Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude ( M ), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement

This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

This paper reviews rock friction and the frictional properties of earthquake faults. The basis for rate- and state-dependent friction laws is reviewed. The friction state variable is discussed, including its interpretation as a measure of average asperity contact time and porosity within granular fault gouge. Data are summarized showing that friction evolves even during truly stationary contact, and the connection between modern friction laws and the concept of “static” friction is discussed. Measurements of frictional healing, as evidenced by increasing static friction during quasistationary contact, are reviewed, as are their implications for fault healing. Shear localization in fault gouge is discussed, and the relationship between microstructures and friction is reviewed. These data indicate differences in the behavior of bare rock surfaces as compared to shear within granular fault gouge that can be attributed to dilation within fault gouge. Physical models for the characteristic friction distance are discussed and related to the problem of scaling this parameter to seismic faults. Earthquake afterslip, its relation to laboratory friction data, and the inverse correlation between afterslip and shallow coseismic slip are discussed in the context of a model for afterslip. Recent observations of the absence of afterslip are predicted by the model.

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Laboratory-derived friction laws and their application to seismic faulting

[1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2007RG000228

A review on Hilbert‐Huang transform: Method and its applications to geophysical studies

A simple and powerful method for simulating ground motions is to combine parametric or functional descriptions of the ground motion’s amplitude spectrum with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to the distance from the source. This method of simulating ground motions often goes by the name “the stochastic method.” It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers (generally, f > 0.1 Hz), and it is widely used to predict ground motions for regions of the world in which recordings of motion from potentially damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude and in diverse tectonic environments. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers in this volume can be incorporated into practical predictions of ground motion.

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Simulation of Ground Motion Using the Stochastic Method

A least-squares point-by-point inversion of strong ground motion and teleseismic body waves is used to infer the fault rupture history of the 1979 Imperial Valley, California, earthquake. The Imperial fault is represented by a plane embedded in a half-space where the elastic properties vary with depth. The inversion yields both the spatial and temporal variations in dislocation on the fault plane for both right-lateral strike-slip and normal dip-slip components of motion. Inversions are run for different fault dips and for both constant and variable rupture velocity models. Effects of different data sets are also investigated. Inversions are compared which use the strong ground motions alone, the teleseismic body waves alone, and simultaneously the strong ground motion and teleseismic records. The inversions are stabilized by adding both smoothing and positivity constraints.
The moment is estimated to be 5.0 × 10^(25) dyne-cm and the fault dip 90° ± 5°. Dislocation in the hypocentral region south of the United States-Mexican border is relatively small and almost dies out near the border. Dislocation then increases sharply north of the border to a maximum of about 2 m under Interstate 8. Dipslip motion is minor compared to strike-slip motion and is concentrated in the sediments. The best-fitting constant rupture velocity is 80 per cent of the local shear-wave velocity. However, there is a suggestion that the rupture front accelerated from the hypocenter northward. The 1979 Imperial Valley earthquake can be characterized as a magnitude 5 earthquake at the hypocenter which then grew into or triggered a magnitude 6 earthquake north of the border.

/pdf/inversion-of-strong-ground-motion-and-teleseismic-waveform-74bcy5k05q.pdf

Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake

A method is presented for modeling earthquake strong ground motion, which uses the aftershocks associated with a large earthquake as Green's functions. A major earthquake, with a large rupture surface, is modeled by a collection of point sources distributed over the fault plane. The response of each point source is approximated by the ground motion of the closest associated aftershock. By using the aftershock responses, the effects of the true earth structure are included in the modeling process. This method is used to model the El Centro displacement record for the 1940 Imperial Valley earthquake.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/GL005i001p00001%4010.1002/%28ISSN%291944-8007.GRL40

Earthquake aftershocks as Green's functions

We have compared aftershock patterns following several moderate to large earthquakes with the corresponding distributions of coseismic slip obtained from previous analyses of the recorded strong ground motion and teleseismic waveforms. Well-located aftershock hypocenters are projected onto the main shock fault plane, and their positions are examined relative to the zones of coseismic displacement indicated by the estimated distributions of main shock slip. We also examine the aftershock focal mechanisms, when these data are available, in an attempt to identify possible patterns of secondary faulting within the aftershock zone.

Our results are consistent with a hypothesis of aftershock occurrence that requires a secondary redistribution of stress following primary failure on the earthquake fault. Aftershocks following the earthquakes examined in this study occur mostly outside of or near the edges of the source areas indicated by the patterns of main shock slip. The spatial distribution of aftershocks reflects either a continuation of slip in the outer regions of the areas of maximum coseismic displacement or the activation of subsidiary faults within the volume surrounding the boundaries of main shock rupture.

Aftershock patterns and main shock faulting

Near-source strong motion velocity records and teleseismic short-period P waveforms are modeled to obtain the spatial and temporal distribution of slip for the 1984 Morgan Hill earthquake. Both forward modeling and constrained, least-squares inversion techniques are used to interpret the strong motion velocity waveforms in the frequency range of approximately 0.2 to 2.0 Hz. These data support a nearly unilateral rupture to the southeast with a rupture propagation velocity of nine-tenths of the local S-wave velocity. The majority of the slip occurs over a fault length of 25 km and to a first approximation can be interpreted as two main source regions, each with an extent of about 5 km with their centers separated by about 12 km. However, each of the sources has detailed structure of its own, and a simple two-point-source model is not an accurate representation of the Morgan Hill earthquake. The second source occurs about 4.5 sec after the first and is approximately 3 times larger. The maximum dislocation on the fault plane is about 1 m. The total moment of the earthquake is estimated to be 2.1 × 10^(25) dyne-cm. The Morgan Hill earthquake offers convincing evidence for very inhomogeneous slip and stress distributions on shallow strike-slip faults.

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Rupture history of the 1984 morgan hill, california, earthquake from the inversion of strong motion records

This article compares techniques for calculating broadband time histories of ground motion in the near field of a finite fault by comparing synthetics with the strong-motion data set for the 1994 Northridge earthquake. Based on this comparison, a preferred methodology is presented. Ground-motion-simulation techniques are divided into two general methods: kinematic- and composite-fault models. Green's functions of three types are evaluated: stochastic, empirical, and theoretical. A hybrid scheme is found to give the best fit to the Northridge data. Low frequencies ( 1 Hz) are calculated using a composite-fault model with a fractal subevent size distribution and stochastic, bandlimited, white-noise Green's functions. At frequencies below 1 Hz, theoretical elastic-wave-propagation synthetics introduce proper seismic-phase arrivals of body waves and surface waves. The 3D velocity structure more accurately reproduces record durations for the deep sedimentary basin structures found in the Los Angeles region. At frequencies above 1 Hz, scattering effects become important and wave propagation is more accurately represented by stochastic Green's functions. A fractal subevent size distribution for the composite fault model ensures an ω−2 spectral shape over the entire frequency band considered (0.1-20 Hz).

Calculation of broadband time histories of ground motion: Comparison of methods and validation using strong-ground motion from the 1994 Northridge earthquake

Stephen H. Hartzell

Papers

Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake

Earthquake aftershocks as Green's functions

Aftershock patterns and main shock faulting

Rupture history of the 1984 morgan hill, california, earthquake from the inversion of strong motion records

Calculation of broadband time histories of ground motion: Comparison of methods and validation using strong-ground motion from the 1994 Northridge earthquake