Exploring Martian Magnetic Fields with a Helicopter

Future Mars helicopter missions include Sample Recovery Helicopter–like vehicles (Mier-Hicks et al. 2023), capable of carrying up to 1 kg of payload tens to hundreds of kilometers for a standard mission duration (∼1 Mars year), or larger Mars Science Helicopter concepts that are capable of carrying up to 5 kg of payload hundreds of kilometers (Bapst et al. 2021). Both would enable low-altitude coverage (up to several hundred meters) and offer the possibility of surveying the magnetic field of Martian regions in an unprecedented manner. Because magnetometers are lightweight and consume little power, and they can take advantage of low-altitude aerial mapping, we will now focus on discussing these highly relevant mission strategies.

A possible survey strategy includes several regions of interest (ROIs) that can be defined in advance using results from orbital data depending on the overall mission goals. The helicopter can perform in-depth analysis of those ROIs using its full instrument suite in conjunction with local/regional context from flight traverses (Figure 2(a)).

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Here we explore three magnetic field data set scenarios. In the first, we construct gridded data sets that provide evenly distributed measurements. The data sets and resulting inversions can be compared with those from more realistic survey strategies: one for which data are only collected on the ground and when the helicopter is not moving and one in which in-flight measurements are also possible. The latter option requires a more advanced magnetic cleanliness program (discussed in Section 5) but can take full advantage of the complete flight path.

Generally, contributions to the overall measured magnetic field are of spacecraft and Mars external and internal origin, i.e., sources above and below the planetary surface, respectively. We assume that helicopter-generated fields can be characterized and subtracted, and only naturally occurring fields are discussed. For a typical helicopter survey, mapping of the crustal magnetic field would be the primary mission objective, but regardless of whether external fields are of interest by themselves, separating internal and external contributions is required.

The internal magnetic field depends on the location of the measurement and, due to the absence of a Martian dynamo field, results solely from crustal magnetization. Amplitudes of the crustal magnetic field vary greatly, and satellite data-based surface predictions range from zero to 12,000 nT with an average and median of 450 and 200 nT, respectively (Figure 1; Langlais et al. 2019). However, those predictions are based on orbital data that are insensitive to small-scale (<∼100 km) magnetization. At the InSight landing site, the predicted magnetic field amplitude (Smrekar et al. 2018) was approximately 10% of the observed ∼2000 nT (Johnson et al. 2020). The strength of the predicted field at InSight is close to the global median value, and we might thus expect to find many similar and even stronger fields at the Martian surface. However, in less magnetized regions, such as in the northern hemisphere, crustal fields at the surface could be close to zero. This is, for example, the case for the Zhurong measurement sites (Du et al. 2023).

External magnetic fields at the surface can be of periodic nature, e.g., due to ionospheric currents (Lillis et al. 2019; Johnson et al. 2020; Mittelholz et al. 2020b), the interplanetary magnetic field (Langlais et al. 2017; Luo et al. 2022; Mittelholz et al. 2023), or transients, such as space weather (Mittelholz et al. 2021b) or dust movement (Thorne et al. 2022). InSight provides surface observations over a prolonged time frame, and although external field phenomena are summarized elsewhere (Mittelholz et al. 2023), we list them in Table 2 to assess how large their contributions might be and whether they would affect crustal magnetic field measurements. Note that a different crustal magnetic field environment (that is, in a different location) would affect ionospheric currents and the resulting magnetic fields (Lillis et al. 2019).

Short-period fluctuations are observed at dusk/dawn and around midnight. Even if measurements were taken during those times, the fluctuations are on the order of only a few nanoteslas (Chi et al. 2019; Johnson et al. 2020). Daily fluctuations due to ionospheric currents, however, could lead to signals of tens to hundreds of nanoteslas depending on the strength of the background magnetic field and season (Lillis et al. 2019; Mittelholz et al. 2023). For InSight, daily fluctuations have been found to vary with season and dust content, and individual days can vary by tens of nanoteslas (Mittelholz et al. 2020b). Longer-period fluctuations associated with the interplanetary magnetic field are small at the InSight landing site, and their effect is likely negligible (Mittelholz et al. 2023). For a helicopter survey, identification and characterization of transient sources are unlikely to present a challenge because their amplitude is either too small, e.g., dust devils (Thorne et al. 2022), or, for ionospheric and magnetospheric currents, they can be either recognized by their time/diurnal profile or avoided/ignored during times of space weather (Mittelholz et al. 2021b).

The effect due to spatially and temporally varying magnetic field fluctuations depends on whether data are collected in flight or while landed at ROIs only. For landed measurements, i.e., measurements taken when the helicopter or rotor system is not moving, contributions to the measured magnetic field consist of the crustal magnetic field at that specific landing site and time-varying magnetic fields over a longer time frame (Table 2). Especially if the helicopter collects data during the nighttime, the time-varying external field contributions are minimal and can easily be identified and subtracted from the crustal contribution. For in-flight measurements, subtracting external fields would be more challenging, as the internal field also varies as the helicopter flies across varying crustal magnetic anomalies. Generally, to separate internal and external fields we recommend repeat measurements covering ROIs several times and at magnetically quiet periods, and vertical flights at several locations across the region.

Finally, crustal contributions are expected to outweigh external field contributions at many locations. Landed measurements enable individual robust crustal field measurements because time-varying magnetic fields can be readily identified, especially during magnetically quiet nights. Tracking of diurnal fluctuations while on the ground could then inform on spatially varying crustal fields versus external variations for in-flight measurements. Additional data collected during the traverse would ensure dense coverage of flight paths between landed measurements and enable crustal magnetic field characterization of unprecedented resolution.

One advantage of airborne surveys is the traversability in any terrain, such as boulder fields and along steep walls. We present a range of geological settings that one could encounter on Mars and for which magnetic signatures might be expected. First, magnetization associated with craters (or the lack of magnetization) has been used previously to constrain the timing of the dynamo (Lillis et al. 2013; Vervelidou et al. 2017; Mittelholz et al. 2020a). This addresses questions D1 and D2 in Table 1. (De)magnetization signatures associated with crater interiors arise due to the effect of shock and heating during an impact (Mohit & Arkani-Hamed 2004; Gattacceca et al. 2008). Excavation of magnetized material can also have an effect (Mittelholz et al. 2020a; Ojha & Mittelholz 2023), and this has been used to constrain the dynamo to 3.7 Ga. Craters on Mars are ubiquitous (Robbins et al. 2013), and any landing site would likely offer the opportunity to traverse impact craters and ejecta. As such, in this scenario, we can test if a dynamo operated at the time of the impact. A test of magnetizations of features (not necessarily craters) of several different ages is necessary to construct a timeline of the Martian dynamo and help constrain the evolution of the interior state of Mars, i.e., changing from sustaining a dynamo to being unable to do so. Hence, this is a highly relevant scenario for any future mission with a magnetic focus.

In a second scenario, we investigate the magnetization signature of a dike intrusion. Generally, magmatic activity throughout Martian history is evident (Tanaka et al. 2014), and dikes have been mapped in volcanically active areas such as Tharsis (Brustel et al. 2017; Pieterek et al. 2022) or indirectly inferred from rift structures or seismic data (Nimmo & Stevenson 2000; Stähler et al. 2022). Magnetization associated with dateable volcanic features can address volcanic and dynamo evolution (Johnson & Phillips 2005; Lillis et al. 2006; Mittelholz et al. 2020a). Again, this is linked to questions D1 and D2, but especially in comparison with the above examples, it allows one to characterize magnetization that is known to be linked to thermal effects as opposed to a site in which one observed clear signs of shock or alteration (questions M1–M4). For example, the analysis of the magnetic field of a dike could reveal a demagnetization signature for a young intrusion in a magnetized layer or a magnetization signature if the intrusion and the surrounding layer were emplaced while a dynamo was active. Furthermore, ferrous mineralogies of the dike could enhance the magnetization compared to the background. Moreover, this particular example is defined to address resolvability, i.e., how well very small features can be resolved, irrespective of the science question asked.

Lastly, we consider layering that could be found in a valley or graben structure (Nedell et al. 1987; Le Deit et al. 2010). This would offer ideal conditions to traverse multiple layers of different ages to establish a magnetic timeline and address the question of dynamo activity and possible polarity changes over the range of emplacement ages represented in the set of strata (D2). At least one polarity change has been hypothesized based on orbital data and the meteorite ALH84001 (Thomas et al. 2018; Steele et al. 2023); testing the characteristics of a dynamo over time would provide unprecedented information on interior evolution. Stacked layers of different material and possibly different origins would further allow one to address all questions labeled M in Table 1. From a more technical perspective, this scenario also allows intuition to be gained on expected magnetic signals across at least two distinct blocks of magnetization.

In preparation for future missions, in this study, we model the proposed scenarios and perform inversions to investigate the degree to which we can recover magnetized structure. We use the open-source SimPEG package in Python (Cockett et al. 2015), and an example code is available online. First, we simulate magnetic field data collected by a helicopter above a given magnetization model; this is the forward problem. From Gauss's law, the relation between magnetization per unit volume M in Am⁻¹ and magnetic field B in teslas is

$$\begin{eqnarray}&&{\boldsymbol{B}}(r)=\displaystyle \frac{{\mu }_{0}}{4\pi }{\int }_{V}{\rm{\nabla }}{\rm{\nabla }}\displaystyle \frac{1}{r}\cdot {\boldsymbol{M}}{dV},\end{eqnarray} \tag{ 1 }$$

where r is the radial distance between the measurement point and the magnetic source of volume V, and μ₀ is the magnetic permeability of free space. Using simulated data, d , we then aim to recover our model, m , by solving an inverse problem. First, we define the parameters we aim to estimate by solving the inverse problem. We use a voxel model of the subsurface, where each cell has a vector magnetization that we seek to estimate (Lelièvre & Oldenburg 2009). The inverse problem is nonunique and underdetermined; i.e., there are infinite possible solutions. Therefore, one needs to incorporate additional constraints. Traditionally, the inverse problem can be formulated as an optimization problem (Tikhonov et al. 1995) in which one can impose regularization and minimize an objective function that contains a data misfit term, Φ_d , and a model regularization term, Φ_m . The trade-off parameter β controls the relative importance between the two competing terms, and ${{\rm{\Phi }}}_{d}^{* }$ represents an acceptable target misfit:

$$\begin{eqnarray}&&\min {\rm{\Phi }}\left(m\right)={{\rm{\Phi }}}_{d}+\beta {{\rm{\Phi }}}_{m}\quad \mathrm{subject}\ {\rm{to}}\quad {{\rm{\Phi }}}_{d}\leqslant {{\rm{\Phi }}}_{d}^{* }.\end{eqnarray} \tag{ 2 }$$

The first term, Φ_d , describes the misfit between observed, d_obs, and predicted, d_pred, data,

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{d}=\displaystyle \sum _{i=1}^{N}\displaystyle \frac{({d}_{i}^{\mathrm{pred}}-{d}_{i}^{\mathrm{obs}})}{{\sigma }_{i}},\end{eqnarray} \tag{ 3 }$$

normalized by estimated uncertainties σ for each data point i. Assuming that the noise and error on the data are random, the expected target misfit ${{\rm{\Phi }}}_{d}^{* }$ = N, where N is the number of data.

The second term penalizes differences between the model and a reference model and can be made up of several functions that control the magnitude and roughness of the model,

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{m}=\displaystyle \sum _{r=s,x,y,z}{\int }_{V}{w}_{r}| {f}_{r}(m){| }^{{p}_{r}}{dV},\end{eqnarray} \tag{ 4 }$$

where f_r consists of one or more of f_s = m, f_x = dm/dx, f_y = dm/dy, and f_z = dm/dz, describing the smallness and roughness in all orthogonal directions. The weighting term w_r adjusts the importance of the regularization terms. Lastly, we use the general l_p norm, which can be independently adapted for the different regularization functions with 0 ≤p_r ≤2.

In order to minimize Equation (2), we discretize our model onto a tensor mesh and find a solution such that the gradient of the objective function ∇_m Φ( m ) = 0. The trade-off parameter β is decreased until a defined threshold tolerance is reached or after a given maximum number of iterations. The inexact Gauss–Newton algorithm is used to calculate appropriate model updates; for more details on the inversion, we refer the reader to Fournier & Oldenburg (2019).

We simulate three different survey geometries with a decreasing number of measurements for each of the scenarios described in Section 2.1. First, we construct a regular tensor mesh across the ROI and simulate the data that would result from the magnetization model if the data were collected on an idealized grid (Figures 4(a) and (b)). For example, for the crater scenario, the survey includes 15 × 15 data points across a 600 × 600 m area, resulting in 225 data points (Figures 4(b) and (f)). The next survey geometry simulates the flight path of a helicopter; the helicopter lifts off the ground up to an altitude of 10 m at the center point of each track before it lands. We simulate three tracks with 30 data points on each (Figures 4(c) and (g)). Note that changing altitude contributes to the magnetic field observation; i.e., the magnetic field signal is decreased at times when the helicopter is further away from the surface and the source of magnetization. With an approximate helicopter speed of 10 m s⁻¹, the 30 data points across 10 m equate to a sampling rate of 30 samples s^–1. Lastly, we explore the scenario in which the helicopter only collects data on the ground (i.e., when it is not flying). Six measurements at discrete locations are collected in this survey (Figures 4(d) and (h)). For all models, we assume background noise with a standard deviation of 0.1 nT, but we vary this parameter in Section 5.1.

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We propose a modeling strategy in which different inversion techniques are applied consecutively to achieve confidence in the recovered magnetization and inferred geological models (Figure 3). While some techniques rely on no or minimal a priori information, we also show examples of how a priori information, i.e., information from other data sets, particularly imagery, can be incorporated into the inversion. As sketched in Figure 3, after data acquisition, we initially generate a smooth L2 inversion for a first estimate of the distribution of magnetization and its possible relation to observable surface structures (Section 3.3.1). Next, we aim for a model that will highlight contrasts and produce compact structure in a sparse inversion (Section 3.3.2). We then incorporate knowledge of geological structure or layering in the inversion (Sections 3.3.3, 3.3.4, and 3.3.5). Different techniques are briefly described below and later applied to the different scenarios to showcase the range of different inversion strategies.

3.3.1. Smooth Inversions

3.3.2. Sparse-norm Inversions

3.3.3. Single Layer

3.3.4. Parametric Model

3.3.5. Domain Mapping

The magnetized crater produces a magnetic field signature of approximately 1 nT and is seen in all components. The initial L2 inversion (Figures 4(f)–(h)) produces a relatively smeared-out picture, particularly at depth. As a result, the magnetization amplitude of the feature is underestimated, especially for the landed case, for which there are insufficient data points to determine the exact structure of the anomaly (Figure 4(h)). The model does suggest the presence of a compact feature motivating inversions using a sparse representation. The sparse model (Figures 5(a)–(c)) captures the feature extent well, especially for the dense survey coverage (Figure 5(a)). The somewhat square outline of the crater feature is the result of independent regularization of the three components in combination with poor data coverage for the in-flight and especially the landed cases (Figures 5(b) and (c)). Generally, the amplitude of the feature can be recovered well. In both the sparse and the smooth models, we observe low-amplitude magnetization in the layers closest to the surface, which is inconsistent with our model scenario (Figure 4(e)). This effect arises because of the magnetization direction (45° and downward) we have imposed on the model. As a next step, and because we have identified a compact structure consistent with the hypothesis that it is connected with the crater, we apply the parameterized approach (Figures 5(d)–(f)). We approximate the shape of the crater by a half-sphere and m _crater = [x, y, z, r, m_x , m_y , m_z ] = [0, 0, −40, 120, 7, 0, −7]. No matter the data coverage, we obtain a model representation of the magnetized crater that fits our model scenario well. Thus, even for limited data, the representation is very good and clearly better than the L2 or sparse representation.

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In the dike scenario, we cover a smaller area around a 15 m diameter dike due to the small horizontal extent of the feature (Figures 6(a) and (b)), and only a few data points in closest proximity to the feature are affected (Figures 6(a)–(d)). The initial L2 inversion for the dike again shows a smeared-out dike feature that, even in absence of a priori information, is localized (Figures 6(f)–(h)). Due to lacking depth sensitivity, the feature is less well resolved vertically, and we cannot probe the dike's depth extent. The sparse solution enforces a compact feature and is therefore able to pinpoint the location of the dike very well, but as expected, it does not extend the feature at depth (Figures 7(a)–(c)). In places where a dike is visible via imagery and the goal is to probe whether it is (de)magnetized compared with the surrounding material, this might be sufficient. In the one-layer model, we decide to ignore depth resolution and just focus on locating the dike, which can be achieved exceptionally well (Figures 7(d)–(f)). Note that the detection of the intrusion is only possible because the data points are collected in direct proximity to the feature. For the landed case, we increased the data point density around the dike as we would in regions where such a feature is identified, e.g., in imagery. Furthermore, while we model a purely vertical and horizontally symmetric feature, we would expect some lateral extent due to smaller intrusions and heating in the surrounding crust that would increase the magnetization area and thus the area in which the feature can be detected.

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In the last scenario, we investigate the effect of layers that are much wider than the helicopter altitude (Figure 8(b)). Generally, a magnetic survey detects lateral gradients (Equation (1)) in magnetization. Thus, a uniformly magnetized layer of infinite extent or a uniformly magnetized shell does not lead to a magnetic field signature (Affleck 1958; Parker 1977). As a result, the traversing helicopter measures a (close to) zero magnetic field in the center of the individual layers (Figure 8(a)). Inversions without a priori information will therefore map layer edges rather than the layers themselves. This effect is clearly visible in the data (Figures 8(a)–(d)), and due to the large direction and amplitude changes across the layer boundaries, the amplitude of the magnetic field signal is larger than for previous examples, despite a similar maximum amplitude of magnetization. Note that the noise floor of 0.1 nT is low compared to the signal associated with magnetization in this example (Figures 8(b)–(d)). The edge effect is also clearly visible in the L2 inversion (Figures 8(f)–(h)), and the model predictions fit the data very well (again, as result of a comparably low noise floor). Between approximately 50 and 200 m depth, the direction of the layers can be recovered, while the inversion does not recover near surface magnetizations, as observed previously. The sparse inversion generally localizes what we see in the L2 inversion. Again, transitions can be mapped, and the magnetization direction is approximated reasonably well. Lastly, the domain mapping methodology can obtain a solution that matches the data very well (Figures 9(d)–(f)) even if only a few data are collected, as long as all units are covered. Even if no information on the direction or amplitude is provided a priori, only the layer outlines, the magnetization can be recovered well for all survey scenarios. This method also performs very well for high background noise (not shown) but requires good understanding of the geometry of the layers.

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We now consider varying levels of noise. Previous figures assume a noise level of 0.1 nT, and we now investigate the effect of 0, 0.5, and 1 nT (Figure 10) for the initial L2 inversion for the crater scenario. While 0.1 nT is approximately 10% of the measured peak magnetic field, the increased noise level is substantial with respect to the crater signal. However, we can recover a coherently magnetized structure such as that shown in this example, although the magnetic field amplitude and random noise are of similar order. This is particularly encouraging, as we expect signatures associated with the surface magnetic field to mostly be stronger than what is modeled here.

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Generally, noise sources are an important consideration for any magnetics mission. Above, we have described noise due to external magnetic fields; those fields will be local time–dependent and often vary on different timescales. If the duration of a helicopter traverse is much longer than the fluctuations due to the external magnetic field, we would expect the full traverse data to be affected, including crustal field anomalies. While this might lead to an under- or overestimation of the anomaly amplitude, the detection of the anomaly itself would not be impacted, except for weak magnetization sources. Periodic fluctuations on the order of minutes (i.e., comparable to a flight traverse) or seconds could affect the measurements. At InSight, these have been observed and were on the order of up to a few nanoteslas, but they only occur irregularly and usually at dusk/dawn and at night. Ionospheric fluctuations are expected, and they are strongest during the day. Hence, to mitigate external magnetic field effects, we recommend sampling at magnetically quiet times of the day or, if possible, at night. Any ROI should be covered by multiple tracks and, if possible, at similar local times. External field characterization while on the ground can be used to (i) identify the most opportune times for measurements and (ii) estimate the uncertainties associated with longer-timescale signals.

Artificial sources can be substantial, and thorough cleanliness programs are essential to characterize or account for them as best as possible. Here we do not provide recommendations on cleanliness procedures but acknowledge that artificial sources might be substantial, especially for taking measurements along the flight traverse, and briefly discuss some important considerations. While low-altitude platform surveys are routinely used on Earth, we would like to note that commercial terrestrial drones are generally not designed with magnetic cleanliness in mind. Extensive characterizations of thermal effects and electric and magnetic interference are common for spacecraft missions carrying magnetometers, while terrestrial instrumentation is rarely characterized to the same degree. Spacecraft carrying science-grade magnetometers undergo magnetic cleanliness programs in order to make sure that the artificial sources are smaller than the required measurements. Such magnetic cleanliness programs are best approached from a systems-engineering perspective, working with the spacecraft, magnetometer instrument, and science teams to select best approaches (Acuña 2004).

The requirements for a mission very much depend on mission goals and landing location. Crustal magnetic fields are spatially inhomogeneous and can be very strong locally. If landing were to occur in such a location, these fields would be a dominant contribution compared with time-varying external fields and precharacterized artificial fields created by the lander/helicopter. While the latter can be large, any mission measuring ambient magnetic fields undergoes thorough investigation of artificial contributions. The requirement for accuracy of such a characterization depends on science questions. For example, accuracy to within several nanoteslas would likely be sufficient if only changes in the crustal field are of interest for a survey site in a moderately magnetized region. The noise discussion in the above subsection is relevant here.

Finally, deployable, nonmagnetic booms should be considered to move the magnetometer as far as possible from other instruments and helicopter current sources. The boom length and design will again depend on the exact measurement requirements and the nature of the artificial signals on the platform. For example, tethers have also been suggested, which would allow the magnetometer to dangle from the helicopter while traversing. In this case and ideally, inertial measurement units could determine the instrument's position in space and allow for three component measurements; when landed, the position of the instrument could be established once and allow for reduced data collection (i.e., no constant positioning is required). The amplitude of the field would always be available and not rely on positioning. Additional lightweight magnetic sensors with varying distances to the electronics could provide further information on the fields generated by the helicopter and thus help characterize and subtract those fields (Ness et al. 1971); this, of course, would add payload mass, and this trade-off would have to be carefully considered. In all cases, the detailed design would be a collaboration between science, instrument, and spacecraft teams.

Magnetic field data in the context of other measurements will offer the most comprehensive picture of the survey site (see also Table 1). While we do not attempt to list all possible additional instruments, we suggest a selection of data sets that could aid interpretations of magnetic field measurements.

The combination of existing orbital high-resolution imagery with an added camera on the helicopter is key for interpretation of geological surface features and their associated magnetization (e.g., Langlais & Purucker 2007; Lillis et al. 2013; Mittelholz et al. 2020a). We have shown that the inclusion of prior knowledge from imagery can greatly benefit our modeling efforts. As a further example, if we can identify a magnetic field signal associated with a pebble, rock, or block, one could use imagery to estimate its volume and thus magnetization. This would require one to move/fly around the rock at increments on the order of the size of the pebble. A similar experiment was suggested but not attempted with the robotic arm on the InSight lander (Golombek et al. 2023). Here the measurements at different distances from the pebble were planned by moving the pebble with the robotic arm. The magnetization amplitude depends on the volume extent of the magnetized structure, which can easily be misrepresented, often leading to underestimations of magnetization (see results of L2 inversions). The pebble would provide an alternative and simple way of getting at magnetization from which material properties and possibly the magnetizing field can be inferred.

Other instrumentation that would provide increased science return includes spectrometers that directly identify the elemental and/or mineralogical characteristics of surface material. This additional information can help address the carrier of magnetization and possibly magnetization acquisition mechanisms (Table 1). Landing sites with differing ROIs, e.g., highly altered versus volcanic material, would offer ideal survey sites. However, we note that spectrometers inform on surface composition, and combining these observations with the results of magnetic field inversions would require the surface layer to be magnetized. Global models for magnetization source depth mostly predict magnetization kilometers below the surface, especially in the southern hemisphere, with some regions of more surficial magnetization mostly in the north (Gong & Wieczorek 2021). However, the source depth uncertainties in such models are large (Gong & Wieczorek 2021). Locally, magnetization has been shown to be at least partially surficial in the Medusa Fossae formation, particularly Lucus Planum (Mittelholz et al. 2020a; Ojha & Mittelholz 2023), and in comparison with orbital spectrometer data, composition has been shown to correlate with higher magnetic fields (AlHantoobi et al. 2021).

Lastly, information on physical properties at depth could be obtained with a gravimeter. Because gravity informs on density and thus the compositional constraints of rock, combined magnetic–gravity surveys are particularly informative in addressing the origin of magnetization. Also, because both fields fall off differently with distance to the source, they have different depth sensitivities. Joint modeling techniques for the combination of petrophysical/geological and geophysical data have been shown to more accurately represent physical properties and could provide further modeling strategies that can make use of combined data sets (e.g., Lelièvre & Farquharson 2016; Astic & Oldenburg 2019; Astic et al. 2020; Lösing et al. 2022; Moorkamp 2022).