P. Martin Mai

A spatial random field model to characterize complexity in earthquake slip

[1] Finite-fault source inversions reveal the spatial complexity of earthquake slip over the fault plane. We develop a stochastic characterization of earthquake slip complexity, based on published finite-source rupture models, in which we model the distribution of slip as a spatial random field. The model most consistent with the data follows a von Karman autocorrelation function (ACF) for which the correlation lengths a increase with source dimension. For earthquakes with large fault aspect ratios, we observe substantial differences of the correlation length in the along-strike (a x ) and downdip (a z ) directions. Increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation. The power spectrum of the slip distribution can also be well described with a power law decay (i.e., a fractal distribution) in which the fractal dimension D remains scale invariant, with a median value D = 2.29 ±0.23, while the comer wave number k c , which is inversely proportional to source size, decreases with earthquake magnitude, accounting for larger slip patches for large-magnitude events. Our stochastic slip model can be used to generate realizations of scenario earthquakes for near-source ground motion simulations.

Source Scaling Properties from Finite-Fault-Rupture Models

Finite-source images of earthquake rupture show that fault slip is spatially variable at all resolvable scales. In this study we develop scaling laws that account for this variability by measuring effective fault dimensions derived from the autocorrelation of the slip function for 31 published slip models of 18 earthquakes, 8 strike-slip events, and 10 dip-slip (reverse, normal, or oblique) events. We find that dip-slip events show self-similar scaling, but that scale invariance appears to break down for large strike-slip events for which slip increases with increasing fault length despite the saturation of rupture width. Combining our data with measurements from other studies, we find evidence for a nonlinear relationship between average displacement and fault length, in which displacement increases with fault length at a decreasing rate for large strike-slip events. This observation is inconsistent with pure width or length scaling for simple constant stress-drop models, but suggests that the finite seismogenic width of the fault zone exerts a strong influence on the displacement for very large strike-slip earthquakes.

Hypocenter Locations in Finite-Source Rupture Models

We use a database of more than 80 finite-source rupture models for more than 50 earthquakes ( M w 4.1–8.1) with different faulting styles occurring in both tectonic and subduction environments to analyze the location of the hypocenter within the fault and to consider the correlation between hypocenter location and regions of large slip. Rupture in strike-slip and crustal dip-slip earthquakes tends to nucleate in the deeper sections of the fault; subduction earthquakes do not show this tendency. Ratios of the hypocentral slip to either the average or the maximum slip show that rupture can nucleate at locations with any level of relative displacement. Rupture nucleates in regions of very large slip ( D ≥ 2/3 D max ) in only 16% of the events, in regions of large slip (1/3 D max D D max ) in 35% of the events, and in regions of low slip ( D ≤ 1/3 D max ) in 48% of the events. These percentages significantly exceed the percentages of fault area with very large (∼7%) and large (∼28%) slip. Ruptures that nucleate in regions of low slip, however, tend to nucleate close to regions of large slip and encounter a zone of very large slip within half the total rupture length. Applying several statistical tests we conclude that hypocenters are not randomly located on a fault but are located either within or close to regions of large slip.

A Pseudo-Dynamic Approximation to Dynamic Rupture Models for Strong Ground Motion Prediction

Accurate prediction of the intensity and variability of strong ground motions from future large earthquakes depends on our ability to simulate realistic earthquake source models. We have developed a procedure to generate physically consistent earthquake-rupture models that should help make such simulations more accurate. We term these models “pseudo dynamic” because they are kinematic models that are designed to emulate important characteristics of dynamic rupture. We construct pseudo-dynamic models first by generating a slip distribution as a realization of a spatial random field that is consistent in its scaling and spatial variability with slip distributions observed in past earthquakes. We then compute the static stress drop associated with the slip distribution, which in turn is used to estimate the temporal evolution of slip through a set of empirical relationships derived from the analysis of spontaneous rupture models. Finally, a simple energy-budget calculation is used to eliminate models that are not likely to propagate spontaneously. The principal advantage of the pseudo-dynamic approach is that it avoids the computational demands of generating fully dynamic rupture models for multiple realizations of a scenario earthquake. While the relationships between source parameters described in this paper are simplifications of the true complexity of the physics of rupture, they help identify important interactions between source properties that are relevant for strong ground motion prediction, and should provide an improvement over purely kinematic models.

Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S Backscattering

We present a new approach for computing broadband (0–10 Hz) synthetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green’s functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation ηs, intrinsic attenuation ηi, and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our methodology to the 1994 Northridge earthquake and validating against near-field recordings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broadband simulations. This innovative hybrid ground-motion simulation approach, applicable to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

A hybrid method for calculating near-source, broadband seismograms: application to strong motion prediction

Abstract We present a hybrid method for computing broadband strong motion seismograms in the near-field of large earthquakes. We combine complete seismograms at low-frequency with ray-theory seismograms at high-frequency to form a composite broadband seismogram that spans the entire frequency range of interest. In our approach, the amplitude spectra of the two sets of synthetic seismograms are reconciled at intermediate frequencies where their domain of validity overlaps. We demonstrate the method with scenario earthquakes based on the spatial random-field model for complex earthquake slip [J. Geophys. Res. 107 (B11) (2002) 2308]. The hybrid near-source, broadband seismograms are useful both for detailed source modeling and for incorporating source effects into probabilistic seismic hazard analysis.

Calculation of Broadband Time Histories of Ground Motion, Part II: Kinematic and Dynamic Modeling Using Theoretical Green's Functions and Comparison with the 1994 Northridge Earthquake

In the evolution of methods for calculating synthetic time histories of ground motion for postulated earthquakes, kinematic source models have dominated to date because of their ease of application. Dynamic models, however, which incorporate a physical relationship between important faulting parameters of stress drop, slip, rupture velocity, and rise time, are becoming more accessible. This article compares a class of kinematic models based on the summation of a fractal distribution of subevent sizes with a dynamic model based on the slip-weakening friction law. Kinematic modeling is done for the frequency band 0.2 to 10.0. Hz, dynamic models are calculated from 0.2 to 2.0. Hz. The strong motion data set for the 1994 Northridge earthquake is used to evaluate and compare the synthetic time histories. Source models are propagated to the far field by convolution with 1D and 3D theoretical Green’s functions. In addition, the kinematic model is used to evaluate the importance of propagation path effects: velocity structure, scattering, and nonlinearity. At present, the kinematic model gives a better broadband fit to the Northridge ground motion than the simple slip-weakening dynamic model. In general, the dynamic model overpredicts rise times and produces insufficient shorter-period energy. Within the context of the slip-weakening model, the Northridge ground motion requires a short slip-weakening distance, on the order of 0.15 m or less. A more complex dynamic model including rate weakening or one that allows shorter rise times near the hypocenter may fit the data better.

Scaling Relations of Local Magnitude versus Moment Magnitude for Sequences of Similar Earthquakes in Switzerland

Abstract Theoretical considerations and empirical regressions show that, in the magnitude range between 3 and 5, local magnitude, M L , and moment magnitude, M w , scale 1:1. Previous studies suggest that for smaller magnitudes this 1:1 scaling breaks down. However, the scatter between M L and M w at small magnitudes is usually large and the resulting scaling relations are therefore uncertain. In an attempt to reduce these uncertainties, we first analyze the M L versus M w relation based on 195 events, induced by the stimulation of a geothermal reservoir below the city of Basel, Switzerland. Values of M L range from 0.7 to 3.4. From these data we derive a scaling of M L ∼1.5 M w over the given magnitude range. We then compare peak Wood–Anderson amplitudes to the low-frequency plateau of the displacement spectra for six sequences of similar earthquakes in Switzerland in the range of 0.5≤ M L ≤4.1. Because effects due to the radiation pattern and to the propagation path between source and receiver are nearly identical at a particular station for all events in a given sequence, the scatter in the data is substantially reduced. Again we obtain a scaling equivalent to M L ∼1.5 M w . Based on simulations using synthetic source time functions for different magnitudes and Q values estimated from spectral ratios between downhole and surface recordings, we conclude that the observed scaling can be explained by attenuation and scattering along the path. Other effects that could explain the observed magnitude scaling, such as a possible systematic increase of stress drop or rupture velocity with moment magnitude, are masked by attenuation along the path.

The Earthquake‐Source Inversion Validation (SIV) Project

Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward-modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source-model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake-source imaging problem.

Variability of tsunami inundation footprints considering stochastic scenarios based on a single rupture model: Application to the 2011 Tohoku earthquake

The sensitivity and variability of spatial tsunami inundation footprints in coastal cities and towns due to a megathrust subduction earthquake in the Tohoku region of Japan are investigated by considering different fault geometry and slip distributions. Stochastic tsunami scenarios are generated based on the spectral analysis and synthesis method with regards to an inverted source model. To assess spatial inundation processes accurately, tsunami modeling is conducted using bathymetry and elevation data with 50 m grid resolutions. Using the developed methodology for assessing variability of tsunami hazard estimates, stochastic inundation depth maps can be generated for local coastal communities. These maps are important for improving disaster preparedness by understanding the consequences of different situations/conditions, and by communicating uncertainty associated with hazard predictions. The analysis indicates that the sensitivity of inundation areas to the geometrical parameters (i.e., top-edge depth, strike, and dip) depends on the tsunami source characteristics and the site location, and is therefore complex and highly nonlinear. The variability assessment of inundation footprints indicates significant influence of slip distributions. In particular, topographical features of the region, such as ria coast and near-shore plain, have major influence on the tsunami inundation footprints.