Peak Slip Rate Research Articles

Source properties of dynamic rupture pulses with off‐fault plasticity

Large dynamic stresses near earthquake rupture fronts may induce an inelastic response of the surrounding materials, leading to increased energy absorption that may affect dynamic rupture. We systematically investigate the effects of off‐fault plastic energy dissipation in 2‐D in‐plane dynamic rupture simulations under velocity‐and‐state‐dependent friction with severe weakening at high slip velocity. We find that plasticity does not alter the nature of the transitions between different rupture styles (decaying versus growing, pulse‐like versus crack‐like, and subshear versus supershear ruptures) but increases their required background stress and nucleation size. We systematically quantify the effect of amplitude and orientation of background shear stresses on the asymptotic properties of self‐similar pulse‐like ruptures: peak slip rate, rupture speed, healing front speed, slip gradient, and the relative contribution of plastic strain to seismic moment. Peak slip velocity and rupture speed remain bounded. From fracture mechanics arguments, we derive a nonlinear relation between their limiting values, appropriate also for crack‐like and supershear ruptures. At low background stress, plasticity turns self‐similar pulses into steady state pulses, for which plastic strain contributes significantly to the seismic moment. We find that the closeness to failure of the background stress state is an adequate predictor of rupture speed for relatively slow events. Our proposed relations between state of stress and earthquake source properties in the presence of off‐fault plasticity may contribute to the improved interpretation of earthquake observations and to pseudodynamic source modeling for ground motion prediction.

High‐speed rupture in the first 20 s of the 2011 Tohoku earthquake, Japan

AbstractThe 2011 Tohoku earthquake produced tens of meters of fault slip near the Japan Trench, which generated devastating tsunami. The rupture process before the huge slip is still unclear due to a lack of resolution. Here I perform a multiscale slip inversion analysis to examine the first 10 and 20 s of the rupture process and the whole rupture process at different scales. The result shows that 4 s after the initiation, this earthquake started with a relatively high‐speed rupture that had a peak slip rate faster than 1 m/s and a rupture velocity comparable to 3 km/s. Fourteen seconds after the initiation, the rupture propagation direction changed from northward to westward, near the edge of the M 7.3 foreshock coseismic slip area. The stress release by the foreshock may contribute to the complex small‐scale rupture propagation, which may appear to be slow rupture propagation when only looking at long‐period data.

Assessment of the finite element solutions for 3D spontaneous rupture using GeoFEM

Numerical simulations of spontaneous shear rupture on a planar fault using a slip-weakening model in a three-dimensional uniform elastic medium were conducted using a parallel FE code, GeoFEM, which was originally developed for the solid-Earth simulations on the Earth Simulator. The aim was to evaluate the accuracy and applicability of GeoFEM to earthquake rupture. The present numerical results are compared with published results obtained using a finite-difference (FD) method and a boundary integral (BI) method for rupture times and time functions of slip, slip rate, and shear stress at two particular points on the fault plane. The effects of mesh size and damping on the attenuation of spurious oscillations were also examined in a range of simulations. The appropriate degree of damping depends on mesh size and must be introduced in order to obtain reliable numerical solutions; weak damping leads to significant oscillation and strong damping to artificially low rupture speeds and low slip rates. Our results indicate that mesh size should be sufficiently small to allow the inclusion of a few grids in the cohesive zone, as shown in other numerical methods. The solutions by GeoFEM that have the appropriate mesh size and damping are quite similar to those obtained using the FD and BI methods, the difference between them being generally less than 2% in terms of the rupture time and 5.2% in terms of the peak slip rate.

Late Quaternary slip rate of the southern Elsinore fault, Southern California: Dating offset alluvial fans via 230Th/U on pedogenic carbonate

To understand how strain is accommodated along the Pacific‐North American plate boundary and to assess the associated seismic hazard, estimates of long‐term (103–105 year) slip rates for strands of the San Andreas fault system are needed. The mean slip rate over the past ∼40 kyr for the southernmost Elsinore fault, one of the principal strands of the San Andreas fault system in Southern California, was determined using offset alluvial fans dated by U‐series on pedogenic carbonate. Two displaced fans, correlated with their source drainages using distinctive gravel‐clast assemblages, define offsets of 60 ± 20 and 83 ± 31 m. Milligram‐size samples of dense carbonate clast‐coatings from fan soils provide 230Th/U‐based ages of 39.1 ± 5.3 and 46.4 ± 5.3 kyr (all errors are 2σ), respectively, for the offset fans. Our results indicate that the Elsinore fault near its southern terminus slipped at a mean rate of 1.6 ± 0.4 mm/yr over the past ∼40 kyr. However, slip associated with the most recent earthquake on the southern Elsinore fault increases northward from the study area, and if this pattern has repeated through time, the peak slip rate on the southern Elsinore fault may significantly exceed our measured rate.

Supershear Mach-waves expose the fault breakdown slip

Mikumo et al. (2003) showed that it is possible to estimate the breakdown slip ( D c) as the slip at the time of the peak slip rate for rupture propagation with subshear speeds. Cruz-Atienza et al. (2009) later attempted to extend this method to extract information about D c as the displacement at the time of the peak particle velocity from seismic strong-motion records. However, a reasonably accurate estimate of D c was only possible in a narrow zone adjacent to the fault (typically on the order of hundreds of meters) due to the fast decay with distance from the fault of the seismic energy related to the stress breakdown process. When the rupture propagates with supershear-speeds, on the other hand, this energy is carried much farther away from the fault by Mach waves, in particular Rayleigh Mach waves when rupture reaches the Earth's surface (Dunham and Bhat, 2008). Here, we present a new approach to estimate D c from strong-motion records containing Mach waves. First, we show that the method by Mikumo et al. is valid for supershear rupture propagation. This method is then used to estimate D c via an asymptotic approximation of the slip and slip-rate time histories from the Mach waves. Using spontaneous rupture simulations we demonstrate that, for a visco-elastic half-space model, D c can be estimated within an error of 40% from Mach waves that have propagated a distance of at least 3 km from the fault. The method is applied to estimate D c for the 2002 M w7.9 Denali, Alaska, earthquake (∼ 1.5 m) and for the 1999 Mw7.6 Izmit, Turkey, earthquake (∼ 1.7 m).

Fast inversion of rupture process of the 14 April 2010 Yushu, Qinghai, earthquake

Four results of the rupture process of 14 April 2010 Yushu, Qinghai, earthquake, obtained by inverting the broadband seismic data of Global Seismographic Network (GSN) based on the inversion method of earthquake rupture process, were compared and discussed. It is found that the Yushu earthquake has several basic characteristics as follows: ① There exist two principal sub-events which correspond to two slip-concentrated patches being located near the hypocenter and to the southeast of the epicenter. The rupture of the slip-concentrated patch to the southeast of the epicenter broke though the ground surface; ② The peak slip and peak slip-rate are about 2.1 m and 1.1 m/s, respectively, indicating that the Yushu earthquake is an event with large slip-rate on the fault plane; ③ Overall the Yushu earthquake is a unilateral rupture event with the rupture mainly propagating southeastward. The strong focusing of the seismic energy in the southeast of the epicenter due to the “seismic Doppler effect” reasonably accounts for the tremendous damage in the Yushu city.

Correlation of earthquake source parameters inferred from dynamic rupture simulations

We analyzed 315 dynamic strike‐slip rupture models computed up to 5.0 Hz to get a quantitative understanding of the correlation and amplitude distributions of parameters describing the earthquake source, such as slip and rupture velocity. To account for the epistemic uncertainty of the problem, we constructed a database of dynamic ruptures computed by ourselves and other authors. This database contains ruptures computed using different models of initial stress, peak stress, and critical slip‐weakening distance. Using the set of computed ruptures, we constructed probability density functions (pdfs) for the amplitude distributions of the source parameters and for the correlation between the source parameters. We tried to extract parameter pairs that showed a small variability in the spatial correlation given the large epistemic uncertainty in the input. We only analyzed the areas on the fault with subshear propagation speed. The principal findings are as follows: (1) Final slip amplitude does not show correlation with the local rupture velocity. (2) Final slip amplitude correlates well with risetime. (3) Rupture velocity correlates well with peak slip rate and the duration of the impulsive part of the slip rate function. (4) The pdf of rupture velocity, risetime, and peak slip rate depends on the distance from the nucleation zone. (5) Fracture energy is not the single controlling factor for the rupture velocity; the slope of the linear slip‐weakening curve has a significant effect on the rupture velocity. (6) The crack length (length that is slipping at a given time) decreases with the distance from the nucleation zone.

Dynamic Rupture Models for the Southern San Andreas Fault

Abstract Dynamic rupture, and resultant ground motions up to 0.25 Hz, are simulated for an M w 7.6 earthquake on the southern San Andreas fault. Spontaneous rupture is modeled with slip-weakening friction, and 3D viscoelastic wave solutions are computed with a support-operator numerical method. The initial traction model is derived from inversions of the M w 7.3 1992 Landers strong ground-motion records, and borrows heavily from that used for the TeraShake2 simulations by Olsen et al. (2008). Heterogeneity in the traction model leads to focusing of the rupture front, and the focusing produces cases of supershear rupture velocity in asperities (areas of high initial traction), as well as cases of high peak slip rate and cohesive zone contraction in antiasperities. Separate solutions are computed for version 3.0 and 4.0, respectively, of the Southern California Earthquake Center Community Velocity Model (SCEC-CVM). We also compare the case of a flat ground surface (a common simplification made for finite-difference simulations) to the case of the ground surface conformed to regional topography. The overall distribution of simulated ground motion intensity is consistent with that derived from the empirical model of Campbell and Bozorgnia (2008), in the sense that the bulk of simulated pseudospectral velocity (PSV) values are within the 68% confidence intervals of the empirical model. Simulated PSVs corresponding to low probability in the empirical model are principally associated with basin wave-guide and directivity effects. An important example, first identified by the TeraShake1 simulations (Olsen et al. , 2006), is the stronger than expected ground motions at the site of Montebello due to a basin wave-guide effect. We find that this effect is lessened for version 4.0 of the SCEC-CVM, relative to version 3.0, due to a shallower model for the Chino basin.

Exploring Spatial Coherence between Earthquake Source Parameters

We explore the spatial coherence between earthquake source parameters by analyzing kinematic rupture models of two large strike-slip events, that is, the 1999 Izmit, Turkey, and the 1992 Landers, California, earthquakes. We investigate the coherence not only at zero offset but also at nonzero offset distances on the fault. The analysis shows that earthquake slip has a significant level of correlation with temporal source parameters such as rupture velocity, peak slip rate, and slip duration (rise time). We also show that many interesting features of earthquake source characteristics, such as directional effects of earthquake rupture, can be captured by this type of spatial coherence analysis. A coherence analysis therefore may have potential for understanding earthquake source characteristics and for generating realistic kinematic rupture models that capture the essential physics of the rupture process for strong ground motion prediction.

A support-operator method for 3-D rupture dynamics

SUMMARY We present a numerical method to simulate spontaneous shear crack propagation within a heterogeneous, 3-D, viscoelastic medium. Wave motions are computed on a logically rectangular hexahedral mesh, using the generalized finite-difference method of Support Operators (SOM). This approach enables modelling of non-planar surfaces and non-planar fault ruptures. Our implementation, the Support Operator Rupture Dynamics (SORD) code, is highly scalable, enabling large-scale, multiprocessors calculations. The fault surface is modelled by coupled double nodes, where rupture occurs as dictated by the local stress conditions and a frictional failure law. The method successfully performs test problems developed for the Southern California Earthquake Center (SCEC)/U.S. Geological Survey (USGS) dynamic earthquake rupture code validation exercise, showing good agreement with semi-analytical boundary integral method results. We undertake further dynamic rupture tests to quantify numerical errors introduced by shear deformations to the hexahedral mesh. We generate a family of meshes distorted by simple shearing, in the along-strike direction, up to a maximum of 73 ◦ . For SCEC/USGS validation problem number 3, grid-induced errors increase with mesh shear angle, with the logarithm of error approximately proportional to angle over the range tested. At 73 ◦ , rms misfits are about 10 per cent for peak slip rate, and 0.5 per cent for both rupture time and total slip, indicating that the method (which, up to now, we have applied mainly to near-vertical strike-slip faulting) is also capable of handling geometries appropriate to low-angle surface-rupturing thrust earthquakes. Additionally, we demonstrate non-planar rupture effects, by modifying the test geometry to include, respectively, cylindrical curvature and sharp kinks.

Modelling of rupture propagation using high-order mimetic finite differences

SUMMARY We present a split-node finite difference (FD) method for modelling shear ruptures that is consistently fourth-order accurate in its spatial discretization, both in the interior of the model and at the fault. The method, called mimetic operator split node (MOSN), uses a staggered grid, and the fault plane is discretized using split nodes for both discontinuous displacement and discontinuous stress components. The method differs in several ways from previous FD methods for rupture modelling. (1) It uses one-sided differentiation (in the fault-normal direction) to retain high-order accuracy at the discontinuity. (2) The one-sided differentiation is implemented with mimetic FD operators that conserve the integration-by-parts formula (including boundary terms) in discrete form. (3) The mimetic operators lead naturally to the evaluation of conjugate tractions at the split-node displacement sites, as required to apply the frictionalsliding boundary conditions. In the interior of the grid, the mimetic operators reduce to the conventional fourth-order staggered-grid FD operators. We verify the accuracy of the MOSN method using two test problems: a fixed-speed rupture case (Kostrov’s problem), and the case of a spontaneous rupture with slip-dependent friction. In the former test, comparisons of slip and shear stress waveforms confirm the convergence of numerical results to the analytical solution as the grid is refined. In the latter test, assessment is based on both qualitative waveform characteristics and a quantitative convergence analysis that uses error metrics in rupture time, final slip and peak slip rate. Compared with a previously verified second-order scheme, the MOSN method shows significant reduction in artefacts attributable to numerical dispersion and also yields a considerable improvement in rupture arrival times. While from a practical standpoint the performance gains of MOSN over the second-order scheme are considerable, MOSN has comparatively poorer convergence rates, and loses its advantage in accuracy in the limit of very small spatial steps. We attribute the relatively low convergence rates to our use of a friction law that induces gradient discontinuities in the fault traction, violating the smoothness assumptions underlying the accuracy estimates, a limitation which may not apply to more complex, experimentally derived friction laws with smooth dependence on slip-rate and state variables. Our current implementation is 2-D and assumes a straight fault, but the method is extensible to more general 3-D geometries.

Near-Fault Peak Ground Velocity from Earthquake and Laboratory Data

We test the hypothesis that peak ground velocity (pgv) has an upper bound independent of earthquake magnitude and that this bound is controlled primarily by the strength of the seismogenic crust. The highest pgvs, ranging up to several meters per second, have been measured at sites within a few kilometers of the causative faults. Because the database for near-fault pgv is small, we use earthquake slip models, laboratory experiments, and evidence from a mining-induced earthquake to investigate the factors influencing near-fault pgv and the nature of its scaling. For each earthquake slip model we have calculated the peak slip rates for all subfaults and then chosen the maximum of these rates as an estimate of twice the largest near-fault pgv. Nine slip models for eight earthquakes, with magnitudes ranging from 6.5 to 7.6, yielded maximum peak slip rates ranging from 2.3 to 12 m/ sec with a median of 5.9 m/sec. By making several adjustments, pgvs for small earthquakes can be simulated from peak slip rates measured during laboratory stick- slip experiments. First, we adjust the pgv for differences in the state of stress (i.e., the difference between the laboratory loading stresses and those appropriate for faults at seismogenic depths). To do this, we multiply both the slip and the peak slip rate by the ratio of the effective normal stresses acting on fault planes measured at 6.8 km depth at the KTB site, Germany (deepest available in situ stress measurements), to those acting on the laboratory faults. We also adjust the seismic moment by replacing the laboratory fault with a buried circular shear crack whose radius is chosen to match the experimental unloading stiffness. An additional, less important adjustment is needed for experiments run in triaxial loading conditions. With these adjustments, peak slip rates for 10 stick-slip events, with scaled moment magnitudes from −2.9 to 1.0, range from 3.3 to 10.3 m/sec, with a median of 5.4 m/sec. Both the earthquake and laboratory results are consistent with typical maximum peak slip rates averaging between 5 and 6 m/sec or corresponding maximum near-fault pgvs between 2.5 and 3 m/sec at seismogenic depths, independent of magnitude. Our ability to replicate maximum slip rates in the fault zones of earthquakes by adjusting the corresponding laboratory rates using the ratio of effective normal stresses acting on the fault planes suggests that the strength of the seismogenic crust is the important factor limiting the near-fault pgv.

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a traction‐at‐split‐node formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The three‐dimensional (3‐D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slip‐weakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS differences in rupture time, final slip, and peak slip rate and related these to median and minimum measures of the cohesive zone resolution observed in the numerical solutions. The BI and DFM methods give virtually indistinguishable solutions to the 3‐D spontaneous rupture test problem when their grid spacing Δx is small enough so that the solutions adequately resolve the cohesive zone, with at least three points for BI and at least five node points for DFM. Furthermore, grid‐dependent differences in the results, for each of the two methods taken separately, decay as a power law in Δx, with the same convergence rate for each method, the calculations apparently converging to a common, grid interval invariant solution. This result provides strong evidence for the accuracy of both methods. In addition, the specific solution presented here, by virtue of being demonstrably grid‐independent and consistent between two very different numerical methods, may prove useful for testing new numerical methods for spontaneous rupture problems.

強震動シミュレーションのためのすべり速度時間関数の近似式

Nakamura and Miyatake (2000) had proposed an approximate expression of slip rate time function on the basis of the dynamic rupture model simulation on narrow fault. In the present paper, it is applied to strong ground motion simulation from strike slip fault in order to study the validity of the expression by comparison with dynamic rupture models in several cases. The following three fault rupture processes are considered in the present paper, and the waveforms generated from the approximate slip rate time function for these cases are compared with corresponding dynamic rupture models.(a) almost unilateral rupture on 20km×10km single strike slip fault with uniform 10MPa stress drop distrubution. (b) two asperity models, i. e., b-1) single 8km×6km single asperity located near the center of a 20km×10km strike slip fault and b-2), three asperites located on the same fault. Stress drop is 10MPa in asperity part, and 0MPa in another part. These cases correspond to the heterogeneous fault. (c) 10km×10km fault on which rupture starts from the deepest corner of the fault, and propagate circularly. Since this situation is very different from that assumed in Nakamura and Miyatake (2000), the approximate function might not be valid. In all the cases, the uppermost depth is assumed to be 1km, and the speed of rupture propagation is assumed to be 0.8 times shear wave velocity.In case A, approximate slip rates and the generated seismic waves gave the good agreement with those calculated from dynamic faulting model, although at the initial part of the rupture some discrepancy exists. In case B, the agreement is also good, except the initial part of the rupture. It is possible to improve the agreement by adjusting the rise time and peak slip rate using simple correction function.In case C, it is impossible to apply uniform slip rate function. Slip rates time functions from dynamic model for case C are different from point to point on the fault plane. So rise time and peak slip rate distributions need to be adjusted using the above function.

Characterization of Near-Source Ground Motions with Earthquake Simulations

We examine the characteristics of long-period near-source ground motions by conducting a sensitivity study with variations in six earthquake source parameters for both a strike-slip fault ( M 7.0-7.1) and a thrust fault ( M 6.6-7.0). The directivity of the ruptures creates large displacement and velocity pulses in the forward direction. The dynamic displacements close to the fault are comparable to the average slip. The ground motions exhibit the greatest sensitivity to the fault depth with moderate sensitivity to the rupture speed, peak slip rate, and average slip. For strike-slip faults and thrust faults with surface rupture, the maximum ground displacements and velocities occur in the region where the near-source factor from the 1997 Uniform Building Code is the largest. However, for a buried thrust fault the peak ground motions can occur up-dip from this region.