A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

/pdf/surface-deformation-due-to-shear-and-tensile-faults-in-a-2vckanzx6g.pdf

Surface deformation due to shear and tensile faults in a half-space

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

A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms representing deformations in an infinite medium, a term related to surface deformation and that is multiplied by the depth of observation point. Several practical suggestions to avoid mathematical singularities and computational instabilities are also presented. The expressions derived here represent powerful tools both for the observational and theoretical analyses of static field changes associated with earthquake and volcanic phenomena.

http://arrowsmith510.asu.edu/TheLectures/Lecture18/Okada_1992.pdf

Internal deformation due to shear and tensile faults in a half-space

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.

/pdf/laboratory-derived-friction-laws-and-their-application-to-44s35v6won.pdf

Laboratory-derived friction laws and their application to seismic faulting

Gondwana dispersion and Asian accretion: Tectonic and palaeogeographic evolution of eastern Tethys

SUMMARY We developed a new inversion method to reconstruct static images of seismic sources from geodetic data, using Akaike’s Bayesian Information Criterion (ABIC). Coseismic surface displacements are generally related with a slip distribution on a fault surface by linear integral equations. Parametric expansion of the fault slip distribution by a finite number of known basis functions yields a set of observation equations expressed in a simple vector form. Incorporating prior constraints on the smoothness of slip distribution with the observation equations, we construct a Bayesian model with unknown hyperparameters. The optimal values of the hyperparameters, which control the structure of the Bayesian model, are objectively determined from observed data by using ABIC. Once the values of hyperparameters are determined, we can use the maximum likelihood method to find the optimal distribution of fault slip. We examined the validity of this method through a numerical experiment using theoretical data with random noise. We analysed geodetic data associated with the 1946 Nankaido earthquake (Ms = 8.2) by using this method. The result shows that the fault slip distribution of this earthquake has two main peaks of 4 and 6 m, located off Kii Peninsula and Muroto Promontory. These two high-slip areas are clearly separated by a low-slip zone extending along Kii Strait. Such a slip distribution corresponds with the fact that the rupture process of this earthquake in the western part is notably different from that in the eastern part.

/pdf/geodetic-data-inversion-using-a-bayesian-information-1ncf81i75g.pdf

Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip

Powerful methods are now available for solving linear parametric inverse problems. However, many inverse problems which arise in geohysics are nonlinear. Fortunately, it is possible to treat most of these with the air of linear perturbation theory and liner inversion. But a convenient method is needed for assessing the importance of nonlinearity in these quasi-linear problems. The present paper provides such a method. Matsu'ura and Jackson (1984) have presented a simple algorithm for evaluating the asymptotic covariance matrix fo estimation errors. In the present investigation, aspects of linear inversion are discussed, taking into account linear parametric inverse problems, nonuniqueness, prior information, confidence limits, conditional and marginal statistics, the relative importance of the prior and observational data, and standardized variables. Attention is also given to nonlinear inversion, and the application of the considered approaches to a number of examples.

A Bayesian approach to nonlinear inversion

Maximum-likelihood estimation of hypocenter with origin time eliminated using nonlinear inversion technique

Stress accumulation between earthquakes results from slip that is insufficient to fully accommodate plate movement. An inverse analysis of GPS data from the Kuril–Japan trench reveals a trench-parallel belt of stress accumulation with six peaks in the depth range of 10–40 km, suggesting potential source regions for future earthquakes. In the subduction zones around Japan, where four plates interact with one another, large earthquakes have occurred repeatedly1. These interplate earthquakes are part of the process of tectonic stress accumulation and release that is driven by relative plate motion2,3,4. Stress accumulation between earthquakes results from slip deficit (slip that is insufficient to fully accommodate plate movement). For the prediction of large earthquakes, it is therefore important to monitor the distribution of slip deficit on plate interfaces. Here we apply an inversion method based on Bayesian modelling (using direct and indirect prior information on the magnitude and distribution of fault slip5) to horizontal and vertical velocities from global positioning system data. For the seismically calm period between 1996 and 2000, we obtain a precise distribution of slip-deficit rates on the interface between the North American and Pacific plates around Japan, which reveals a trench-parallel belt of slip deficit with six peaks in the depth range of 10–40 km. These peaks agree with the source regions of past large interplate earthquakes along the Kuril–Japan trench. We conclude that the slip-deficit zones identified with our method are potential source regions of large earthquakes.

Interplate seismogenic zones along the Kuril–Japan trench inferred from GPS data inversion

—We constructed a new calculation scheme of spontaneous rupture propagation on non-planar faults in a 3-D elastic medium using a boundary integral equation method (BIEM) in time domain We removed all singularities in boundary integral equations (BIEs) following the method proposed by Fukuyama and Madariaga (1995, 1998) for a planar fault in a 3-D elastic medium, and analytically evaluated all BIEs for a basic box-like discrete source As an application of the new calculation scheme, we simulated rupture propagation on a bending fault subjected to uniform triaxial compression and examined the effect of fault bend upon the dynamic rupture propagation From the numerical results, we found that rupture propagation is decelerated or arrested for some combination of inclined angle of the bending fault and absolute value of the fault strength The most significant effect of bending is the nonuniform distribution of pre-loaded shear stress due to different orientation of the fault plane under a uniform tectonic stress regime Our results also indicate that low absolute shear stress level is required to progress the rupture propagation ahead of the inclined fault

Mitsuhiro Matsu'ura

Papers

Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip

A Bayesian approach to nonlinear inversion

Maximum-likelihood estimation of hypocenter with origin time eliminated using nonlinear inversion technique

Interplate seismogenic zones along the Kuril–Japan trench inferred from GPS data inversion

Spontaneous Rupture Propagation on a Non-planar Fault in 3-D Elastic Medium