Slip-rate Function Research Articles

Mechanical Energy Dissipation During Seismic Dynamic Weakening in Calcite‐Bearing Faults

AbstractEarthquakes are frictional instabilities caused by the shear stress decrease, that is, dynamic weakening, of faults with slip and slip rate. During dynamic weakening, shear stress depends on slip, slip rate, and temperature, according to constitutive laws governing the earthquake rupture process. In the laboratory, technical limitations in measuring temperature during frictional instabilities inhibit the investigation and interpretation of shear stress evolution. Here we conduct high velocity friction experiments on calcite‐bearing simulated faults, both on bare‐rock and on gouge samples, at 20–30 MPa normal stress, 1–6 m/s slip rate and 1–20 m total slip. Seismic slip pulses are reproduced by imposing boxcar and regularized Yoffe slip rate functions. We measured, together with shear stress, slip, and slip rate, the temperature evolution on the fault by employing an innovative two‐color fiber optic pyrometer. The comparison between modeled and measured temperature reveals that for calcite‐bearing faults the heat sink caused by decarbonation reaction controls the temperature evolution. In bare‐rocks, energy is dissipated as frictional heat, and temperature increase is buffered by the heat sink of the calcite decarbonation reaction. In gouges, energy is dissipated as frictional heat and for plastic deformation processes, balanced by the heat sink caused by the decarbonation reaction enhanced by the mechanochemical effect. Our results suggest that in calcite‐bearing rocks, a common fault zone material for earthquake sources in the continental crust at shallow depth, the type of fault materials (bare‐rocks vs. gouges) controls the energy dissipation during seismic slip.

Spatial Heterogeneity of Fault Slip and the Radiated Spectra of Ground Motions

ABSTRACTKinematic models of simulating earthquake radiation in seismic hazard analysis typically require prescribing the distribution of final slip over the hypothetical fault planes. The spatial spectra of heterogeneous slip affect the frequency spectra of the seismic body waves. The representation integral of elasticity provides a convenient analytical tool by which the relationships between the slip spectra in the wavenumber domain and the wave spectra in the frequency domain can be scrutinized. In the limit of the waves from a small source in the far field, the Fourier spectrum of wave displacement is the spectrum of the slip-rate function multiplied by the spatial slip spectrum representing fault directivity. A popular model for the latter is the k-square slip distribution. Classic results prescribe that for a typical ω-square source time function, such multiplication, conversely to a common assumption that the k-square slip distribution always leads to the ω-square decay of the high-frequency seismic spectra, can result in the ω−4 power-law decay. Such steep fall-off rates are highly unusual in observations, suggesting that the k-square heterogeneous slip in certain cases may significantly underpredict the realistic high-frequency ground motions, including peak velocities and accelerations. An alternative use of heterogeneous slip distributions would be to explain the additional high-frequency diminution of the observed spectra that is usually attributed to ad hoc cutoff (“fmax” or “kappa”) filters. The simple asymptotic relationships between heterogeneous fault slip and body wave spectra may not hold true in the vicinity of large earthquakes, at distances of main interest to hazard calculations.

Refinements to the Graves–Pitarka Kinematic Rupture Generator, Including a Dynamically Consistent Slip-Rate Function, Applied to the 2019 Mw 7.1 Ridgecrest Earthquake

ABSTRACTThe main objective of this study is to develop physics-based constraints on the spatiotemporal variation of the slip-rate function using a simplified dynamic rupture model. First, we performed dynamic rupture modeling of the 2019 Mw 7.1 Ridgecrest, California, earthquake, to analyze the effects of depth-dependent stress and material friction on slip rate. Then, we used our modeling results to guide refinements to the slip-rate function that were implemented in the Graves–Pitarka kinematic rupture generation technique. The dynamic ruptures were computed on a surface-rupturing, planar strike-slip fault that includes a weak (negative to low-stress-drop) zone in the upper 4 km of the crust. Below the weak zone, we placed high-stress-drop patches designed to mirror the large-slip areas seen in various rupture model inversions of the event. The locations of the high-stress-drop patches and the hypocenter were varied in multiple realizations to investigate how changing the dynamic conditions affected the resulting rupture kinematics, in particular, the slip rate. From these simulations, we observed a systematic change in the shape of the slip-rate function from Kostrov type below the weak zone to a predominantly symmetric shape within the weak zone, along with a depth-dependent reduction of peak slip rate. We generalized these shallow rupture features into a depth-dependent parametric variation of the slip-rate function and implemented it in the Graves–Pitarka kinematic rupture model generator. The performance of the updated kinematic approach was then verified in 0–4 Hz simulations of the Mw 7.1 Ridgecrest earthquake, which showed that incorporating the depth-dependent variation in the shape of the slip-rate function improves the fit to the observed near-fault ground motions in the 0.5–3 s period range.

Multicycle Simulation of Strike-Slip Earthquake Rupture for Use in Near-Source Ground-Motion Simulations

ABSTRACTRealistic dynamic rupture modeling validated by observed earthquakes is necessary for estimating parameters that are poorly resolved by seismic source inversion, such as stress drop, rupture velocity, and slip rate function. Source inversions using forward dynamic modeling are increasingly used to obtain earthquake rupture models. In this study, to generate a large number of physically self-consistent rupture models, rupture process of which is consistent with the spatiotemporal heterogeneity of stress produced by previous earthquakes on the same fault, we use multicycle simulations under the rate and state (RS) friction law.We adopt a one-way coupling from multicycle simulations to dynamic rupture simulations; the quasidynamic solver QDYN is used to nucleate the seismic events and the spectral element dynamic solver SPECFEM3D to resolve their rupture process. To simulate realistic seismicity, with a wide range of magnitudes and irregular recurrence, several realizations of 2D-correlated heterogeneous random distributions of characteristic weakening distance (Dc) in RS friction are tested. Other important parameters are the normal stress, which controls the stress drop and rupture velocity during an earthquake, and the maximum value of Dc, which controls rupture velocity but not stress drop. We perform a parametric study on a vertical planar fault and generate a set of a hundred spontaneous rupture models in a wide magnitude range (Mw 5.5–7.4).We validate the rupture models by comparison of source scaling, ground motion (GM), and surface slip properties to observations. We compare the source-scaling relations between rupture area, average slip, and seismic moment of the modeled events with empirical ones derived from source inversions. Near-fault GMs are computed from the source models. Their peak ground velocities and peak ground accelerations agree well with the ground-motion prediction equation values. We also obtain good agreement of the surface fault displacements with observed values.

Parameter interdependence of dynamic self-similar crack with distance-weakening friction

SUMMARY In several analytical and numerical studies, the slip rate function and energy release rate for dynamic self-similar crack growth have been investigated, and the results obtained have contributed to a theoretical understanding and estimation of on-fault energetics. However, the relationships among physical parameters, including stress state, process zone size, rupture velocity, peak slip rate and energy release rate, are still unclear. Therefore, the aim of this study is to derive an analytical solution of the slip rate distribution of antiplane self-similar crack growth under distance-weakening friction that mimics slip-weakening friction. To satisfy the condition that the slip rate starts from zero at the rupture front, a trade-off relationship among rupture velocity, process zone size and breakdown stress-to-stress drop ratio is proposed. The peak slip rate, slip-weakening distance and fracture energy obtained using the proposed model provide a possible mechanism for the determination of the rupture velocity and the estimation of the fracture energy of the self-similar crack growth, based on the seismic observables.

Development of an inversion method to extract information on fault geometry from teleseismic data

SUMMARYTeleseismic waveforms contain information on fault slip evolution during an earthquake, as well as on the fault geometry. A linear finite-fault inversion method is a tool for solving the slip-rate function distribution under an assumption of fault geometry as a single or multiple-fault-plane model. An inappropriate assumption of fault geometry would tend to distort the solution due to Green’s function modelling errors. We developed a new inversion method to extract information on fault geometry along with the slip-rate function from observed teleseismic waveforms. In this method, as in most previous studies, we assumed a flat fault plane, but we allowed arbitrary directions of slip not necessarily parallel to the assumed fault plane. More precisely, the method represents fault slip on the assumed fault by the superposition of five basis components of potency-density tensor, which can express arbitrary fault slip that occurs underground. We tested the developed method by applying it to real teleseismic P waveforms of the MW 7.7 2013 Balochistan, Pakistan, earthquake, which is thought to have occurred along a curved fault system. The obtained spatiotemporal distribution of potency-density tensors showed that the focal mechanism at each source knot was dominated by a strike-slip component with successive strike angle rotation from 205° to 240° as the rupture propagated unilaterally towards the south-west from the epicentre. This result is consistent with Earth’s surface deformation observed in optical satellite images. The success of the developed method is attributable to the fact that teleseismic body waves are not very sensitive to the spatial location of fault slip, whereas they are very sensitive to the direction of fault slip. The method may be a powerful tool to extract information on fault geometry along with the slip-rate function without requiring detailed assumptions about fault geometry.

A combinatorial approach to determine earthquake magnitude distributions on a variable slip-rate fault

SUMMARYCombinatorial methods are used to determine the spatial distribution of earthquake magnitudes on a fault whose slip rate varies along strike. Input to the problem is a finite sample of earthquake magnitudes that span 5 kyr drawn from a truncated Pareto distribution. The primary constraints to the problem are maximum and minimum values around the target slip-rate function indicating where feasible solutions can occur. Two methods are used to determine the spatial distribution of earthquakes: integer programming and the greedy-sequential algorithm. For the integer-programming method, the binary decision vector includes all possible locations along the fault where each earthquake can occur. Once a set of solutions that satisfy the constraints is found, the cumulative slip misfit on the fault is globally minimized relative to the target slip-rate function. The greedy algorithm sequentially places earthquakes to locally optimize slip accumulation. As a case study, we calculate how earthquakes are distributed along the megathrust of the Nankai subduction zone, in which the slip rate varies significantly along strike. For both methods, the spatial distribution of magnitudes depends on slip rate, except for the largest magnitude earthquakes that span multiple sections of the fault. The greedy-sequential algorithm, previously applied to this fault (Parsons et al., 2012), tends to produce smoother spatial distributions and fewer lower magnitude earthquakes in the low slip-rate section of the fault compared to the integer-programming method. Differences in results from the two methods relate to how much emphasis is placed on minimizing the misfit to the target slip rate (integer programming) compared to finding a solution within the slip-rate constraints (greedy sequential). Specifics of the spatial distribution of magnitudes also depend on the shape of the target slip-rate function: that is, stepped at the section boundaries versus a smooth function. This study isolates the effects of slip-rate variation along a single fault in determining the spatial distribution of earthquake magnitudes, helping to better interpret results from more complex, interconnected fault systems.

An Evolutive Linear Kinematic Source Inversion

AbstractWe present a new hierarchical time kinematic source inversion method able to assimilate data traces through evolutive time windows. A linear time domain formulation relates the slip rate function and seismograms, preserving the positivity of this function and the causality when spanning the model space: taking benefit of the time‐space sparsity of the rupture model evolution is as essential as considering the causality between rupture and each record delayed by the known propagator operator different for each station. This progressive approach, both on the data space and on the model space, does require mild assumptions on prior slip rate functions or preconditioning strategies on the slip rate local gradient estimations. These assumptions are based on simple physical expected rupture models we foresee. Successful applications of this method to a well‐known benchmark (Source Inversion Validation Exercise 1) and to the recorded data of the 2016 Kumamoto mainshock (Mw=7.0) illustrate the advantages of this alternative approach of a linear kinematic source inversion. This stabilized overparameterized optimization of a linear forward problem has a potential extension to stochastic inversion in a Bayesian framework in the future to assess uncertainties on kinematic source inversions, which is more difficult to investigate under nonlinear formulations.

Azimuthal Dependence of the Ground Motion Variability from Scenario Modeling of the 2014 Mw6.0 South Napa, California, Earthquake Using an Advanced Kinematic Source Model

Strong ground motion simulations require physically plausible earthquake source model. Here, I present the application of such a kinematic model introduced originally by Ruiz et al. (Geophys J Int 186:226–244, 2011). The model is constructed to inherently provide synthetics with the desired omega-squared spectral decay in the full frequency range. The source is composed of randomly distributed overlapping subsources with fractal number-size distribution. The position of the subsources can be constrained by prior knowledge of major asperities (stemming, e.g., from slip inversions), or can be completely random. From earthquake physics point of view, the model includes positive correlation between slip and rise time as found in dynamic source simulations. Rupture velocity and rise time follows local S-wave velocity profile, so that the rupture slows down and rise times increase close to the surface, avoiding unrealistically strong ground motions. Rupture velocity can also have random variations, which result in irregular rupture front while satisfying the causality principle. This advanced kinematic broadband source model is freely available and can be easily incorporated into any numerical wave propagation code, as the source is described by spatially distributed slip rate functions, not requiring any stochastic Green’s functions. The source model has been previously validated against the observed data due to the very shallow unilateral 2014 Mw6 South Napa, California, earthquake; the model reproduces well the observed data including the near-fault directivity (Seism Res Lett 87:2–14, 2016). The performance of the source model is shown here on the scenario simulations for the same event. In particular, synthetics are compared with existing ground motion prediction equations (GMPEs), emphasizing the azimuthal dependence of the between-event ground motion variability. I propose a simple model reproducing the azimuthal variations of the betweenevent ground motion variability, providing an insight into possible refinement of GMPEs’ functional forms.

New perspectives on self‐similarity for shallow thrust earthquakes

AbstractScaling of dynamic rupture processes from small to large earthquakes is critical to seismic hazard assessment. Large subduction earthquakes are typically remote, and we mostly rely on teleseismic body waves to extract information on their slip rate functions. We estimate the P wave source spectra of 942 thrust earthquakes of magnitude Mw 5.5 and above by carefully removing wave propagation effects (geometrical spreading, attenuation, and free surface effects). The conventional spectral model of a single‐corner frequency and high‐frequency falloff rate does not explain our data, and we instead introduce a double‐corner‐frequency model, modified from the Haskell propagating source model, with an intermediate falloff of f−1. The first corner frequency f1 relates closely to the source duration T1, its scaling follows for Mw<7.5, and changes to for larger earthquakes. An elliptical rupture geometry better explains the observed scaling than circular crack models. The second time scale T2 varies more weakly with moment, , varies weakly with depth, and can be interpreted either as expressions of starting and stopping phases, as a pulse‐like rupture, or a dynamic weakening process. Estimated stress drops and scaled energy (ratio of radiated energy over seismic moment) are both invariant with seismic moment. However, the observed earthquakes are not self‐similar because their source geometry and spectral shapes vary with earthquake size. We find and map global variations of these source parameters.

Kinematic earthquake source inversion and tsunami runup prediction with regional geophysical data

AbstractRapid near‐source earthquake source modeling relying only on strong motion data is limited by instrumental offsets and magnitude saturation, adversely affecting subsequent tsunami prediction. Seismogeodetic displacement and velocity waveforms estimated from an optimal combination of high‐rate GPS and strong motion data overcome these limitations. Supplementing land‐based data with offshore wave measurements by seafloor pressure sensors and GPS‐equipped buoys can further improve the image of the earthquake source and prediction of tsunami extent, inundation, and runup. We present a kinematic source model obtained from a retrospective real‐time analysis of a heterogeneous data set for the 2011 Mw9.0 Tohoku‐Oki, Japan, earthquake. Our model is consistent with conceptual models of subduction zones, exhibiting depth dependent behavior that is quantified through frequency domain analysis of slip rate functions. The stress drop distribution is found to be significantly more correlated with aftershock locations and mechanism types when off‐shore data are included. The kinematic model parameters are then used as initial conditions in a fully nonlinear tsunami propagation analysis. Notably, we include the horizontal advection of steeply sloping bathymetric features. Comparison with post‐event on‐land survey measurements demonstrates that the tsunami's inundation and runup are predicted with considerable accuracy, only limited in scale by the resolution of available topography and bathymetry. We conclude that it is possible to produce credible and rapid, kinematic source models and tsunami predictions within minutes of earthquake onset time for near‐source coastal regions most susceptible to loss of life and damage to critical infrastructure, regardless of earthquake magnitude.

Kinematic earthquake rupture inversion in the frequency domain

We develop a frequency-based approach to earthquake slip inversion that requires no prior information on the rupture velocity or slip-rate functions. Because the inversion is linear and is performed separately at each frequency, it is computationally efficient and suited to imaging the finest resolvable spatial details of rupture. We demonstrate the approach on synthetic seismograms based on the Source Inversion Validation Exercise 1 (SIV1) of a crustal Mw 6.6 strike-slip earthquake recorded locally. A robust inversion approach is obtained by applying a combination of damping, smoothing and forcing zero slip at the edge of the fault model. This approach achieves reasonable data fits, overall agreement to the SIV1 model, including slip-rate functions of each subfault, from which its total slip, slip time history and rupture velocity can be extracted. We demonstrate the method's robustness by exploring the effects of noise, random timing errors, and fault geometry errors. The worst effects on the inversion are seen from errors in the assumed fault geometry.

A Bayesian approach to determine the average shape of the slip-rate function and the rupture velocity using near-field phases: the 2003 Mw6.6 Bam earthquake example

SUMMARY Slip-rate function and the rupture velocity are two important parameters that are critical in understanding the physics of earthquakes. When conventional objective functions are used, the slip-rate function is not well resolved from seismic data. Here, we propose a new method to obtain the slip-rate function by utilizing the near-field phases recorded near the fault rupture. First we illustrate the sensitivity of near-field phases to the moment accumulation and modify the objective function in order to take advantage of this sensitivity. By utilizing near-field P waves along with S pulses on the near-source records and using a Bayesian approach, we show that we can constrain the average slip-rate function as well as the average rupture velocity for a strike-slip earthquake. As a case example, we apply this technique to the record of the 2003, Mw6.6 Bam Earthquake. Our results indicate an asymmetric slip-rate function, with acceleration duration of about 0.4s, and deceleration duration of 1.4s. The slip-rate function obtained from kinematic modelling of the 2003 Bam earthquake is consistent with those predicted by dynamic rupture simulations. The rupture velocity is about 82–90 per cent of the shear wave velocity, implying a sub-Rayleigh rupture velocity close to the Rayleigh wave speed. In future cases where abundant near-source strong-motion data exist and slip is well constrained, the method described in this study can be applied to obtain the variation of the slip-rate function along the fault which would improve our understanding of earthquake rupture physics.

Earthquake ruptures modulated by waves in damaged fault zones

AbstractFaults are usually surrounded by damaged zones of lower elastic moduli and seismic wave velocities than their host rocks. If the interface between the damaged rocks and host rocks is sharp enough, earthquakes happening inside the fault zone generate reflected waves and head waves, which can interact with earthquake ruptures and modulate rupture properties such as rupture speed, slip rate, and rise time. We find through 2–D dynamic rupture simulations the following: (1) Reflected waves can induce multiple slip pulses. The rise time of the primary pulse is controlled by fault zone properties, rather than by frictional properties. (2) Head waves can cause oscillations of rupture speed and, in a certain range of fault zone widths, a permanent transition to supershear rupture with speeds that would be unstable in homogeneous media. (3) Large attenuation smears the slip rate function and delays the initial acceleration of rupture speed but does not affect significantly the rise time or the period of rupture speed oscillations. (4) Fault zones cause a rotation of the background stress field and can induce plastic deformations on both extensional and compressional sides of the fault. The plastic deformations are accumulated both inside and outside the fault zone, which indicates a correlation between fault zone development and repeating ruptures. Spatially periodic patterns of plastic deformations are formed due to oscillating rupture speed, which may leave a permanent signature in the geological record. Our results indicate that damaged fault zones with sharp boundaries promote multiple slip pulses and supershear ruptures.

A kinematic rupture model generator incorporating spatial interdependency of earthquake source parameters

S U M M A R Y Based on the results obtained by analysing a large number of dynamic strike slip and dipping fault ruptures we construct a kinematic rupture model generator that incorporates some of the key source parameters extracted from the dynamic rupture models. In this kinematic rupture model, the slip rate function includes the final slip, the rise time, the local rupture velocity and the peak time (a measure of the impulsive part of the slip rate function). A four-dimensional correlation matrix is used to describe the spatial interdependency between the four source parameters—each of which is modelled as correlated random field. Each source parameter has a different marginal distribution determined from the analysis of the dynamic models. The marginal distributions are allowed to change as a function of distance from the hypocentre. The autocorrelation of each parameter is modelled by a power spectrum that follows a power law. The value of the spectral decay of the power law for the different source parameters is based on the results obtained from the dynamic rupture models. Finally, the values of rise time and peak time are adjusted such that the moment rate function fits a Brune spectrum for a specified corner frequency. We validate the rupture model generator using observed strong motion near field recording for the 1994 Northridge earthquake and the 1989 Loma Prieta earthquake. We perform comparisons with the rupture model generator of Liu et al. We find that only considering the response spectral bias of a best model is not sufficient to validate a rupture model generator. Thus we test the predictive power of the two rupture model generators if multiple ruptures are computed. Overall, the new rupture model generator yields a better prediction, compared to Liu et al., for the two validation events, especially in predicting observed PGV values and pseudospectral velocity at low frequencies (<1Hz).

What the exercise of the SPICE source inversion validation BlindTest 1 did not tell you

Uncertainties of earthquake finite-fault inversions based upon strong motion data are investigated using the source inversion validation BlindTest 1 exercise of the SPICE (Seismic Wave Propagation and Imaging in Complex Media: A European Network) project, motivated by previous counterintuitive results. The distribution of slip and the shapes of asymmetric slip rate functions are simultaneously inverted by matching 10 or 33 broad-band three-component velocity waveforms within the period ranging from 0.02 to 2 Hz, using a finite-fault method that carries out the waveform inversion in the wavelet domain. The effects of subfault size, data noise and the number of stations have been explored. Our results suggest: (1) Although there are inevitable discrepancies between the inverted model and the target model because of ignoring the spatial slip variations within individual subfaults, the fault slip and rise-time distributions can be well constrained even with the data including large Gaussian noise. (2) It is crucial for source studies to develop new inversion schemes that can properly honour the frequency- and time-dependent energy distribution of seismic radiation and data noise. For instance, inversions using the variance reduction function of velocity waveforms as the objective function have low sensitivities to the total seismic moment and peak slip. (3) Although the relative value of the objective function is guided in the inversion, the absolute value of the objective function cannot be used to evaluate the quality of an inverted model. (4) Because the source inversion is based on surface observations, the spatiotemporal resolution of source inversion is affected not only by the data quality but also by the earthquake itself. For vertical strike-slip faults, the along-strike resolution is better than that along the downdip direction.

Broadband Ground-Motion Simulation Using a Hybrid Approach

This paper describes refinements to the hybrid broadband ground-motion simulation methodology of Graves and Pitarka (2004), which combines a deterministic approach at low frequencies ( f 1 Hz). In our approach, fault rupture is represented kinematically and incorporates spatial heterogeneity in slip, rupture speed, and rise time. The prescribed slip distribution is constrained to follow an inverse wavenumber-squared fall-off and the average rupture speed is set at 80% of the local shear-wave velocity, which is then adjusted such that the rupture propagates faster in regions of high slip and slower in regions of low slip. We use a Kostrov-like slip-rate function having a rise time proportional to the square root of slip, with the average rise time across the entire fault constrained empirically. Recent observations from large surface rupturing earthquakes indicate a reduction of rupture propagation speed and lengthening of rise time in the near surface, which we model by applying a 70% reduction of the rupture speed and increasing the rise time by a factor of 2 in a zone extending from the surface to a depth of 5 km. We demonstrate the fidelity of the technique by modeling the strong-motion recordings from the Imperial Valley, Loma Prieta, Landers, and Northridge earthquakes.

Hybrid Broadband Ground-Motion Simulation Using Scattering Green's Functions: Application to Large-Magnitude Events

We calculate near-source broadband (0-10 Hz) seismograms by combin- ing low-frequency three-dimensional (3D) finite-difference seismograms (0-0.5 Hz) computed in a 3D velocity model using site-specific scattering Green's functions for random, isotropic scattering media. The scattering Green's functions are convolved with a slip-rate function to form local scattering operators (scatterograms), which constitute the high-frequency scattered wave field. The low-frequency and high- frequency scatterograms are then combined in the frequency domain to generate broadband waveforms. Our broadband method extends the Mai et al. (2010) approach by incorporating dynamically consistent source-time functions and account- ing for finite-fault effects in the computation of the high-frequency waveforms. We used the proposed method to generate broadband ground motions at 44 sites located 5-100 km from the fault, for Mw 7.7 earthquake scenarios (TeraShake) on the south- ern San Andreas fault, which include north-to-south, south-to-north, and bilateral rupture propagation from kinematic and spontaneous dynamic rupture models. The broadband ground motions computed with the new method are validated by com- paring peak ground acceleration, peak ground velocity, and spectral acceleration with recently proposed ground-motion prediction equations (GMPEs). Our simulated ground motions are consistent with the median ground motions predicted by the GMPEs. In addition, we examine overturning probabilities for 18 precariously balanced rock sites (PBR). Our broadband synthetics for the Mw 7.7 TeraShake sce- narios show no preferred rupture direction on the southern San Andreas fault but are inconsistent with the existence of PBRs at several of the sites analyzed.

The 24 May 2009 Mw5.2 earthquake sequence near Lake Doirani (FYROM-Greek borders): Focal mechanisms and slip model using empirical source time functions inversion

On 24 May 2009 (GMT 16:17) a moderate size (Mw5.2) earthquake sequence burst north of Lake Doirani along the Greek-FYROM borders and ruptured a N282°E striking normal fault of ∼ 6 km in length dipping at an angle of ∼ 60° to the north. The focal mechanisms for 25 of the stronger events, obtained through time-domain moment tensor inversion, reveal the prevalence of normal faulting along ∼ WNW–ESE striking planes, sometimes dip slip motions are combined with a considerable strike-slip component. Broad band waveforms from the Hellenic Unified Seismological Network (HUSN) and neighbouring networks were used to invert source time functions (STFs) and calculate the slip model for the strongest event (GMT 16:17). STFs were obtained through an empirical Green's function approach. No directivity could be clearly identified for this moderate magnitude event. Slip was released in a single patch of dimensions 6 km × 8 km, maximum slip is estimated at 15 cm, while average slip on the ruptured area (area of subfaults of non-zero slip) was 3 cm. One characteristic of the slip model was the large rise time, for a moderate size event, which was estimated to be 1.0 s, implying a slow slip-rate function. Brune's static stress drop is calculated ∼ 5 bars. It must be noted that the north dipping plane is identified as the fault plane, (slip vector trending N332°E) based on the model variance of the STFs inversion.

A Characteristic Rupture Model for the 2001 Geiyo, Japan, Earthquake

In this study we present a characteristic kinematic rupture model for an intraslab earthquake of the type of the 2001 Geiyo earthquake. The procedure for developing the characteristic rupture model follows the recipe developed by Irikura and Miyake (Proceedings of the 8th US National Conference on Earthquake Engineering, San Francisco, 2006) with a few modifications. We used the functional form of Nakamura and Miyatake [Zisin (J Seism Soc Jpn), 53, 1–9, 2000] to model the spatial and temporal variability of the slip rate function. In our procedure the earthquake source is specified by the kinematic description of the fault model that incorporates spatial heterogeneity in slip and rise time and constant rupture velocity. In the proposed characteristic model the asperity locations and rupture initiation point were the only parameters that were constrained by the available earthquake rupture models of the target earthquake. The quality of the characteristic rupture model was assessed by comparing recorded and synthetic ground motion time histories from the 2001 Geiyo earthquake calculated with a standard broadband (0.1–10 Hz) ground motion simulation technique. Our analyses show that the characteristic rupture model performs well in reproducing the recorded ground motion, in spite of its simple representation of the fault geometry and kinematic rupture complexity. The analyses of ground motion sensitivity to relative location of asperities, and their stress drop contrast suggest that the overall ground motion goodness of fit remains the same at short periods, but decreases slightly at periods longer than 1 s. We suspect that, due to the depth of the intraslab source (40–50 km), the higher-frequency ground motions are relatively insensitive to the details of the slip distribution and slip contrast. On the other hand, even for intraslab events, the lower-frequency motions are influenced by rupture directivity effects and slip distribution.