Analysis methods for kinematic data from local earthquakes

Abstract

A review of the techniques underlying the basic analysis of local and regional earthquakes is presented, describing modern methods for earthquake location, velocity inversion, and fault plane solution. These three topics require a method for ray tracing, determining the seismic ray path connecting the earthquake source to the observing station. A basic introduction to common ray tracing techniques is presented. Earthquake location based on Geiger's method remains the most common in use. Our understanding of this fundamental problem has been enhanced by a variety of studies, and by progress in geophysical inverse theory, but difficulties with the method remain. Alternatives to Geiger's method are reviewed to emphasize the continuing need for study of earthquake location techniques. The more complex problem of simultaneous inversion is receiving increasing attention. Algorithms have been developed to deal with a wide range of velocity structures, including layered, continuous one‐dimensional, and three‐dimensional models. Modern techniques for manipulating and transforming large matrix equations have been critical to the success of simultaneous inversion. Finally, methods for determining fault plane solutions are reviewed, such as first motion, amplitude ratio, and polarization, and techniques are discussed for inferring stress orientation from sets of focal mechanisms.

Hengill geothermal volcanic complex (Iceland) characterized by integrated geophysical observations

“…The theory and method of local tomography inversion have been described by a number of authors (e.g., Thurber, 1983;1986;Kissling, 1988;Ellsworth et al, 1991;Eberhart-Phillips, 1993;Iyer and Hirahara, 1993;Kissling et al, 1994;EberhartPhillips and Michael, 1998;Tryggvason et al, 2002;Koulakov et al, 2007).…”

Earthquake locations in southern California obtained using source‐specific station terms

“…The traditional way, apparently dating back to at least Geiger [1910], is to use least squares and to expand the residuals in a first-order Taylor series about some initial guess for ti and •. The resulting linear least squares problem is then solved via the normal equations (or modifications thereof; [see Thurber, 1986, and references therein]) to yield an improved location estimate, and the method then iterates to convergence. Other misfit criteria can be handled using a similar approach by iteratively reweighting the residuals to simulate the desired misfit measure [Anderson, 1982].…”

Seismic Tomography of the Lithosphere with Body Waves

“…For a starting model that is a homogeneous and isotropic medium, as assumed in the A&L method, the derivatives are proportional to the corresponding direction cosines of the vector connecting the source to the receiver. For the general case, the derivatives are proportional to the direction cosines of the ray direction at the source (THURBER, 1986).…”