Achim Morschhauser

A spherical harmonic model of the lithospheric magnetic field of Mars

We present a model of the lithospheric magnetic field of Mars which is based on Mars Global Surveyor orbiting satellite data and represented by an expansion of spherical harmonic (SH) functions up to degree and order 110. Several techniques were applied in order to obtain a reliable and well-resolved model of the Martian lithospheric magnetic field: A modified Huber-Norm was used to properly treat data outliers, the mapping phase orbit data was weighted based on an a priori analysis of the data, and static external fields were treated by a joint inversion of external and internal fields. Further, temporal variabilities in the data which lead to unrealistically strong anomalies were considered as noise and handled by additionally minimizing a measure of the horizontal gradient of the vertically down internal field component at surface altitude. Here we use an iteratively reweighted least squares algorithm to approach an absolute measure (L1 norm), allowing for a better representation of strong localized magnetic anomalies as compared to the conventional least squares measure (L2 norm). The resulting model reproduces all known characteristics of the Martian lithospheric field and shows a rich level of detail. It is characterized by a low level of noise and robust when downward continued to the surface. We show how these properties can help to improve the knowledge of the Martian past and present magnetic field by investigating magnetic signatures associated with impacts and volcanoes. Additionally, we present some previously undescribed isolated anomalies, which can be used to determine paleopole positions and magnetization strengths.

Paleopole Reconstruction of Martian Magnetic Field Anomalies

Introduction: Investigating a planets magnetic paleopole position can reveal important information on events like polar reversals or true polar wander (TPW). A variety of investigations have been performed [1,2,3,4,5] usually reporting the best fitting, or a cluster of paleopole positions. These investigations indicate that analyzing the same anomaly using different assumptions can lead to different conclusions for the paleopole positions associated with the underlying sources [5]. To address this issue we applied the method developed by [6] which has the benefit that no assumptions concerning the geometry of the magnetic source are necessary. In addition, this method provides a measure of misfit for the calculated paleopole position and a confidence limit can be defined to determine an area of admissible paleopole locations. Five crustal magnetic field anomalies will be discussed here. One is the Australe Montes anomaly which has been investigated by [4], four of them are isolated anomalies identified by [7]. They will be denoted as follows: The four anomalies from the publication of [7] will be denoted A1, A2, A3, and A4. They are located at 52°S / 2.5°W, 64°S / 28°E, 57°N / 167°E, and 49.5°N / 169°E, respectively. The Australe Montes anomaly is located at 81°S / 23.4°E and will be denoted A. Montes. Method: To apply the method of [6], isolated crustal magnetic field anomalies are chosen. Here an isolated anomaly is defined by the absence of a surrounding magnetic field from sources outside the anomaly itself. Further, it is assumed that the anomalys magnetization has been acquired during a geologically short period within a constant main magnetic field, leading to an anomaly with uniform magnetic orientation [6]. To calculate a paleopole position, a number of N equally spaced dipoles with uniform orientation are distributed within the radius R0 (Fig. 1 / red circle) [6] on the Martian surface. In the same way a distribution of N observation points inside the radius R1 (Fig.1 / black circle), with R0 < R1, is generated and the downward component of the magnetic field is determined from a magnetic field model at 120 km altitude. Here we use the spherical harmonic model up to degree and order 110 by [7] calculated from the entire Mars Global Surveyor (MGS) data set. Because the magnetic orientation is set a priori, the remaining unknowns are the N magnetization strengths Mi of the N dipoles. Since it is assumed that Mi ≥ 0, Mi is calculated using a non negative least square fit algorithm [8], taking only Bz into account. From Mi, a forward model of the magnetic model field can be calculated and the residuals and standard deviation between the model and the spherical harmonic magnetic field can be determined (Fig. 1). The repetition of this calculation for all possible magnetic orientations in steps of 1° in inclination and 2° in declination leads to a distribution of standard deviations for the different magnetic orientations. The paleopole position of every forward model can then be calculated from the magnetization orientation unit vectors using standard coordinate transformations [9] that take the location of the anomaly into account. Here we adopt the convention that the paleopole location is defined as the south magnetic pole [9].

Constraining the date of the Martian dynamo shutdown by means of crater magnetization signatures

Mars is characterized by a strong crustal magnetic field, particularly over its southern hemisphere, which is believed to be the remnant of an ancient core dynamo. The dynamo ceased operating approximately 4 Ga ago, although the exact time is still under debate. The scope of this study is to introduce constraints on the possible timing of its cessation by studying the magnetization signatures over some craters which have reliable crater retention ages and are large enough for the impact to have reset the crustal magnetization within.

Mars’ Crustal Magnetic Field

Fossil magnetic fields within the Martian crust record the history of the planet’s ancient dynamo and hence retain valuable information on the thermal and chemical evolution of Mars. In order to decode this information, we have derived a spherical harmonic model of the crustal magnetic field. This model was derived from satellite vector magnetometer data, and allows to study the crustal magnetic field at high resolution down to surface altitudes. Based on this model, we calculate the required magnetization of the Martian crust, and discuss how the resulting strong magnetization might be explained. Further, we study the magnetization of impact craters and volcanoes, and conclude that the Martian core dynamo shut down most probably in the Noachian, at about 4.1 Gyr ago. Finally, we address the derivation of magnetic paleopole positions. In a first step, we use synthetic tests in order to outline under which constraints paleopole positions can be determined from satellite measurements. In a second step, we use these insights to present a scheme to estimate paleopole positions including an assessment of their underlying uncertainties.