Introduction

The early Martian dynamo may have played a key role in the planet’s climatic evolution and habitability, with its termination potentially triggering the shift to Mars’s present cold and dry conditions1. The dynamo’s cessation may also mark the end of significant convection in the Martian core. Although Mars’s magnetic history is key to understanding the planet’s early atmosphere and deep interior, the dynamo’s longevity remains heavily debated.

On one hand, many Martian impact basins, including the very large basins Hellas, Utopia, Isidis, and Argyre (HUIA), appear only weakly magnetic in satellite magnetic field measurements2,3,4. Since basin formation heats large volumes of material which then acquires magnetization during cooling, basins formed in a strong, stable field are expected to produce strong magnetic fields. It has therefore typically been argued that the weak magnetic fields measured above these basins (which in many cases represent upper bounds on the actual field strength) are evidence that the basins formed in the absence of a dynamo5,6. The 3.7–4.1 Ga formation ages of the HUIA and other apparently demagnetized basins have therefore been interpreted as evidence that Mars’s dynamo was not active when they formed2,5,6,7 (Fig. 1). In this framework, recent evidence for an active dynamo as early as 4.5 Ga8 and generally strong magnetization in (pre)Noachian regions would imply the dynamo shut down before 4.1 Ga. Some models of post-formation interior cooling also favor a dynamo persisting <500 Myr9.

Fig. 1: Summary of constraints on Mars’s magnetic history.
figure 1

Summary of constraints on the longevity of the Martian dynamo from magnetically characterized impact basins (green)5,108, young magnetized volcanics (blue)8,10,11,109, and paleomagnetic study of the meteorite ALH 84001 (pink)17. Error bars reflect uncertainties in the age estimates; points without error bars lack estimated uncertainties. With the exception of Borealis basin, the age of which has only been estimated from geochemical constraints110, the ages reported here for large basins are isochron ages108. ALH 84001 population I and II refer to two distinct groups of magnetized sources in the meteorite which place unique age constraints. Much of Mars’s Noachian and pre-Noachian terrain—including some impact basins—appears to be strongly magnetized2, suggesting the dynamo was active early in the planet’s history. Although some large basins formed after 4.1–4.0 Ga appear demagnetized, young volcanics and the paleomagnetic record of ALH 84001 may require an active dynamo as late as 3.6 Ga.

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However, other crustal magnetic and paleomagnetic observations challenge this inferred early cessation age. Some volcanics formed between 3.9–3.5 Ga appear strongly magnetized, suggesting the dynamo was active during their emplacement8,10,11,12, although in most cases the age and depth of their magnetization cannot be conclusively determined. The Martian meteorite ALH 84001 provides further insight into the dynamo’s longevity since it carries strong but heterogeneous magnetization which must postdate the rock’s crystallization at 4.1 Ga13,14,15,16. Recent paleomagnetic results show that strong magnetization was acquired during an impact event at ~3.9 Ga, almost certainly requiring an active dynamo at that time17. Together, these observations imply that the Martian dynamo was active until at least 3.9–3.7 Ga. Here we note that meteorite ages are radiometric, whereas basin and volcanic ages are derived from crater densities extrapolated from lunar craters and may therefore have significant systematic uncertainties18.

The difference between the early (~4.1 Ga) and late (≤3.9 Ga) proposed cessation ages may have important implications for Mars’s deep interior. Since Mars’s dynamo was likely powered by early core cooling—especially in light of evidence that Mars may have no inner core19,20—its longevity is fundamentally limited by deep interior cooling timescales. Although many models of the planet’s thermal history assume the dynamo shut down at 4.0 Ga21,22,23,24, some imply that certain ranges of mantle reference viscosity, core conductivity, and initial core superheating could permit a later cessation21,22,23,24. Improved estimates of Mars’s core conductivity also suggest thermal convection could power the dynamo until 3.9–3.7 Ga or later25. However, the recent detection of an enriched molten silicate layer above Mars’s core may inhibit the removal of heat from the core26,27. Due to these relationships, a more precise estimate of the dynamo’s cessation age would place valuable constraints on Mars’s thermal history and deep interior structure.

A longer-lived dynamo would also have important implications for Mars’s climate history. Whether early Mars was warm and wet28 or cold and icy29,30,31, the planet underwent a significant climate shift following the loss of more than 66% of its atmosphere32. An early dynamo cessation would pre-date the formation of Martian valley networks between 3.8 and 3.5 Ga33,34,35 by at least 0.4 billion years, suggesting the dynamo was not necessary for the planet to maintain its early atmosphere. In contrast, a later dynamo cessation may imply a closer relationship between the early Martian dynamo and the planet’s climate. Defining the precise lifetime of Mars’s dynamo would provide critical empirical context regarding the relationship between dynamo action and atmospheric loss, potentially informing which processes predominantly drove the loss of Mars’s early atmosphere (see Note S2 for a detailed discussion of climatic implications).

These important implications of the dynamo’s cessation age have motivated attempts to reconcile the weak fields above large, apparently demagnetized basins with observations of younger material that could be strongly magnetized. Although it has been proposed that an intermittently active or weakened dynamo could account for both sets of observations8,36, this would require forming tens of large weakly magnetic basins in a short window between 3.7–4.1 Ga5,6. Reinitiating dynamo action after cessation could be possible24 but may have been prohibitively difficult37,38.

Another proposed possibility is that large Martian impact basins formed in a reversing field39. Because each of these basins cooled over 10–500 Myr timescales, different sub-volumes of cooling material acquired their respective magnetizations at different times. In principle, this would lead to the formation of oppositely magnetized sub-volumes within the basin, the magnetic fields from which would partially cancel out at spacecraft altitudes39.

This possibility is particularly compelling in light of independent evidence for a reversing Martian dynamo. Paleopole inversion studies of orbitally mapped magnetic fields infer clusters of poles separated by >130°, typically interpreted as evidence that the global field reversed, although the fundamental non-uniqueness of such inversions introduces substantial uncertainties11,40,41,42. More robustly, a recent paleomagnetic study of the Martian meteorite ALH 84001 identified two populations of mineral assemblages magnetized in two directions separated by ~140°, likely representing a record of ancient Martian polarity reversals17.

This evidence motivates renewed consideration of reversals as a mechanism for producing weak magnetic fields over large Martian impact basins. Although Rochette (2006) previously proposed this concept39, no study to-date has quantified the expected magnetic signal of such basins at spacecraft altitudes using detailed and spatially resolved cooling models, realistic magnetic mineralogies, and a broad range of reversal histories.

In this work, we use analytical and finite element frameworks to model cooling and magnetization acquisition of Martian impact basins. We identify the range of reversal conditions that are compatible with observed orbital magnetic field signals over large basins and predict low-altitude magnetic fields structures that, if observed in future surveys, would strongly constrain the time history of the Martian dynamo.

Results

Analytical approximation

We begin with the results of our simple analytical model of a shallow region magnetized in a reversing field (see Methods). Here we consider the magnetic field signal from a uniformly magnetized, near-surface volume of material within a basin that acquired magnetization before the first reversal. As a first-order approximation, this volume dominates the total magnetic field signal because cooling rate increases with depth, and therefore (1) the layers of coherent magnetization are thinner at greater depths and (2) single parcels of deeper material may cool over multiple polarity chrons, resulting in a smaller per-volume magnetization.

Setting the conductive cooling timescale equal to the average chron duration, we find that the thickness of this magnetized layer, and therefore the final field strength, should scale with reversal frequency f as \(\sqrt{\frac{1}{f}}\). The upper bound on field strength is set by the Curie depth (about 50 km for the expected magnetite-bearing mineralogy43), where equilibrium temperatures are too high to retain magnetization. This relationship therefore predicts that Earth-like reversal frequencies of >1.5 Myr−1 would reduce field strengths by an order of magnitude compared to a non-reversing case. Although this result forms a point of comparison and encourages further analysis of the reversal-magnetic field relationship, the simple underlying model does not include magnetization geometry or the expected variance in field strength for different random reversal histories.

Numerical approach

Motivated by these analytical results, we employed a finite element numerical approach to characterize the magnetic signatures of basins cooled in reversing dynamo fields (see Methods). For each modeled basin, our process involved five steps (Fig. 2). First, we computed the initial post-impact temperature field using published analytical scaling laws44 or hydrocode impact simulations, depending on the size of the basin. Second, we used finite element methods to simulate basin cooling after the end of any convective phase. Third, we computed the post-cooling magnetization of each sub-volume within the basin from the assumed unblocking temperature spectrum and reversal history. Fourth, we simulated the demagnetizing effects of subsequent impacts and, fifth, computed the magnetic field arising from the final magnetization configuration. We used this process to model final magnetization structures and magnetic fields at 200 km altitudes for impact basins with diameters from 200–2200 km, each for 420 random reversal histories with mean frequencies between 0–10 Myr−1.

Fig. 2: Illustration of the process for calculating basin cooling and magnetization acquisition.
figure 2

An illustration of the process by which cooling and magnetization acquisition were simulated for an example 1000 km diameter basin and magnetic maps were produced for different reversal histories in this work. A We began by calculating a post-impact temperature field for each basin by the process outlined in Abramov et al. 44 or using hydrocode simulations and (B) then calculated the temperatures of melted material at the end of convection. C We then simulated the basin’s cooling using a conductive finite element thermal evolution model. D The thermal history of each voxel was then used to compute its magnetization history, which we then paired with a random reversal history to calculate the net magnetization of the voxel. E Demagnetization from excavation by a random population of late impacts consistent with a 4.075 Ga formation age was then added to the domain52. F By summing the contributions of each voxel to the magnetic field at 200 km altitude—or lower for analysis of low-altitude field geometries—we produced a map of the magnetic field at specified altitude above the simulated basin.

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General relationships between reversal history, magnetization, and magnetic field

We found that reversals efficiently reduced the field strengths above large basins over a broad range of reversal rates. Even reversal frequencies as low as 0.1 Myr−1 could sometimes reduce the strongest 200 km altitude fields by an order of magnitude compared to an identical basin cooled in a uniform field (Fig. 3). Basin fields were reduced even further when reversals were frequent.

Fig. 3: Magnetization and magnetic field maps for an 800 km diameter basin cooled in a nonreversing dynamo, a slowly reversing dynamo, and a rapidly reversing dynamo.
figure 3

Simulated maps of an 800 km diameter basin for a non-reversing field and two sample reversal histories with different characteristic reversal rates showing (A) the simulated vertical magnetic field (Bz) at 200 km altitude, (B) the simulated vertical magnetic field at 10 km altitude, and (C) a profile of the net magnetization beneath the basin along a transect from the basin’s center to its final radius. The dashed and dotted lines in all panels indicate the rim-to-rim radius of the transient crater (RTR) and the final basin radius (Rfinal), respectively. Even relatively infrequent reversals significantly reduce the amplitude of basin fields, with more rapid reversals weakening fields even further. Although complex field structures are present in low-altitude magnetic maps, high-altitude field morphologies are generally dipolar. See Note S3 for versions of this figure for other basin sizes (Figs. S1–S5).

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Comparing the final magnetic field maps to their corresponding magnetization profiles (Fig. 3), we found these trends were driven primarily by the development of alternating-polarity layers within the cooling material. For rapid reversals, this effect was compounded by an overall decrease in net magnetization, arising because sub-volumes of material acquired magnetization over multiple polarity chrons when reversals were sufficiently frequent.

At 10 km altitude, these complex magnetization polarity structures produced magnetic stripes with characteristic length scales that decreased from ~100 km to ≤1 km with increasing average reversal frequency (Figs. 3 and S1–S5). If detected, these structures would be strong evidence for reversals. However, late remagnetization processes such as late impacts could disrupt these characteristic structures and cause large areas within the basin to appear weakly or randomly magnetized. Long (~100 km) magnetic mapping transects at or below 10 km altitude (e.g. by balloons or helicopters45) may therefore be required to determine the strength and variability of the magnetic field during basin formation.

Nearly all of this fine field structure was smoothed to simple morphologies at spacecraft mapping altitudes (Figs. 3 and S1–S5). This reflects the fact that the resolvable spatial scale of magnetic field structure is approximately equal to the altitude of the measurement, representing a fundamental limitation of orbital magnetic field measurements.

Quantifying relationships between reversal rate, basin size, and field morphology and strength

To understand the extent to which these relationships generalize to other reversal histories and basin sizes, we consider trends across the range of basin sizes and tested reversal histories.

We first consider the morphologies of the remanent magnetic fields. Comparing radial profiles of magnetic field strength, two regimes of field geometry emerge. For basins with diameters ≤1000 km, where the lateral extent of magnetization was not significantly greater than the 200 km mapping altitude, field morphologies were generally dipolar and relatively consistent across reversal histories (Figs. 3 and 4). Any relationship between mean reversal rate and field geometry for these basins would therefore likely not be observable from orbit.

Fig. 4: Normalized radial magnetic field profiles for basins with diameters of 200 km, 800 km, and 2200 km.
figure 4

Radial profiles of the normalized magnetic field strength simulated at 200 km altitude above (A) 200 km, (B) 800 km, and (C) 2200 km diameter basins. Each blue line represents one tested reversal history and the dashed line marks one basin radius. The red line in each plot corresponds to the profile from an example 200 km altitude Bz map for each basin size, shown at right. The dashed line in each example map marks the final basin diameter. High-altitude field morphologies of 200 km and 800 km basins are consistent across most tested reversal histories, with field strengths peaking close to the basin center. In contrast, the 2200 km diameter basin displays much greater variability in field geometry, with peak fields more typically occurring close to the basin’s rim. Peak fields restricted to near the basin’s rim may overlap substantially with signals from adjacent structures, making larger basins more likely to appear demagnetized in high altitude measurements.

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High altitude field geometries for the simulated 2200 km basins were much more varied and significantly less dipolar. Unlike for smaller basins, where field strengths peaked close to the basin’s center, peak fields above these very large basins typically occurred closer to the crater rim, with fields near the center weaker by a factor of 5–10 (Figs. 4 and S5). These weak fields arise because the 200 km mapping altitude is much smaller than the basin size; in this case, near the basin center the layers of magnetization within the basin below appear approximately like uniformly magnetized infinite sheets, which produce no external field. Since basins are typically classified as magnetized or demagnetized by comparing the field strengths in the basin’s interior to those outside5,6, often excluding fields near the basin rims, this morphology could make very large basins far more likely to be misclassified as demagnetized.

Field strength at 200 km altitude was much more stochastic than field morphology and displayed a much stronger dependence on reversal history. For all basin sizes, we found that the peak field strengths decreased with increasing reversal rate up to 10 Myr−1 (Fig. 5), consistent with expectations from previous work39 and our earlier analytical approximation. Even infrequent reversals substantially reduced fields at orbital altitudes; for a given basin size, reversal rates as low as 1.5 Myr−1 typically yielded a ~5–10 × attenuation compared to the non-reversing case.

Fig. 5: Magnetic field strength as a function of mean reversal frequency for basins with diameters of 200 km, 800 km, and 2200 km.
figure 5

Peak magnetic field strength (black) and magnetic field strength at the basin center (red) at 200 km altitude versus mean reversal frequency for basins with diameters of 200 km (top), 800 km (center), and 2200 km (bottom). Plotted points assume a saturation remanence intensity of 0.1 A m2 kg−1, and blue arrows indicate the peak field value at zero reversals for that case. The lines show the best-fit curves to the peak field strength data for each basin size, following a square root of reversal frequency relationship as predicted by our analytical approximation, for saturation remanences (MRS) of 0.02 A m2 kg−1 (solid), 0.04 A m2 kg−1 (dashed-dotted), 0.1 A m2 kg−1 (dashed), and 0.5 A m2 kg−1 (dotted).

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However, increasing the mean reversal rate above 1.5 Myr−1 had a diminishing impact on peak field strength. This slower decline at higher mean reversal rates matched the predictions of our simple analytical model, suggesting this trend reflects the persistent magnetic contribution of shallow material; even at the highest tested reversal rates, several kilometers of material typically cooled before the first reversal. This validates the approximation in our analytical model and suggests the magnetization of the layer cooled in the first polarity chron has an outsized effect on the final magnetic field strength, especially at high reversal rates.

Although peak fields generally decreased with increasing reversal frequency, values at any given mean reversal rate varied by approximately an order of magnitude. This confirms that the specific timing of reversals—especially those occurring soon after the basin’s formation—could be just as important for the final basin field strength as their characteristic frequency. Despite this variability, the modeled peak fields above basins cooled in reversing fields were nearly always significantly weaker than those above a uniformly magnetized basin (Fig. 5). Depending on basin size, 81–96% were weaker by more than a factor of 2 and 45–83% were weaker by more than a factor of 5. For reversal rates > 1.5 Myr−1, >99% of basins were weaker by more than a factor of 2 and 61–98% were weaker by more than a factor of 5. This suggests reversals occurring at virtually any rates could have substantially reduced the magnetic fields above Martian basins.

Estimating the likelihood that basins are misclassified as demagnetized

We next estimated the likelihood that our modeled basins, magnetized in reversing fields, would be misclassified as demagnetized based on orbital magnetic field data. Since this work neglects contributions from heterogeneously magnetized surrounding material, we do not classify basins as magnetized or demagnetized based on the ratio of field strengths inside and outside of the basin5,6. Instead, we adopt a threshold peak field strength of 5 nT at 200 km altitude below which we expect that a basin would be classified as demagnetized. Since typical crustal fields at 200 km altitude range from 5–500 nT above unambiguously magnetized terrain3, basins with peak fields below 5 nT in this work would likely be misclassified as demagnetized regardless of the specific classification method.

In this framework, the relationships between mean reversal rate and peak basin field strength could be used to estimate the likelihood that a reversing dynamo could have produced Mars’s large weakly magnetic basins. Specifically, we used our model output to quantify the probability that a basin of a given size cooled in a particular reversal regime would be misclassified as demagnetized.

The probability of this misclassification depends also on the magnetic properties of the target material. Most important is the assumed saturation remanent magnetization intensity MRS, which relates the net fractional magnetization modeled at each location to the predicted field strength. Despite its importance, this property is highly uncertain, with saturation remanence intensities inferred from Mars’s crustal fields and observed in Martian meteorites spanning multiple orders of magnitude. Saturation remanence intensities range from 6 × 10−4−1.9 A m2 kg−1 among magnetically characterized Martian meteorites with a median of 0.05 A m2 kg−143,46. The corresponding intensity of thermoremanent magnetization acquired in a 50 µT field would range from 0.04 to 97 A/m with a median of 2.7 A/m. This is substantially lower than the 15–60 A/m magnetization intensities inferred for the strongly magnetic Terra Cimmeria and Terra Sirenum3,46,47, implying that these high values may be restricted to small areas of Mars’s crust.

Because excavation during the impact may remove most crustal material48, selecting an appropriate saturation magnetization intensity is further complicated by the poorly constrained magnetic mineralogy of Mars’s mantle. If cool, uplifted mantle material is much less magnetic than the crust, as has been previously proposed8, saturation remanence intensities relevant to large impact basin magnetism may be much lower than inferred typical crustal values.

We considered four values for saturation remanence intensity and evaluated the expected orbitally-measured magnetic field intensities in each case. For magnetic properties similar to the strongly magnetic southern highlands, we would predict >800 km diameter basins to only rarely appear demagnetized regardless of reversal rate. Some 200–800 km diameter basins would also appear magnetized. In this case, a dynamo cessation may be necessary to produce the tens of observed weakly magnetic large basins5,6.

If saturation remanence intensities were instead comparable to average Martian crust, we would expect both strongly and weakly magnetic >800 km basins to occur over a broad range of mean reversal rates, with the dynamo’s specific reversal history determining whether a given basin would appear magnetized (Figs. 5 and 6). In this scenario, nearly all smaller basins would appear demagnetized at reversal frequencies ≥0.1 Myr−1. Additionally, because the largest basins have weak fields in their interiors, considering just the peak field strength likely overestimates the fraction of basins that would be classified as demagnetized (Fig. 6). In this case, it may still be possible to produce tens of apparently demagnetized basins for sufficiently high mean reversal frequencies.

Fig. 6: Fraction of basins which would appear demagnetized as a function of reversal rate.
figure 6

The fraction of simulated basins in each mean reversal rate bin that would be classified as demagnetized for two different late remagnetization cases and three different saturation remanent magnetization values. In this analysis, a basin is classified as demagnetized if its peak field (solid line) is below 5 nT at 200 km altitude. However, if the field above the basin center (dashed line) is much lower than the peak field—often the case for the largest basins modeled here—a basin may be misclassified as demagnetized even if the peak field strength is much higher. The likelihood of producing a weakly magnetic basin at a given reversal rate varies substantially depending on the assumed saturation remanent magnetization value. The degree of late remagnetization also has a pronounced effect; compared to a case where the only remagnetization is due to excavation by late impacts (top), demagnetization of the top 2 km (bottom) would significantly increase the predicted likelihood of producing a weakly magnetic basin.

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However, it has recently been proposed that excavation may play an important role in the interpretation of crustal field signatures and may offer an explanation for the observation that most basins appear demagnetized48. If excavation is efficient and Martian mantle material has a similar saturation remanence intensity to most Martian meteorites43 and the Earth’s mantle49, we find that essentially all basins would appear demagnetized at 200 km altitude for reversal rates >1.5 Myr−1 (Figs. 5 and 6). This suggests that the uplift of less magnetic, mantle-derived material, combined with reversals, can explain the population of apparently demagnetized Martian basins. Although producing such weakly magnetic basins in a non-reversing dynamo field would require extremely small NRM intensities of <0.25 A/m, the combined effects of excavation and magnetic reversals could efficiently produce apparently demagnetized basins.

Exploring the sensitivity of our model results to other parameters, we also considered the effects of different assumed unblocking spectra. The two most common magnetic minerals in Martian meteorites are pyrrhotite and magnetite43 which have Néel/Curie temperatures that differ by about 250 °C (approximately 320 and 580 °C, respectively). This could have significant implications for both the duration and maximum depth of magnetization acquisition. We found that changing from the pyrrhotite-dominated thermal unblocking spectrum of Tissint to a pure-magnetite endmember (Fig. 7) for a test 800 km diameter basin increased the 50% blocking depth by ~22% and increased the mean peak field by 15% on average. Similarly, the poorly constrained early Martian temperature-depth profile had a weak effect on modeled field strengths. For a test 800 km basin, varying the background heat flux from 35 mW m−2 to 70 mW m−2 changed the 50% blocking depth from 42 to 30 km, but only changed the mean peak field by <1% on average (although the peak field of the nonreversing case was reduced by half). Physically, these low sensitivities arise from the fact that deep material is likely to have a small net magnetization under almost any reversal scenario due to its slow cooling.

Fig. 7: Thermal unblocking spectra used in this work.
figure 7

The thermal demagnetization curves, or unblocking spectra, for Tissint (black)101 and magnetite (red)104 used in this work.

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Another potentially important process is melt migration. Although we model conductive heat transport beginning after convective lockup of the melt pool (see Methods), up to 40% melt by mass may be present until material cools to the solidus. Buoyant melt sourced from sub-solidus regions of the impact structure transports heat as it rises until it is erupted or emplaced closer to the surface. This process decreases cooling timescales for super-solidus material at depth but effectively increases the cooling timescales of sub-solidus material, slowing magnetization acquisition. Since modeling suggests melt migration can persist in large basins for 107−108 years50,51—timescales comparable to typical conductive cooling timescales within the basin—melt transport may cause material above the Curie depth to cool more slowly than projected over much of the basin’s cooling history.

Melt migration could have a particularly important effect on near-surface magnetization. Since the upper few kilometers of material are completely magnetized in just ~105 years in our baseline model, the magnetic contribution of the near surface could dominate the basin’s final magnetic field at high reversal rates. However, because melt can be brought to very shallow depths (or even erupted), it could reset some fraction of this shallow magnetization long after it was initially magnetized, potentially in a distinct field polarity. Depending on the extent and geometry of melt emplacement, this process could substantially reduce the magnetization of large basins.

A related potentially important effect is remagnetization after basin formation. Although shallow material may initially contribute disproportionately to the final basin field, it is susceptible to re- or demagnetization by late modification processes including impacts, aqueous alteration, volcanism, and erosion. We therefore included excavation by late impacts predicted for a 4.075 Ga formation age52, effectively demagnetizing ~10% of the upper 2 km or ~5% of the upper 10 km. This produced a median ~5% decrease in the peak field for all tested basin sizes and would be even less important for basins younger than 4.075 Ga.

Although this would seem to suggest late impact excavation had only a small effect on large basin magnetism, our approach represents a lower bound on late remagnetization. Heating and pressure during late impact events would substantially increase the remagnetized volume in each impact. More heterogeneous processes such as volcanism, erosion, and alteration could remagnetize even greater fractions of the near surface, with some authors estimating that alteration alone could remagnetize the entire upper few kilometers46. If these late modification processes either removed magnetic material or produced extensive demagnetization, they could substantially reduce the magnitude of basin fields. The heterogeneous and relatively weak near-surface fields may make late modification processes more likely to result in demagnetization (Figs. 3, S1–S5). Demagnetizing the top 1–4 km would reduce peak fields above simulated basins by >25% compared to late impact excavation alone (Fig. 6). If the mantle is relatively non-magnetic and late demagnetization of the near surface is efficient, we might expect upwards of 80% of large basins to appear demagnetized at 200 km altitude. Constraining the extent, distribution, and timing of remagnetization may therefore be key to predicting the field strengths above specific large impact basins in future work.

Deeper material could also be remagnetized by deep alteration and magmatic intrusions. These processes would likely have a smaller effect on the overall magnetic field strength since material at depth is typically already less magnetic, but could introduce additional heterogeneities in the field (similar to those produced by late impacts) which could be observable at low altitudes.

Sensitivity of results to method of generating post-impact thermal profiles

We used both analytical scaling laws and hydrocode impact simulations to generate post-impact temperature fields due to the large range of basin sizes explored (see Methods). Here we compare the consistency between the two methods for 800 km diameters basins where both approaches are applicable. For a nonreversing dynamo, peak fields differed by only ~7%, suggesting both approaches agree on the approximate volume of impact heating. This difference grew to ~15% for a dynamo reversing at 1–10 Myr−1. Analytical scaling laws underestimated both the magnitude and spatial extent of heating, especially near the surface, but this resulted in only moderately different peak fields. The magnetic field morphologies at 200 km were similar between the two approached. (Fig. 8).

Fig. 8: Comparison of thermal conditions and the resulting magnetic fields for analytical and hydrocode approaches to calculating post-impact heating.
figure 8

Comparison of thermal conditions immediately post-impact for a 800 km diameter basin from (A) analytical scaling laws44 and (B) a hydrocode impact simulation. We also show example magnetic field maps resulting from post-impact temperature profiles generated from (C) analytical scaling laws and (D) hydrocode simulations, as well as (E) the final peak fields as a function of men reversal rate for both methods of estimating post-impact temperature conditions. For this test 800 km basin, hydrocode simulations predicted a larger volume and magnitude of heating, resulting in a small but systematic shift in the final estimated peak field strengths.

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These results suggest our analytical scaling-based calculations (used in this work for 200–1000 km diameter basins) may underestimate peak field strengths by ~15%. Because this is primarily a result of excess shallow heating, any remagnetization of the near surface would reduce this discrepancy. Analytical post-impact thermal conditions therefore remain a valuable tool for understanding key first-order effects of a reversing dynamo on magnetic fields produced by smaller basins.

Sensitivity of results to impact angle

The final basin diameter depends on the heating volume and is only a weak function of the impact angle53,54. However, our assumption of axisymmetry may still affect our results since variation in the distribution of heat with impact angle55 is not explicitly captured in our axisymmetric simulations. This may introduce additional complexity into the structure of basin magnetization, especially for very low impact angles.

The net effects of this asymmetry on the final magnetization structure can be summarized as 1) an offset between the shallow and deep magnetization regions and 2) a slight distortion of the whole thermal anomaly55. This could yield more complex geometric effects on basin magnetic fields for slow reversals, where the geometry plays a key role in the magnetic field attenuation. However, for rapid reversals where net magnetizations are typically small at depth, geometry plays a minimal role in field attenuation since the overall magnetic field is dominated by contribution of the near-surface. Accordingly, for the range of reversal rates with high probabilities of producing weakly magnetic basins, the dominant effect would be an offset and distortion of the region of the shallow material which cools during a single chron.

Changes to the shape of this upper layer may yield more complex magnetic field structures, especially at low mapping altitudes. However, because heating and melting volumes should be similar regardless of impact angle53,54, and cooling timescales are foremost a function of depth, the volume of material cooled in the first chron should not vary significantly with impact angle. This would imply that even highly oblique impacts should yield comparable peak field strengths.

Discussion

In summary, we modeled the cooling and magnetization of Martian impact basins with diameters between 200–2200 km in magnetic fields reversing at average frequencies of 0–10 Myr−1. Our results affirm that a reversing Martian dynamo, for which there is evidence from crustal magnetic fields and meteorite paleomagnetism, can reduce basin field strengths at orbital altitude by more than an order of magnitude. This process may be particularly effective if Mars’s mantle has magnetic properties similar to the Earth’s mantle or most Martian meteorites43,49; in this case, most basins—including most very large basins with diameters >800 km—should appear demagnetized if the dynamo reversed at rates ≥1.5 Myr−1 (Fig. 6). Very large basins with diameters ~2000 km or larger may be even more likely to appear demagnetized since their peak fields typically occur close to their rims, exceeding field strengths in their centers by a factor of 5 to 10 (Figs. 4 and S5). Ultimately, these results imply that satellite magnetic field measurements alone cannot distinguish basins formed in a reversing dynamo from basins formed after the dynamo’s cessation. Weakly magnetic impact basins—and particularly Mars’s very large basins—therefore do not require the Martian dynamo to have been inactive during their formation.

By identifying a mechanism to form apparently demagnetized basins while the dynamo was active, we remove the strongest argument in favor of an early, ≥4.1 Ga dynamo cessation. A Martian dynamo persisting until 3.9–3.7 Ga and reversing at characteristic frequencies above ~1.5 Myr−1 could simultaneously satisfy magnetic constraints from large impact basins, young volcanics, and the meteorite ALH 84001. Because the occurrence of reversals seems necessary to reconcile these lines of evidence, we further conclude that the ancient Martian dynamo likely underwent reversals unless an alternative mechanism is identified to produce weakly magnetic impact basins prior to the dynamo’s cessation.

A dynamo persisting beyond 3.9 Ga would require long-lived core convection. Although core crystallization is not a likely power source for the dynamo, especially if Mars does not have a solid inner core19,20, appropriate mantle reference viscosities, core conductivities, and initial core superheating could allow a thermal dynamo to persist beyond 4.0 Ga21,24. Recent experiments have also shown that the predicted 1.3–3.5% O content for a Martian core containing 14–19% S should yield a lower core thermal conductivity than previously expected56,57, potentially permitting an even longer-lived dynamo. If the dynamo was reversing, this could place additional constraints on the nature of core convection, since reversals in dynamo experiments and simulations have been connected to a specific range of Rayleigh and local Rossby numbers58,59.

A dynamo persisting until 3.9–3.7 Ga would also likely produce a different atmospheric escape history than one ceasing before 4.1 Ga. Constraints from Mars’s modern D/H ratio and estimated exchangeable water inventory over time suggest Mars lost an 80–1500 m global equivalent layer (GEL) of water (see Note S2).

The timing and mechanisms by which Mars lost such a large volume of water are uncertain. Although H can be removed efficiently by thermal escape mechanisms, which operate independently of the planet’s magnetic field60, ion escape processes may have driven significant loss of O+ and other heavy ions to space61. The efficiency of ion escape processes varies depending on the solar wind intensity and the global field’s strength and structure. In the absence of a planetary magnetic field, it is estimated that the solar wind could have removed O equivalent to a 10–70 m GEL of water in the first 150 Myr of Mars’s history62. Since models suggest that an Earth-strength dynamo could decrease ion loss by a factor of a few under early solar system conditions61, shifting the dynamo’s cessation from 4.1 to 3.6 Ga could prevent the escape of most of this water before the end of the Noachian, consistent with evidence for valley network formation persisting until 3.5 Ga or later34.

On the other hand, a dynamo with intermediate strength may have instead enhanced ion escape through the polar caps and cusps and thereby facilitated early O loss61. In this case, a long-lived, weak dynamo could have led to the loss of O equivalent to ~20 m GEL water during the 4.1–3.6 Ga interval (see Note S2). Overall, this suggests that the contribution of Mars’s intrinsic magnetic field may be an important, albeit poorly constrained, element of Mars’s lifetime O and H2O budgets.

Finally, a long-lived and reversing dynamo would have important implications for the interpretation of crustal fields elsewhere on Mars. A reversing dynamo is compatible with the moderately strong fields observed over much of Mars’s surface since most features cool much more quickly than large impact basins (virtually all other geologic features are much smaller and/or episodically emplaced in thin, fast-cooling layers) and will therefore experience lower degrees of field attenuation. Furthermore, as previously discussed, impact basins may be systematically less magnetic than most Martian crust due to the excavation of crustal material. However, crustal fields in excess of 500 nT at 200 km altitude above Terra Cimmeria and Terra Sirenum may be difficult to reconcile with a frequently reversing dynamo. These regions require magnetizations >20 A/m—equivalent to saturation remanence intensities of 0.4 A m2 kg−1 in a 50 µT magnetizing field—even for a thick 30 km magnetized layer47,63. If they were magnetized nonuniformly through multiple polarity chrons, the saturation remanence intensity would have to be even higher. Although this terrain may have formed by a process allowing more rapid cooling, such as emplacement of layered volcanic deposits, these strong fields may ultimately imply that the dynamo was reversing infrequently when these regions formed. Future modeling of the cooling and magnetization of these regions, which have surface ages younger than the early and mid-Noachian formation ages of most large impact basins64, could provide insight into changes in the dynamo’s average reversal rate over time.

Our results from simulated low altitude magnetic mapping motivate future low altitude or surface magnetic measurements of Martian impact basins. Reversals produce characteristic alternating striping in the magnetic field at low altitudes (Fig. 2), with more rapid reversals yielding thinner stripes and overall weaker field strengths. Therefore, mapping at altitudes less than tens of kilometers by rovers, helicopters, or balloons45 could be used to determine the existence and timing of Martian dynamo reversals. However, these structures can be disrupted and masked by late remagnetization of the near surface and short measurement transects could recover uniformly weak fields, compatible with observations of <5 nT surface fields from the Zhurong rover65 (for further discussion of constraints from Zhurong data, see Note S4 and Fig. S6). To conclusively distinguish between an inactive and reversing dynamo, low-altitude magnetic transects would have to span relatively long distances (~100 km). More sophisticated modeling will ultimately be necessary to fully characterize expected low-altitude fields above specific basins.

The simple approach to modeling basin thermal evolution in this work neglects several potentially significant elements of heat transport including secular planetary thermal evolution, explicitly modeled mantle convection, melt migration, and hydrothermal circulation. For most of these processes, we would not expect a more detailed treatment to result in significant changes to the final magnetization state either because their effects are minimal over ~100 Myr basin cooling timescales (e.g. secular cooling) or the affected regions are deep and therefore typically weakly magnetized for any reversal rates which significantly reduce basin fields (e.g. mantle convection). However, processes such as melt migration and hydrothermal circulation may prolong cooling in the near surface, resulting in greater field attenuation than predicted here. We may therefore underestimate the efficiency of magnetic field attenuation (see Results and Note S6.3 for further justification and discussion). Future work including these effects, as well as the impact of preexisting magnetization and additional post-impact remagnetization processes, may permit characterization of low-altitude fields with sufficient confidence to allow inversion of Mars’s reversal history from surface or airborne measurements.

In summary, in this work we used simple thermal models to simulate the cooling and magnetization acquisition of Martian impact basins in dynamo fields with average reversal frequencies between 0 –10 Myr−1. Although even an infrequently reversing dynamo could substantially reduce basin field strengths, reversal frequencies >1.5 Myr−1 could reduce the peak fields above large basins by an order of magnitude. Because this process is highly sensitive to the assumed saturation remanence intensity, it would be particularly efficient if the uplifted Martian mantle material is relatively depleted in magnetic minerals. Given typical saturation remanence intensities of Martian meteorites and expected mantle material, and assuming Earth-like reversal rates, we would expect 50–90% of >800 km basins to appear completely demagnetized at 200 km altitude (| B | < 5 nT everywhere) even if all formed in an active dynamo. This process could be particularly efficient for very large basins, where peak fields are typically produced near the crater rim and typically exceed field strengths at the basin’s center by a factor of 5 to 10.

Our models also show that at low altitudes, basin fields display fine structure with characteristic coherence scales that vary with mean reversal rate. However, regions in the interiors of these basins can still appear weakly magnetic at low altitudes, especially for rapid reversals. Thus, low altitude measurements of large basins may be key to answering whether, and how frequently, the dynamo was reversing. The results of this work motivate development of improved models of basin magnetization including more accurate thermal modeling, more precise estimates of late remagnetization processes, and pre-impact magnetization.

Ultimately, our results suggest a long-lived and reversing Martian dynamo can satisfy all remote sensing and meteoritic constraints on Mars’s magnetic history. Unless another mechanism is identified to produce weakly magnetic impact basins prior to the dynamo’s cessation, this finding implies that the ancient Martian dynamo was likely reversing. If the dynamo persisted until at least 3.7 Ga, convection in Mars’ core may have persisted for ≥300 Myr longer than typically assumed. A long-lived dynamo also implies that atmospheric escape between 4.5 Ga and 3.7 Ga took place in the presence of a substantial global field.

Methods

Analytical approximation

We estimated the depth of the uniformly magnetized layer by solving for the depth d at which the average duration of a polarity chron equals the conductive cooling timescale \({\tau }_{c}=\frac{{d}^{2}}{k}\), where κ~10−6 m2 s−1 is the thermal diffusivity. Recasting in terms of the reversal frequency gives \(d=\sqrt{\frac{\kappa }{f}}\). Estimating a 50 km Curie depth—the depth at which equilibrium temperatures are too high for magnetization to be retained—we found that a reversing dynamo with f < 0.013 Myr-1 would typically produce basins that appear uniformly magnetized; this sets the upper limit on the volume of magnetized material.

Assuming the radial extent of remagnetization is approximately the transient crater radius (rTC)44, the volume of the resulting cylinder is given by d π \({r}_{{TC}}^{2}\). Taking NRM/MRS ~ Bpaleo/3000, appropriate for a thermal natural remanent magnetization (NRM) acquired in a magnetizing paleofield of strength Bpaleo in µT66,67, we estimated the total magnetization M and the 200 km-altitude field strength |B|200 km as

$$M\approx \frac{{{B}_{{paleo}}M}_{{RS}}}{3000}\rho \left(\pi {r}_{{TC}}^{2}\right)\sqrt{\frac{\kappa }{f}}$$
(1)
$${\left|{{{\bf{B}}}}\right|}_{200{km}}\, \approx \, \left\{\begin{array}{c}{{{{\rm{\mu }}}}}_{0}\frac{{{B}_{{paleo}}M}_{{RS}}}{3000}\rho \left(\pi {r}_{{TC}}^{2}\right)(50{{{\rm{km}}}})\, {(4\pi {\left(200{{{\rm{km}}}}\right)}^{3})}^{-1},\hfill f < \, 0.013\,{{{{\rm{Myr}}}}}^{-1}\\ {{{{\rm{\mu }}}}}_{0}\frac{{{B}_{{paleo}}M}_{{RS}}}{3000}\rho \left(\pi \,{r}_{{TC}}^{2}\right)\sqrt{\frac{\kappa }{f}}{(4\pi {\left(200{{{\rm{km}}}}\right)}^{3})}^{-1},\; \; \; \; \; \; \; \; \; \; f\ge 0.013\,{{{{\rm{Myr}}}}}^{-1}\end{array}\right.$$
(2)

The predicted peak field from this layer For ρ = 3000 kg m−3, κ = 10−6 m2 s−1, and Bpaleo = 50 µT, and for rTC in km and f in Myr−1, the final field strength at 200 km altitude is approximately

$${\left|{{{\bf{B}}}}\right|}_{200{km}}\, \approx \, \left\{\begin{array}{c}0.098\,{r}_{{TC}}^{2}\,{M}_{{RS}}\ \ {{\hfill{\rm{nT}}}},\hfill f < \, 0.013\,{{{{\rm{Myr}}}}}^{-1}\\ 0.011\,{r}_{{TC}}^{2}{M}_{{RS}}\sqrt{\frac{1}{f}}{\ \ {\hfill{\rm{nT}}}},\; \; \; \; \; f\ge 0.013\,{{{{\rm{Myr}}}}}^{-1}\end{array}\right.$$
(3)

The magnetic field strength of this top layer as a function of f and MRS is plotted in Fig. S7 for a range of basin sizes.

Setting analytical post-impact thermal conditions

We began by analytically calculating post-impact temperature conditions for basins with final diameters of 200, 400, 600, 800, and 1000 km (corresponding to impactor diameters of 19, 42, 67, 93, and 120 km, respectively). First, we computed the pre-impact thermal structure in a domain containing a porous, low-conductivity surface layer that overlies intact crust, lithospheric mantle, and asthenospheric mantle layers with thermal and material properties described in Table 1. The resulting unperturbed thermal profiles assumed a fixed equilibrium surface temperature of 210 K29 and a constant heat flux of 35 mW m−2 (Fig. S8), appropriate for Mars between 4.2–3.8 Ga68.

Table 1 Domain thermal parameters
Full size table

To calculate the post-impact temperature perturbations for each basin size, we followed the approach of Abramov et al. 44. First, we calculated the pressure produced by the impact using an expression for specific waste heat \(\Delta {E}_{w}\) derived from the Murnaghan equation of state69:

$$\Delta {E}_{w}= \frac{1}{2}\left[P{V}_{0}-\frac{2{K}_{0}{V}_{0}}{n}\right]\left[1-{\left(\frac{{Pn}}{{K}_{0}}+1\right)}^{-1/n}\right]\\ +\frac{{K}_{0}{V}_{0}}{n(1-n)}\left[1-{\left(\frac{{Pn}}{{K}_{0}}+1\right)}^{1-(1/n)}\right]$$
(4)

where P is the peak shock pressure, K0 is the adiabatic bulk modulus at zero pressure, n is the pressure derivative of the bulk modulus, and V0 is the specific uncompressed target volume (1/ ρt) for an uncompressed target density ρt. We set K0 = 19.3 GPa, n = 5.5, and ρt = 3000 kg/m3 70,71, consistent with a basaltic lithology. Assuming the center of the impact (and source of the shock) is at a depth of approximately one impactor radius, and an isobaric core extends to approximately an impactor radius around that point, we calculated pressure as a function of distance r from the impact center using the power law55:

$$P=A{\left(\frac{r}{{R}_{p}}\right)}^{-k}$$
(5)

where Rp is the radius of the projectile, A is pressure at \({r=R}_{p}\), and k is the decay exponent which varies with impact velocity vi:

$$k\, \approx \, 0.625{{\mathrm{log}}}\left({v}_{i}\right)+1.25$$
(6)

where vi is given in km/s72. In this work, we assumed an impact velocity of 10 km/s, appropriate for Mars73. The term A in Eq. (5) depends on both the impactor velocity and impact angle55,74:

$$A=\frac{\rho {v}_{i}^{2}}{4}\sin \theta$$
(7)

where ρ is the impactor and target density, which we assumed to be the same, and θ is the impact angle which we took to be 45° since this is the most probable value75.

Next, Rp was derived from the desired final crater diameter. We first calculated the rim-to-rim diameter of the transient cavity Dtr which is related to the desired final diameter D by the following equation:

$$D=0.91\frac{{D}_{{tr}}^{1.125}}{{D}_{Q}^{0.09}}$$
(8)

where DQ is the simple-to-complex transition diameter, which we assumed to be 8 km for early Mars76. Next, we calculated the apparent diameter of the transient crater Dtc by assuming Dtr is approximately 1.2 times the apparent diameter of Dtc77. We then used the Pi-group scaling laws78,79 corrected for impact angle80, assuming the target and impactor had the same density, to solve for Rp:

$${R}_{p}=\frac{1}{2}{\left(\frac{{D}_{{tc}}}{1.16}{v}_{i}^{-0.44}{g}^{0.22}{\sin }^{-\frac{1}{3}}\theta \right)}^{1/0.78}$$
(9)

where g is the surface gravitational acceleration of Mars. We then calculated the temperature distribution from the impactor by dividing the waste heat ΔEw calculated from Eq. (4) by the specific heat capacity of the rock, assumed to be 800 J kg−1 K−1 81. To produce the final thermal perturbation from the impact, we then removed the material corresponding to the transient crater; here we assumed the transient crater was parabolic with a maximum depth of 0.25 Dtr77 and intersecting with the surface at the horizontal distance \({D}_{{tc}}/2\).

The subsurface temperature distribution was produced by adding this perturbation from the impact to the background temperature distribution, which was modified to account for the uplift of deep, warm material during basin formation. Observations of terrestrial craters suggest this stratigraphic uplift produces a maximum vertical displacement of:

$${h}_{{su}}=0.06\,{D}^{1.1}$$
(10)

where D is the final basin diameter in kilometers82. Following Abramov et al. 44, we assumed that the vertical displacement scaled linearly with depth, reaching zero at 1.25 the depth of the transient crater, and with radial distance r from the crater as (r – 0.11 D)2 to reach zero at r = 0.11 D. An example temperature distribution for a 1000 km diameter basin is shown in Fig. 2A.

Setting post-impact thermal conditions from hydrocode simulations

Although most of the basins used to constrain dynamo timing have diameters between 300–1000 km5,6, many prominent weakly magnetic basins—including the HUIA basins—are even larger. We therefore chose to simulate the cooling and magnetization of an 2200 km diameter basin, similar in size to Hellas. Because the heating from such a large basin cannot be adequately modeled using analytical scaling laws, we used initial thermal profiles computed from hydrocode impact simulations to model its cooling. We conducted a numerical impact simulation using the iSALE shock physics code83. We assumed a vertical impact with a velocity of 10 km/s and an impactor diameter of 300 km. Materials were modeled using the M-ANEOS equation of state package84,85,86. The Martian mantle and projectile were modeled using a simplified pyrolite composition87, and the 50 km thick Martian crust was modeled using updated ANEOS parameters for basalt88. Strength was modeled using a strain-rate dependent damage accumulation model89, with material parameters appropriate for mantle and basalt90. The initial thermal profile had a surface temperature of 210 K and a thermal gradient of 14 K/km that transitioned to an adiabatic profile below a lithospheric thickness of 100 km (Fig. S8). The model resolution was 20 cells per projectile radius. We approximated the effects of early viscoelastic relaxation, which should occur over relatively rapid ~1000 year timescales91, by translating the final thermal profile upward to a flat surface. We repeated this with a 100 km diameter impactor to produce a ~800 km diameter basin for comparison with results from analytical initial temperature profiles (Fig. 8).

Modeling basin cooling

This process for computing post-impact heating yields temperatures above the melting point of basalt where material is melted or vaporized by the impact. After the impact, convection within the melt pool would efficiently mix and cool the material, homogenizing its temperature distribution until the crystal fraction in the melt reaches ~0.6 and the viscosity of the material increases by two orders of magnitude92,93. Since cooling to this lockup temperature occurs over timescales of just 102–104 years50, the thermal profile outside the melt region does not evolve appreciably before lockup. We therefore began our cooling models immediately after convection ceased. To produce a post-lockup temperature distribution, we truncated the post-impact temperature distribution at the lockup temperature, which we defined as 60% of the distance between the solidus and liquidus at the relevant depth (e.g. Fig. 2B; see Note S6.2 for more details). For basaltic and Martian mantle compositions at relevant depths, typical lockup temperatures were ~1400–1500 K92,93,94,95,96,97.

We then simulated the cooling of each axisymmetric post-impact thermal profile using a finite element model built with the deal.ii library98,99,100. Our cooling models used adaptively refined meshes with 1–15 km base resolution. The depths of the domains ranged from 50 km for the 200 km diameter basin to 1000 km for the 2200 km diameter basin, chosen such that the thermal perturbation of the impact at the bottom boundary was on the order of tens of K (equivalent to a temperature increase of ~5%). This choice allowed us to capture nearly all of the heating from the impact without sacrificing spatial resolution in our cooling models. The widths of the axisymmetric domains ranged from 80 km to 2,000 km, and heating at the right boundary was negligible in all cases.

We fixed the bottom temperature to the equilibrium value throughout each cooling simulation, in line with our requirement that initial temperatures everywhere along the bottom of the domain were not significantly perturbed by the impact (for further discussion of this assumption, see Note S6.3). The thermal profile of the outer edge was fixed to the background equilibrium temperature profile throughout the simulation while a flux-free boundary condition was imposed on the central symmetry axis. The resulting system of equations to be solved with finite element methods was:

$$\begin{array}{cc}\frac{\partial T}{\partial t}-\frac{k}{\rho {C}_{p}}\Delta T=0 & {\rm{in}}\space{\Omega} \\ \widehat{{{{\bf{n}}}}}\cdot \nabla T=\frac{\sigma }{k}\left({T}^{4}-{T}_{{eq}}^{4}\right) & {\rm{on}}\space\, {\varGamma }_{1}\subset d{\Omega }\\ \frac{\partial T}{\partial {{x}}}=0 & {\rm{on}}\space\, {\varGamma }_{2}\subset d{\Omega }\\ T\left({{{\bf{x}}}},\, t\right)=T\left({{{\bf{x}}}},\, 0\right) & {\rm{on}}\space\, {\varGamma }_{3}=d\Omega {{\space{\rm{\backslash}}}}\, \left({\varGamma }_{1}\cup {\varGamma }_{2}\right)\end{array}$$
(11)

for position x = (x,y,z), time t, temperature T, equilibrium surface temperature Teq, domain Ω with boundary dΩ, top boundary Γ1, and left boundary Γ2 (the axis of symmetry). Here, σ is the Stefan–Boltzmann constant, ρ is the density, Cp is the specific heat capacity at constant pressure, and k is the conductivity.

We allowed the interior of the domain to cool conductively and imposed a radiative boundary condition at the surface. For smaller basins, the T4 dependence at this radiative boundary, where T is the local temperature, was linearized as

$${T}_{n+1}^{4} \sim {T}_{n}^{4}+4{T}_{n}^{3}\left({T}_{n+1}-{T}_{n}\right)$$
(12)

where n denotes the time step number. For the 2200 km basin, we implemented Newton iterations within each time step of our finite element model in order to more accurately include this nonlinear contribution. After the entire surface was within 5% of the equilibrium surface temperature, we implemented a Dirichlet top boundary condition for the remaining time steps. Since the surface temperature is well below the unblocking temperatures of all significant magnetic minerals, this approximation allowed us to model thermal evolution much more efficiently without sacrificing solution quality. We used the well-known theta scheme for time discretization:

$$T\, \approx \, \theta {T}_{n+1}+\left(1-\theta \right){T}_{n}$$
(13)

taking \(\theta=\frac{1}{2}\) for smaller basins and θ = 1 for the 2200 km basin, reflecting the different treatments of the radiative boundary condition.

Because we considered only conductive cooling, we defined post-impact rheologies to ensure our pre-impact thermal profiles remained in thermal equilibrium. This simplification ensured that our basin magnetization profiles did not include artifacts from re-equilibration of the background temperature profile. For basins with analytically-derived post-impact temperature profiles, we assumed the layered conductivity structure defined in Table 1 (Fig. S8). Since our thermal models were purely conductive, for these basins we parameterized convection in the mantle with a high conductivity (k ~ 100 W m−1 K−1; for further discussion of mantle heat transport, see Note S6.3)).

To match the more complex background temperature profile of the 2200 km diameter basin, we assumed a conductivity profile (Fig. S8) consistent with a heat flux of 42 mW m−2 and the pre-impact temperature profile (a thermal gradient of 14 K/km in the crust transitioning to an adiabatic profile in the mantle). We assumed the same layered structure of Cp and ρ and imposed a 1 km relatively insulating regolith layer (k = 2 W m−1 K−1) in all models (Table 1).

Cooling models proceeded for 100–300 Myr, depending on the size of the basin, after which time the temperature at every location was within 5% of the equilibrium value. We set the initial time step at 100 years and increased the length of each subsequent step by 5%. Neither shortening the initial time step nor maintaining a constant small time step size throughout the simulation significantly changed our results.

Calculating basin magnetization and magnetic fields

In this work, we adopted the well-characterized thermal unblocking spectrum of the Tissint meteorite101, a slowly cooled, depleted olivine-phyric shergottite which crystallized from a mantle source102,103. To quantify the sensitivity of our results to this choice, we also tested the thermal unblocking spectrum for pure magnetite described in Lillis et al. 104 (shown in Fig. 7 of this work). We paired the selected thermal unblocking spectrum with our simulated cooling histories to compute the fraction of magnetization blocked during each time step at each location within the basin. This fractional magnetization was then assigned a magnetic polarity based on the current dynamo state. Summing across all magnetization fractions at the end of cooling then provided the net magnetization at each location as a proportion of the total, which we label F (e.g. Fig. 2D). We then projected the resulting axisymmetric magnetization profile around the central axis to produce a final three-dimensional fractional magnetization structure.

Following this process, we computed fractional magnetization structures for each basin size for 420 random reversal histories. Each reversal history was generated by sampling from a Poisson distribution at each time step and changing the field polarity if the sampled value exceeded a set threshold. The Poisson distribution mean and threshold value were varied to produce magnetic histories with different characteristic reversal frequencies from 0–10 Myr−1, corresponding to characteristic chron durations as short as 100 kyr. This range was chosen to be comparable to Phanerozoic Earth-like reversal rates105,106, with the lowest and highest ends of the range consistent with superchron durations and periods of rapid terrestrial reversals107, respectively.

As a final step, we superimposed late impacts onto the modeled domains. As previously discussed, a quickly cooled, shallow layer can carry uniform magnetization and dominate the magnetic field signal at altitude, especially when reversals are frequent. Therefore, late modification processes such as impacts, aqueous alteration, and emplacement of volcanic materials may exert a strong control over the observed magnetism of basins despite affecting a relatively small volume. Since volcanism and alteration may be highly heterogeneous, we consider only excavation by late impacts. The excavated volume for each impact was defined as the volume of the hemispherical transient crater, where the transient crater diameter Dtc was estimated from Eq. (9).

Since the distribution of late impacts, and their resulting effects on magnetization, may be highly stochastic, we produced unique late impact distributions for each random reversal history. Each simulation result therefore represents a potential final cratering state for the modeled basin. We generated the positions and sizes of late impacts using the size-frequency distribution from Marchi (2021)52 for a main-belt asteroid impactor population and a late instability, assuming a 4.075 Ga basin formation age. Although many basins may be younger and therefore experience less remagnetization by late impacts than we model here, the overall extent of remagnetization predicted by this approach is likely always underestimated because we neglect all other sources of late demagnetization (i.e. heating, shock).

Finally, we set the magnetic properties of the domain to calculate magnetic field maps in physical units at altitude. The first of these is the saturation remanent magnetization intensity, for which we consider four values: one high value characteristic of the highest estimates for the strongly magnetized southern highlands (0.5 A m2 kg−1)46,47,63, one representative of average Martian crust (0.1 A m2 kg−1)3, one similar to the median value for Martian meteorites (0.04 A m2 kg−1)43,46, and one value comparable to Earth’s mantle and the lower quartile for Martian meteorites (0.02 A m2 kg−1)43,46. To translate this into a natural remanent magnetization intensity we assume a 50 µT magnetizing field, consistent with paleointensities inferred from ALH 8400116,17. Taking NRM/MRS ~ Bpaleo/3000, appropriate for a thermally acquired NRM in a paleofield of strength Bpaleo given in µT66,67, these saturation remanence intensities would correspond to NRM intensities of approximately 1, 2, 5, and 25 A/m. We then set the orientation of the normal polarity vector to the positive ŷ direction. The normal and reversed polarity directions were assumed to be antipodal.

To produce a final magnetic field map above the basin, we computed the vector magnetic field contribution from each grid cell (1 × 1 × 1 km for 200 and 400 km diameter basins, 2 × 2 × 2 km for 600–1000 km diameter basins, or 4 × 4 × 4 km for the 2200 km diameter basin) assuming that each is a dipolar source. The magnetic field dBi of cell i measured at location r is then defined as:

$${{{{\bf{dB}}}}}_{{{{\bf{i}}}}}\left({{{\bf{r}}}}\right)=\frac{{\mu }_{0}}{4\pi }\left[\frac{3\left({{{\bf{r}}}}-{{{{\bf{r}}}}}_{{{{\bf{i}}}}}\right)\left(\left({{{\bf{r}}}}-{{{{\bf{r}}}}}_{{{{\bf{i}}}}}\right)\cdot {{{{\bf{m}}}}}_{{{{\bf{i}}}}}\right)}{{\left|{{{{\bf{r}}}}}_{{{{\bf{im}}}}}-{{{{\bf{r}}}}}_{{{{\bf{i}}}}}\right|}^{5}}-\frac{{{{{\bf{m}}}}}_{{{{\bf{i}}}}}}{{\left|{{{{\bf{r}}}}}_{{{{\bf{im}}}}}-{{{{\bf{r}}}}}_{{{{\bf{i}}}}}\right|}^{3}}\right]$$
(14)
$${{{{\bf{m}}}}}_{{{{\bf{i}}}}}={\widehat{{{{\bf{m}}}}}}_{{{{\bf{normal}}}}}{M}_{{RS}}\,{V}_{i}\; {F}_{i}$$
(15)

ri is the location of the center of the cell, F is the net fractional magnetization (which is defined as a proportion of the maximum possible magnetization in the normal polarity direction, and can accordingly be positive or negative), V is the cell volume, and \({\widehat{{{{\bf{m}}}}}}_{{{{\bf{normal}}}}}\) is the normal polarity direction. The total magnetic field B at location r was then calculated by summing over all cells:

$${{{\bf{B}}}}\left({{{\bf{r}}}}\right)={\sum}_{i}{{{{\bf{dB}}}}}_{{{{\bf{i}}}}}({{{\bf{r}}}})$$
(16)

For field structure analysis of smaller basins at both high (200 km) and low (10 km) altitudes, we produced 1000 × 1000 km (15 km resolution) or 1500 × 1500 km (25 km resolution) field maps centered over the basin. For larger basins, 2500 × 2500 km maps with 50 km resolution were used to characterize field structure. Since peak fields at 200 km altitude nearly always occurred along the magnetization axis, we used less computationally expensive 10 × 20 km resolution field maps over a 100 × 2500 km area oriented along the dynamo polarity axis for peak field analysis.