrekar, S. E. et al. (2004), 
JGR, 109, El 1002, doi:10.1029/2004JE002260. [2] 
Dimitriou A.M. (1990) Masters Thesis, Univ. Mass. 
Amherst. [3] Arkani-Hamed, J. (2001), Geophys. 
Res. Lett., 28, 3409-3412. [4] Hood L.L. and 
Zakharian A. (2001) JGR, 106, 14601-14619. [5] 
Zeyen, H., and J. Pous, Geophys. J. Int., 112, 244- 
256, 1993. [6] Jewell et al. (2004) Trans. Am. 
Geophys. Union, Fall Mtg, Abstract NG34A-02.