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Backprojection has proven useful in imaging large earthquake rupture processes. The method is generally robust and requires relatively simple assumptions about the fault geometry or the Earth velocity model. It can be applied in both the time and frequency domain. Backprojection images are often obtained from records filtered in a narrow frequency band, limiting its ability to uncover the whole rupture process. Here, we develop and apply a novel frequency-difference backprojection (FDBP) technique to image large earthquakes, which imitates frequencies below the bandwidth of the signal. The new approach originates from frequency-difference beamforming, which was initially designed to locate acoustic sources. Our method stacks the phase-difference of frequency pairs, given by the autoproduct, and is less affected by scattering and -time errors from 3-D Earth structures. It can potentially locate sources more accurately, albeit with lower resolution. In this study, we first develop the FDBP algorithm and then validate it by performing synthetic tests. We further compare two stacking techniques of the FDBP method, Band Width Averaged Autoproduct and its counterpart (BWAP and non-BWAP), and their effects in the backprojection images. We then apply both the FDBP and conventional backprojection methods to the 2015 M7.8 Gorkha earthquake as a case study. The backprojection results from the two methods agree well with each other, and we find that the peak radiation loci of the FDBP non-BWAP snapshots have standard error of less than 0.33° during the rupture process. The FDBP method shows promise in resolving complex earthquake rupture processes in tectonically complex regions.

 

We study the mechanical response of two‐dimensional vertical strike‐slip fault to coseismic damage evolution and interseismic healing of fault damage zones by simulating fully dynamic earthquake cycles. Our models show that fault zone structure evolution during the seismic cycle can have pronounced effects on mechanical behavior of locked and creeping fault segments. Immature fault damage zone models exhibit small and moderate subsurface earthquakes with irregular recurrence intervals and abundance of slow‐slip events during the interseismic period. In contrast, mature fault damage zone models host pulse‐like earthquake ruptures that can propagate to the surface and extend throughout the seismogenic zone, resulting in large stress drop, characteristic rupture extents, and regular recurrence intervals. Our results suggest that interseismic healing and coseismic damage accumulation in fault zones can explain the observed differences of earthquake behaviors between mature and immature fault zones and indicate a link between regional seismic hazard and fault structural maturity.

 

Mature strike‐slip faults are usually surrounded by a narrow zone of damaged rocks characterized by low seismic wave velocities. Observations of earthquakes along such faults indicate that seismicity is highly concentrated within this fault damage zone. However, the long‐term influence of the fault damage zone on complete earthquake cycles, that is, years to centuries, is not well understood. We simulate aseismic slip and dynamic earthquake rupture on a vertical strike‐slip fault surrounded by a fault damage zone for a thousand‐year timescale using fault zone material properties and geometries motivated by observations along major strike‐slip faults. The fault damage zone is approximated asan elastic layer with lower shear wave velocity than the surrounding rock. We find that dynamic wave reflections, whose characteristics are strongly dependent on the width and the rigidity contrast of the fault damage zone, have a prominent effect on the stressing history of the fault. The presence of elastic damage can partially explain the variability in the earthquake sizes and hypocenter locations along a single fault, which vary with fault damage zone depth, width and rigidity contrast from the host rock. The depth extent of the fault damage zone has a pronounced effect on the earthquake hypocenter locations, and shallower fault damage zones favor shallower hypocenters with a bimodal distribution of seismicity along depth. Our findings also suggest significant effects on the hypocenter distribution when the fault damage zone penetrates to the nucleation sites of earthquakes, likely being influenced by both lithological (material) and rheological (frictional) boundaries.

 

Fault damage zones can influence various aspects of the earthquake cycle, such as the recurrence intervals and magnitudes of large earthquakes. Hence, our research aims to develop a novel method to image fault damage zones using high-frequency P-waves reflected within them. Previous studies have demonstrated that fault damage zones can amplify high-frequency waves along directions close to fault strike. The associated frequency band of the amplified secondary peak may be used to estimate the width and velocity contrast of the fault damage zone. Here we use the stacked P-wave velocity spectra of M1.5–3 earthquakes in the Parkfield region to identify the azimuthal variation in high-frequency energy. Our preliminary results show that for 62% of the Parkfield clusters, stations close to the fault strike record more high-frequency energies around 10–20 Hz. The frequency band is lower than what we observed for the 2019 Ridgecrest earthquakes region, and corresponds to a fault zone velocity reduction of ~50% assuming a fault zone width of 200m. We also observe along-strike differences in our results, where clusters along some fault sections show greater azimuthal variation than clusters in other sections. Moreover, to account for the possible effects of site conditions underneath the stations, we will quantify their effects using the spectra of regional earthquakes. We will compute the root-mean-square spectra at different frequency bands for each event, and calculate the average deviation in spectra at each station. We can then generate an empirical correction term for each station as a function of frequency. By applying these corrections to the stacked P-wave velocity spectra of our earthquake clusters, we can separate the contribution of site effects from fault zone structures. Our results demonstrate that the new method can be applied to search for fault damage zone structures in different tectonic regions with broadband stations in order to enhance our understanding of the co-evolution of fault zones and earthquake cycle. 

Earthquake nucleation is a crucial preparation process of the following coseismic rupture propagation. Under the framework of rate-and-state friction, it was found that the ratios of a to b parameters control whether earthquakes nucleate as an expanding crack or a fixed length patch. However, as an essential parameter in earthquake physics, critical slip distance DRS controls the weakening efficiency of fault strength and can influence the nucleation styles. Here we investigate the effects of DRS on nucleation styles in the context of fully dynamic seismic cycles by evaluating the evolution of the nucleation zone quantitatively when it accelerates from the tectonic loading rate to seismic slip velocity. The inferred values of DRS from small-scale laboratory faults are 1-100 μm, several orders smaller than those obtained from geophysical observations on large natural faults. Considering the scale-dependence of widely observed DRS, the ratio of DRS to velocity weakening asperity size W is applied to substitute the absolute value of DRS in this study. We find when DRS/W is relatively large (~10-5), a/b=0.5 can separate two nucleation styles as found previously. For a relatively small DRS/W (~10-6), however, a/b larger than 0.7 is necessary to produce the typical expanding crack-like nucleation style. When DRS/W<4x10-7 and a/b<0.8, the fixed length nucleation style dominates. For some cases with a/b>0.75, the initial yielding phase accelerates to a considerable slip velocity just before the subsequent expanding fracture phase, which may explain the generation of foreshock activities. Specially, the first yielding phase is possible to trigger dynamic events without a secondary fracture phase. Furthermore, when the nucleation site is not in the middle of the asperity, large enough a/b (e.g., 0.8) could induce a complex nucleation style as well as abundant interseismic aseismic transients. We also recognize a special twin nucleation style that incorporates a failed acceleration phase. Our results reveal the critical role of DRS on earthquake nucleation styles and suggest that the fixed length nucleation style may be more common for the range of DRS/W (~10-4-~10-7) observed on natural and laboratory faults. 

Fault damage zones can influence various aspects of the earthquake cycle, such as the recurrence intervals and magnitudes of large earthquakes. The properties and structure of fault damage zones are often characterized using dense arrays of seismic stations located directly above the faults. However, such arrays may not always be available. Hence, our research aims to develop a novel method to image fault damage zones using broadband stations at relatively larger distances. Previous kinematic simulations and a case study of the 2003 Big Bear earthquake sequence demonstrated that fault damage zones can act as effective waveguides, amplifying high-frequency waves along directions close to fault strike via multiple reflections within the fault damage zone. The amplified high-frequency energy can be observed by stacking P-wave spectra of earthquake clusters with highly-similar waveforms (Huang et al., 2016), and the frequency band which is amplified may be used to estimate the width and velocity contrast of the fault damage zone. We attempt to identify the high-frequency peak associated with fault zone waves in stacked spectra by conducting a large-scale study of small earthquakes (M1.5–3). We use high quality broadband data from seismic stations at hypocentral distances of 20-80 km in the 2019 Ridgecrest earthquake regions. First, we group the Ridgecrest earthquakes in clusters by their locations and their waveform similarity, and then stack their velocity spectra to average the source effects of individual earthquakes. Our results show that the stations close to the fault strike record more high-frequency energies around the characteristic frequency of fault zone reflections. We find that the increase in the amount of high-frequencies is consistent across clusters with average magnitudes ranging from 1.6-2.4, which suggests that the azimuthal variation in spectra is caused by fault zone amplification rather than rupture directivity. We will apply our method to other fault zones in California, in order to search for fault damage zone structures and estimate their material properties. 

The temporal variation of elastic property of the bulk material surrounding the fault is considered an important contribution to the observed co-seismic velocity reduction and interseismic healing. Paglialunga et al. [2021] found that as fault normal stress increases, co-seismic velocity reduction becomes larger because more cracks reopen with higher stress drops. Larger normal stress can lead to smaller nucleation size and contribute to larger co-seismic slip. By contrast, with larger co-seismic velocity reduction and interseismic healing, more slow slip events can propagate in the seismogenic zone [Thakur and Huang, 2021], because the temporal velocity change related to fault zone damage modulates earthquake nucleation. Hence, fault normal stress and temporal damage zone structure evolution have opposite influences on the spatial distribution and recurrence intervals of earthquakes. We conducted 2-D anti-plane fully-dynamic seismic cycle simulations and explored the effects of fault normal stress on seismic cycle when there is coseismic damage and interseismic healing in the fault damage zone. The normal stress is in a range of 40-70 MPa and the co-seismic rigidity reduction is in a range of 5-8%. We find larger normal stress results in larger co-seismic slip and fewer slow slip events, while more co-seismic velocity reduction and interseismic healing leads to more partial ruptures as well as slow slip events. With the increase of both normal stress and seismic velocity change, more regular earthquakes occur and slow slip events gradually disappear. For the selected parameter space, the influence of seismic velocity change is not as significant as the effect of normal stress. However, fault zone maturity or the initial rigidity of fault damage zones should also affect the competitive relationship between normal stress and seismic velocity change, and we will characterize earthquakes and slow-slip events in immature and mature fault damage zones when both on-fault normal stress and off-fault seismic velocity vary over earthquake cycles. 

Abstract Dynamic rupture models are physics-based simulations that couple fracture mechanics to wave propagation and are used to explain specific earthquake observations or to generate a suite of predictions to understand the influence of frictional, geometrical, stress, and material parameters. These simulations can model single earthquakes or multiple earthquake cycles. The objective of this article is to provide a self-contained and practical guide for students starting in the field of earthquake dynamics. Senior researchers who are interested in learning the first-order constraints and general approaches to dynamic rupture problems will also benefit. We believe this guide is timely given the recent growth of computational resources and the range of sophisticated modeling software that are now available. We start with a succinct discussion of the essential physics of earthquake rupture propagation and walk the reader through the main concepts in dynamic rupture model design. We briefly touch on fully dynamic earthquake cycle models but leave the details of this topic for other publications. We also highlight examples throughout that demonstrate the use of dynamic rupture models to investigate various aspects of the faulting process. 

Faults are usually surrounded by damage zones associated with localized deformation. Here we use fully dynamic earthquake cycle simulations to quantify the behaviors of earthquakes in fault damage zones. We show that fault damage zones can make a significant contribution to the spatial and temporal seismicity distribution. Fault stress heterogeneities generated by fault zone waves persist over multiple earthquake cycles that, in turn, produce small earthquakes that are absent in homogeneous simulations with the same friction conditions. Shallow fault zones can produce a bimodal depth distribution of earthquakes with clustering of seismicity at both shallower and deeper depths. Fault zone healing during the interseismic period also promotes the penetration of aseismic slip into the locked region and reduces the sizes of fault asperities that host earthquakes. Hence, small and moderate subsurface earthquakes with irregular recurrence intervals are commonly observed in immature fault zone simulations with interseismic healing. To link our simulation results to geological observations, we will use simulated fault slip at different depths to infer the timing and recurrence intervals of earthquakes and discuss how such measurements can affect our understanding of earthquake behaviors. We will also show that the maturity and material properties of fault damage zones have strong influence on whether long-term earthquake characteristics are represented by single events. 

Fault damage zones can influence various aspects of the earthquake cycle, such as the recurrence intervals and magnitudes of large earthquakes. The properties and structure of fault damage zones are often characterized using dense arrays of seismic stations located directly above the faults. However, such arrays may not always be available. Hence, our research aims to develop a novel method to image fault damage zones using broadband stations at relatively larger distances. Previous kinematic simulations and a case study of the 2003 Big Bear earthquake sequence demonstrated that fault damage zones can act as effective waveguides, amplifying high-frequency waves along directions close to fault strike via multiple reflections within the fault damage zone. The amplified high-frequency energy can be observed using the stacked P-wave spectra of earthquake clusters with highly-similar waveforms (Huang et al., 2016). We attempt to identify the high-frequency peak associated with fault zone waves in stacked spectra by conducting a large-scale study of small earthquakes (M1.5–3). We use high quality broadband data from seismic stations at hypocentral distances of 20-100km in the 2004 Parkfield and 2019 Ridgecrest earthquake regions. First, we group earthquakes in clusters by their locations and their waveform similarity, and then stack their velocity spectra to average the source effects of individual earthquakes. We applied our method to the 2019 Ridgecrest earthquake sequence, and our preliminary results show that stations close to the fault strike tend to record more high-frequency energies around the characteristic frequency of fault zone reflections. The frequency bands in which amplified high-frequency energies are observed may be used to estimate the width and velocity contrast of the fault damage zone. We aim to develop a robust and versatile method that can be used to search for fault damage zone structures and estimate their material properties, in order to shed light on earthquake source processes.