Geodetic Inversion Research Articles

Effect of fault discretization on geodetic source inversion and usefulness of the trans-dimensional inversion approach

SUMMARYEarthquake source inversion, which estimates the heterogeneous slip distribution on fault from geophysical data, is a fundamental technique for estimating earthquake rupture process and obtaining information about the physics of fault rupture. Source inversion requires the spatial discretization of fault, which can be performed uniformly and non-uniformly. Uniform fault discretization is a conventional approach that requires smoothing and/or non-negative constraints of slips as prior information to obtain a stable and reliable solution; however, the combination of uniform discretization and these prior constraints may distort a source-inversion solution. As a non-uniform discretization approach, source inversion using a trans-dimensional inversion approach has recently attracted attention. To study the effect of fault discretization on geodetic source inversion, through the analysis of geodetic data on the 2015 Gorkha, Nepal, earthquake and synthetic tests, we investigated what kind of solution the conventional source inversion with uniform discretization and the trans-dimensional source inversion provide and what kind of uncertainty their solutions have. We found that the combination of uniform discretization and non-negative constraint led to excessively smooth solutions with poor data fit. Even without using the non-negative constraint, the conventional inversion with uniform discretization provided distorted and sometimes overfitted solutions, which could not be identified based on uncertainty information. In contrast, the trans-dimensional source inversion provided reasonable solutions composed only of meaningful slips, which were required to explain the data. We also found that uncertainty information depends on the source-inversion method; consequently, the evaluation of method-induced uncertainty is difficult. This suggests that we look at earthquake ruptures through the lens of source inversion with inherent method-dependent bias.

2000 Uglegorsk earthquake

The paper presents the results of waveform inversion of the Mw 6.8 August 4 (5), 2000 Uglegorsk earthquake (Sakhalin Island, Russia). The detailed rupture process of the 2000 Uglegorsk earthquake was simulated using the waveform inversion method. The average parameters were calculated for both nodal planes. Waveform inversion was carried out on the basis of Global Seismographic Network (GSN) data. Only P-waves from BHZ channels of all stations from the GSN were used. The simulated source parameters included a double-couple source, the scalar seismic moment, the source time function, and the slip directions. The performed studies made it possible to investigate the features of the rupture development and the amplitude of displacements along the east and west-dipping nodal planes of the August 4 (5), 2000 Uglegorsk earthquake. The obtained P-slip model for the 2000 Uglegorsk earthquake source area is in good agreement with the surface manifestations of the rupture according to the field geology data and the results of geodetic inversion.

Geodetic Model of the March 2021 Thessaly Seismic Sequence Inferred from Seismological and InSAR Data

In this work, we propose a geodetic model for the March 2021 Thessaly seismic sequence (TSS). We used the interferometric synthetic aperture radar (InSAR) technique and exploited a dataset of Sentinel-1 images to successfully detect the surface deformation caused by three major events of the sequence and constrain their kinematics, further strengthened by seismic data analysis. Our geodetic inversions are consistent with the activation of distinct blind faults previously unknown in this region: three belonging to the NE-dipping normal fault associated with the Mw 6.3 and Mw 6.0 events, and one belonging to the SW-dipping normal fault associated with the Mw 5.6, the last TSS major event. We performed a Coulomb stress transfer analysis and a 1D pore pressure diffusivity modeling to investigate the space–time evolution of the sequence; our results indicate that the seismic sequence developed in a sort of domino effect. The combination of the lack of historical records of large earthquakes in this area and the absence of mapped surface features produced by past faulting make seismic hazard estimation difficult for this area: InSAR data analysis and modeling have proven to be an extremely useful tool in helping to constrain the rupture characteristics.

Combined Geodetic and Seismological Study of the December 2020 Mw = 4.6 Thiva (Central Greece) Shallow Earthquake

On 2 December 2020, a moderate and shallow Mw = 4.6 earthquake occurred in Boeotia (Central Greece) near the city of Thiva. Despite its magnitude, the co-seismic ground deformation field was detectable and measurable by Sentinel-1, ascending and descending, synthetic aperture interferometry radar (InSAR) acquisitions. The closest available GNSS station to the epicenter, located 11 km west, measured no deformation, as expected. We proceeded to the inversion of the deformation source. Moreover, we reassessed seismological data to identify the activated zone, associated with the mainshock and the aftershock sequence. Additionally, we used the rupture plane information from InSAR to better determine the focal mechanism and the centroid location of the mainshock. We observed that the mainshock occurred at a shallower depth and the rupture then expanded downdip, as revealed by the aftershock distribution. Our geodetic inversion modelling indicated the activation of a normal fault with a small left-lateral component, length of 2.0 km, width of 1.7 km, average slip of 0.2 m, a low dip angle of 33°, and a SW dip-direction. The inferred fault top was buried at a depth of ~0.5 km, rooted at a depth of ~1.4 km, with its geodetic centroid buried at 1.0 km. It was aligned with the Kallithea fault. In addition, the dip-up projection of the modeled fault to the surface was located very close (~0.4 km SW) to the mapped (by existing geological observations) trace of the Kallithea fault. The ruptured area was settled in a transition zone. We suggest the installation of at least one GNSS and seismological station near Kallithea; as the activated zone (inferred by the aftershock sequence and InSAR results) could yield events with M ≥ 5.0, according to empirical laws relating to rupture zone dimensions and earthquake magnitude.

Southward growth of Mauna Loa\u2019s dike-like magma body driven by topographic stress

Space-geodetic observations of a new period of inflation at Mauna Loa volcano, Hawaii, recorded an influx of 0.11 km3 of new magma into it’s dike-like magma body during 2014–2020. The intrusion started after at least 4 years of decollement slip under the eastern flank creating > 0.15 MPa opening stresses in the rift zone favorable for magma intrusion. Volcanoes commonly respond to magma pressure increase with the injection of a dike, but Mauna Loa responded with lateral growth of its magma body in the direction of decreasing topographic stress. In 2017, deformation migrated back, and inflation continued at the pre-2015 location. Geodetic inversions reveal a 8 × 8.5, 10 × 3 and 9 × 4 km2 dike-like magma body during the 2014–2015, 2015–2018 and 2018–2020 periods, respectively, and an average decollement slip of ~ 23 cm/year along a 10 × 5 km2 fault. The evolution of the dike-like magma body including the reduction in vertical extent is consistent with a slowly ascending dike propagating laterally when encountering a stress barrier and freezing its tip when magma influx waned. Overall, the magma body widened about 4.5 m during 2002–2020.

Joint Inversion of Geodetic Observations and Relative Weighting—The 1999 Mw 7.6 Chi-Chi Earthquake Revisited

The Mw 7.6 Chi-Chi earthquake struck central western Taiwan in 1999. The rupture was complex with several dislocations along the 100-km long Chelungpu thrust fault. Revisiting this earthquake is a challenge, as the precision and coverage of the data sets available are quite poor. Furthermore, the topographic and vegetation coverage complexity of the area prevents coherent radar images. In this paper, radar and optical images, and terrestrial geodetic measurements, were utilised to study the fault. The Particle Swarm Optimization and Okada Inversion (PSOKINV) geodetic inversion package was used with the generalized Akaike’s Bayesian Information Criterion (gABIC) to precisely determine the slip distribution and relative weighting of datasets. Differences in results using the data sets jointly or separately (e.g., under-estimation due to InSAR, inconsistencies in SPOT offsets, smoother slip distribution with gABIC weighting) are observable. Most of the energy was released in the northern part of the fault, where the strike veers toward the east, and mainly at depths less than 4 km. The PSOKINV-gABIC approach is viable for the study of complicated cases such as the Chi-Chi earthquake and can significantly benefit the weight determination and physical realism of the fault geometry.

InSAR Evidence Indicates a Link Between Fluid Injection for Salt Mining and the 2019 Changning (China) Earthquake Sequence

AbstractIn June 2019, an earthquake sequence comprising five M > 5 events occurred in a region of southwest China with fluid injection for both hydraulic fracturing and salt mining, which raised an extensive controversy on the cause. Here we use interferometric synthetic aperture radar (InSAR) observations to determine the source parameters of the sequence and to investigate the relationship with local injection activities. Both Sentinel‐1 and Advanced Land Observing Satellite 2 SAR images are collected to measure coseismic and preseismic surface deformation. Geodetic inversions with coseismic observations show that the sequence ruptured a previously unmapped southwest‐dipping thrust fault above 3 km depth, which intersects with the open‐hole sections of wells for solution mining of salt. In the 4 months before the sequence, cumulative line‐of‐sight displacements near the wells are around 1–2 cm after correcting seasonal‐like deformation. Our results indicate that water injection likely enhanced pore pressure within the fault zone and thus contributed to inducing the sequence.

3-D joint geodetic and strong-motion finite fault inversion of the 2008 May 12, Wenchuan, China Earthquake

SUMMARYWe present a source inversion of the 2008 Wenchuan, China earthquake, using strong-motion waveforms and geodetic offsets together with 3-D synthetic ground motions. We applied the linear multiple time window technique considering geodetic and dynamic Green's functions computed with the finite-element method and the reciprocity and Strain Green's Tensor formalism. All ground motion estimates, valid up to 1 Hz, accounted for 3-D effects, including the topography and the geometry of the Beichuan and Pengguan faults. Our joint inversion has a higher moment (M0) than a purely geodetic inversion and the slip distribution presents differences when compared to 1-D model source inversions. The moment is estimated to be M0 = 1.2 × 1021 N·m, slightly larger than other works. Our results show that considering a complex 3-D structure reduces the size of large areas of 10 m slip or greater by distributing it in wider zones, with reduced slips, in the central portion of the Beichuan and the Pengguan faults. Finally, we compare our source with a relocated aftershock catalogue and conclude that the 4–5 m slip contours approximately bound the absence or presence of aftershocks.

A physics-based approach of deep interseismic creep for viscoelastic strike-slip earthquake cycle models

SUMMARYMost geodetic inversions of surface deformation rates consider the depth distribution of interseismic fault slip-rate to be time invariant. However, some numerical simulations show downdip penetration of dynamic rupture into regions with velocity-strengthening friction, with subsequent updip propagation of the locked-to-creeping transition. Recently, Bruhat and Segall developed a new method to characterize interseismic slip rates, that allows slip to penetrate up dip into the locked region. This simple model considered deep interseismic slip as a crack loaded at its downdip end, and provided analytical expressions for stress drop within the crack, slip and slip rate along the fault. This study extends this approach to strike-slip fault environments, and includes coupling of creep to viscoelastic flow in the lower crust and upper mantle. I use this model to investigate interseismic deformation rates along the Carrizo Plain section of the San Andreas fault. This study reviews possible models, elastic and viscoelastic, for fitting horizontal surface rates. Using this updated approach, I develop a physics-based solution for deep interseismic creep which accounts for possible slow vertical propagation, and investigate how it improves the fit of the horizontal deformation rates in the Carrizo Plain region. I found solutions for fitting the surface deformation rates that allow for reasonable estimates for earthquake rupture depth and coseismic displacement and improves the overall fit to the data. Best-fitting solutions present half-space relaxation time around 70 yr, and very low propagation speeds, less than a metre per year, suggesting a lack of creep propagation.

Multi-Sensor Geodetic Observations and Modeling of the 2017 Mw 6.3 Jinghe Earthquake

The Mw 6.3 Jinghe earthquake struck Xingjiang Province, China, on 8 August 2017 (05:15:04 UTC); the epicenter was near the Kusongmuxieke Piedmont Fault (KPF) of the northern Tian Shan Mountains. We used multi-source and multi-track satellite Synthetic Aperture Radar (SAR) imagery and Interferometric SAR (InSAR) techniques to reconstruct the coseismic displacement field from different line-of-sight geometries. To reduce the phase artifacts, we employed multi-temporal scenes acquired by Sentinel-1, and reconstructed the coseismic deformation through a temporal averaging strategy. Together with a single interferometric pair obtained using the Phased Array type L-band Synthetic Aperture Radar 2 (PALSAR2) sensor aboard the Advanced Land Observing Satellite 2 (ALOS2), we obtained five displacement maps with slightly different viewing geometries; all of which were used to constrain a geodetic inversion to retrieve the fault geometry parameters and slip distribution. Based on the focal mechanism and regional geology, we constructed multiple fault models that differ in dip direction (south and north dipping), and various striking angles. Both models fit the InSAR displacement maps, but have slip distributions of different depths. The slip depth of the south dipping model, with a dip of ~42°, is the most consistent with the relocated earthquake sequence and regional geological structure. Through the geodetic inversion, the maximum slip (0.25 m) occurred at 14.05 km and the associated rake was 89.56°. The result implies that the seismogenic fault is a blind thrust fault north of KPF (towards the foreland). Considering the relative locations of the suggested blind fault, the KPF, and the continuing north to south (N–S) shortening of the Tian Shan Mountains, this fault could be formed by the northward propagation of the regional fold-thrust belt.

Heterogeneous Behavior of the Campotosto Normal Fault (Central Italy) Imaged by InSAR GPS and Strong-Motion Data: Insights from the 18 January 2017 Events

On 18 January 2017, the 2016–2017 central Italy seismic sequence reached the Campotosto area with four events with magnitude larger than 5 in three hours (major event MW 5.5). To study the slip behavior on the causative fault/faults we followed two different methodologies: (1) we use Interferometric Synthetic Aperture Radar (InSAR) interferograms (Sentinel-1 satellites) and Global Positioning System (GPS) coseismic displacements to constrain the fault geometry and the cumulative slip distribution; (2) we invert near-source strong-motion, high-sampling-rate GPS waveforms, and high-rate GPS-derived static offsets to retrieve the rupture history of the two largest events. The geodetic inversion shows that the earthquake sequence occurred along the southern segment of the SW-dipping Mts. Laga normal fault system with an average slip of about 40 cm and an estimated cumulative geodetic moment of 9.29 × 1017 Nm (equivalent to a MW~6). This latter estimate is larger than the cumulative seismic moment of all the events, with MW > 4 which occurred in the corresponding time interval, suggesting that a fraction (~35%) of the overall deformation imaged by InSAR and GPS may have been released aseismically. Geodetic and seismological data agree with the geological information pointing out the Campotosto fault segment as the causative structure of the main shocks. The position of the hypocenters supports the evidence of an up-dip and northwestward rupture directivity during the major shocks of the sequence for both static and kinematic inferred slip models. The activated two main slip patches are characterized by rise time and peak slip velocity in the ranges 0.7–1.1 s and 2.3–3.2 km/s, respectively, and by ~35–50 cm of slip mainly concentrated in the shallower northern part of causative fault. Our results show that shallow slip (depth < 5 km) is required by the geodetic and seismological observations and that the inferred slip distribution is complementary with respect to the previous April 2009 seismic sequence affecting the southern half of the Campotosto fault. The recent moderate strain-release episodes (multiple M~5–5.5 earthquakes) and the paleoseismological evidence of surface-rupturing events (M~6.5) suggests therefore a heterogeneous behavior of the Campotosto fault.

Coseismic deformation and source model of the 12 November 2017 MW 7.3 Kermanshah Earthquake (Iran–Iraq border) investigated through DInSAR measurements

ABSTRACTA large earthquake with a magnitude of MW 7.3 struck the border of Iran and Iraq at the province of Kermanshah, Iran. In our study, coseismic deformation and source model of the 12 November 2017 Kermanshah Earthquake are investigated using ALOS-2 ScanSAR and Sentinel-1A/B TOPSAR Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques. Geodetic inversion has been performed to constrain source parameters and invert slip distribution on the fault plane. The optimised source model from joint inversion shows a blind reverse fault with a relatively large right-lateral component, striking 353.5° NNW-SSE and dipping 16.3° NE. The maximum slip is up to 3.8 m at 12–14 km depth and the inferred seismic moment is 1.01 × 1020 Nm, corresponding to MW 7.3, consistent with seismological solutions. The high-resolution optical images from SuperView-1 satellite suggest that most of the linear surface features mapped by DInSAR measurements are landslides or surface cracks triggered by the earthquake. Coulomb stress changes on the source fault indicating consistency between aftershock distribution and high loaded stress zones. Based on the stress change on neighbouring active faults around this area, the Kermanshah Earthquake has brought two segments of the Zagros Mountain Front Fault (MFF), MFF-1 and MFF-2, 0.5–3.1 MPa and 0.5–1.96 MPa closer to failure, respectively, suggesting the risk of future earthquakes. Recent major aftershocks (MW≥ 5.0) could probably ease the seismic hazard on MFF-2, but the risk of earthquakes on MFF-2 is still increasing.

Geodetically Inferred Locking State of the Cascadia Megathrust Based on a Viscoelastic Earth Model

AbstractIn a viscoelastic Earth, stresses slowly built up due to fault locking are relaxed concurrently during the entire interseismic period. This interseismic stress relaxation causes crustal deformation much farther away from the locked fault than can be explained using elastic models that neglect the relaxation. Here we develop a viscoelastic geodetic inversion model to address this problem at Cascadia. We invert ~500 horizontal velocity vectors based on continuous and campaign geodetic measurements over the past two decades. Ambiguities arising from long‐term rotation of upper‐plate crustal blocks are addressed by test‐correcting the geodetic velocities with two different block‐motion models. Fault back slip (i.e., slip deficit) Green's functions are derived using a Maxwell viscoelastic finite element model with realistic subduction zone structure and megathrust geometry. The preferred model features a narrow and shallow megathrust locked zone, consistent with earlier thermorheological reasoning. For an elastic model to fit the data to the same fidelity, megathrust locking has to extend to much greater depths. However, even with the viscoelastic model, the land‐based geodetic data still cannot resolve whether there is some creep (incomplete locking) in the shallowest part of the megathrust far offshore. Neither can the land data fully resolve along‐strike variations of the locking state. These ambiguities can be resolved only when adequate seafloor geodetic data are obtained.

The Impact of Realistic Elastic Properties on Inversions of Shallow Subduction Interface Slow Slip Events Using Seafloor Geodetic Data

AbstractWe examine the effects of topography and material heterogeneity on geodetic inversions of shallow slow slip at the Hikurangi Subduction Margin, New Zealand. Offshore vertical data from absolute pressure gauges constrain our results. Using a finite element code to generate our Green's functions, we find that topography has a relatively small effect, reducing the seismic potency by only about 5% when compared to a flat model. When material heterogeneity from a New Zealand‐wide seismic velocity model is taken into account, we find an extremely large effect, with the seismic potency increasing by 58% or more. In previous work, we found the opposite effect for deeper slip events, where models including elastic property variations result in ~20% more slip than when they are neglected. Our previous results for deeper events are consistent with a simplified model that considers the elastic property contrasts between a strong subducting slab and a weaker overriding plate. To understand the opposite behavior of our shallower models, we use synthetic forward models and view material property gradients in terms of additional body forces. We find that gradients in elastic properties can produce very different surface displacements near the source than simple contrasts, thus explaining the contrasting results for shallow slip events. Combined with our previous results for deeper events, this implies that neglecting material heterogeneity in slow slip inversions may result in overestimates in the amount of slip for deeper events and underestimates for shallow events.

A NE-Trending Oblique-Slip Fault Responsible for the 2016 Zaduo Earthquake (Qinghai, China) Revealed by InSAR Data

Twelve Sentinel-1 images are used to measure the surface displacements caused by the Zaduo earthquake on 17 October 2016 in Qinghai, China. Comprehensive analysis of the local geologic structure, focal mechanisms, relocated aftershocks, and fault geometrical parameters from nonlinear inversions of the InSAR data indicates that a NE-trending fault with a strike of ~ 61°, namely the Aduo fault, was responsible for this event. Further geodetic inversions for finite fault models show that the dip angle of this fault is 75° to the SE. The majority of the slip occurred at the depth from 5 km to 17 km, and the normal-slip component was comparable to the strike-slip component. The peak slip of ~ 31 cm occurred at a depth of ~ 10 km. The InSAR determined moment is 9.61 × 1017 N m with a rigidity of 30 GPa, equivalent to Mw 5.9. The geological map reveals that the Aduo fault was characterized by a left-lateral strike-slip component in the past, as evidenced by the offset of Paleogene sedimentary rocks. Our results for the Zaduo earthquake suggest that the Qiangtang block probably consists of two or more sub-blocks with different eastward extrusion velocities and that the deformation of the Qiangtang block is occurring not only along its boundaries but also in its interior.

Coseismic Displacements from Moderate-Size Earthquakes Mapped by Sentinel-1 Differential Interferometry: The Case of February 2017 Gulpinar Earthquake Sequence (Biga Peninsula, Turkey)

We study the tectonic deformation from the February 2017 shallow earthquake sequence onshore Biga Peninsula (NW Turkey, NE Aegean region). We use InSAR interferograms (Sentinel-1 satellites) to identify the seismic fault (striking N110°E) and seismological data (parametric data and Moment Tensor solutions from NOA and KOERI catalogues) so as to refine its geometry and kinematics using inversion techniques. Despite the moderate magnitudes of the main events of the sequence (5.0 ≤ Mw ≤ 5.2), the total surface deformation is 2.2 fringes (or maximum 6.2 cm along LOS) and it is well visible with InSAR because of the shallow depth of the four main events (6–8 km) and the good coherence of the signal phase. Our geodetic inversion showed that the fault has normal-slip kinematics, dimensions of 6 by 6 km (length, width) and dips at 45°. The InSAR data are fitted by a uniform slip of 28 cm. In addition, 429 earthquakes were relocated with the HypoDD software and the use of a 1-D velocity model. The dip-direction of the fault is not retrievable from InSAR, but a south-dipping plane is clear from seismology and the aftershocks distribution. The spatial distribution of relocated events indicates the activation of one fault with a rupture zone length of about 10 km, a result of the occurrence of off-fault aftershocks along strike the main rupture. A stress inversion using 20 focal mechanisms (M ≥ 3.6; NOA solutions) indicates that faulting accommodates a N196°E extension. It is confirmed that moderate (5.0 ≤ M ≤ 5.2) shallow events can be traced in InSAR studies and can produce surface displacements that provide useful data in fault inversion.

Spatial-temporal evolution of slow slip movements triggered by the 2016 Mw 7.8 Kaikoura earthquake, New Zealand

The 2016 Mw 7.8 Kaikoura earthquake involved complex rupture across multiple faults and triggered large-scale slow slip movements on the Hikurangi subduction zone. The complex seismically triggered slow slip events (SSEs) contribute to the understanding of triggering mechanisms of SSEs in New Zealand. Here, we invert the continuous Global Positioning System (cGPS) observations to investigate the temporal evolution of the seismically triggered slow-slip behaviour on the Hikurangi subduction interface. Similar to previous studies, our optimal geodetic inversion model reproduces deep (30–50 km) Marlborough afterslip of over 60 cm, deep Kapiti slow slip of up to 31 cm and shallow (<15 km), moderate (>10 cm) east coast slow slip on the Hikurangi subduction interface. The slow accumulated seismic moment over the past eight months from the large-scale slow slip motion is ~3.12 × 1020 Nm, which is equivalent to a magnitude 7.6 earthquake. Both the Marlborough afterslip and Kapiti slow slip were considerably active during the first week after the mainshock and gradually slowed down in the following months. These deep ongoing fault motions may continue for at least several months and are expected to decay logarithmically with time. In agreement with previous studies, the east coast slow slip motion occurred rapidly within 2–3 weeks, which stretched from the central to northern Hikurangi subduction margin. The coseismic Coulomb failure stress change investigation suggests that large-scale stress increase (over 1–2 MPa) appears on the southern Hikurangi subduction interface, which encourages afterslip underlying the Marlborough fault system and slow slip beneath the Kapiti coast. Consistent with previous studies, the long-distance slow slip motion offshore the east coast was likely dynamically triggered by the Kaikoura earthquake, where the static Coulomb stress increase is insignificant (<5 kPa).

Geodetic inversion for spatial distribution of slow earthquakes under sparsity constraints

In geodetic data inversion, insufficient observational data and smoothness constraints for model parameters make it difficult to clearly resolve small-scale heterogeneous structures with discontinuous boundaries. We therefore applied sparse modelling to geodetic data inversion. In this paper, we reported two examples; one is developed a novel regularization scheme for the inversion problem that uses discontinuity, sparsity, and smoothness constraints. In order to assess its usefulness and applicability, the proposed method was applied to synthetic displacements calculated by a ring-shaped and sharply varying afterslip distribution on the plate interface beneath the Hyuga-nada region in southwest Japan. The discontinuous boundary was sharper than that obtained by using smoothness constraint only. The other is used the fused regularization, a type of sparse modelling suitable for detecting discontinuous changes in the model parameters. We estimated spatial distribution of the long-term slow slip events beneath the Bungo channel in southwest Japan. We found that the largest slip abruptly becomes zero at the down-dip limit of the seismogenic zone, and is immediately reduced to half at the up-dip limit of the deep low-frequency tremors, and becomes zero near its down-dip limit. Such correspondences imply that some thresholds exist in the generation processes for both tremors and SSEs. These results suggest that geodetic data inversion with sparse modelling can detect such abrupt changes and discontinuous boundaries in the slip distribution of slow earthquakes.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Dynamic Rupture Modeling of the M7.2 2010 El Mayor‐Cucapah Earthquake: Comparison With a Geodetic Model

AbstractThe 2010 Mw 7.2 El Mayor‐Cucapah earthquake is the largest event recorded in the broader Southern California‐Baja California region in the last 18 years. Here we try to analyze primary features of this type of event by using dynamic rupture simulations based on a multifault interface and later compare our results with space geodetic models. Our results show that starting from homogeneous prestress conditions, slip heterogeneity can be achieved as a result of variable dip angle along strike and the modulation imposed by step over segments. We also considered effects from a topographic free surface and find that although this does not produce significant first‐order effects for this earthquake, even a low topographic dome such as the Cucapah range can affect the rupture front pattern and fault slip rate. Finally, we inverted available interferometric synthetic aperture radar data, using the same geometry as the dynamic rupture model, and retrieved the space geodetic slip distribution that serves to constrain the dynamic rupture models. The one to one comparison of the final fault slip pattern generated with dynamic rupture models and the space geodetic inversion show good agreement. Our results lead us to the following conclusion: in a possible multifault rupture scenario, and if we have first‐order geometry constraints, dynamic rupture models can be very efficient in predicting large‐scale slip heterogeneities that are important for the correct assessment of seismic hazard and the magnitude of future events. Our work contributes to understanding the complex nature of multifault systems.