Joint Inversion and Forward Modeling of Gravity and Magnetic Data in the Ismenius Region of Mars

Lunar and Planetary Science XXXVI (2005)

2075.pdf

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; cmilbury@ess.ucla.edu; ^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)

2075.pdf

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).

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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
positions.

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.