The Physics of the Earthquake Source and Radiated Waves: Frequency Dependence, Spatial Distribution, and Directivity in Elastodynamic Models of Repeated Fault Ruptures

Columbia University, New York NY

Investigators

Abstract

The main thrust of this work is to seek a deeper understanding of the radiated waves emitted by earthquakes. In previous work, the investigator has examined how total radiated energy can be sensitive to the source physics, showing dfferences for slip versus velocity weakening friction in elastodynamic faults. This work was expanded to look at the frequency content and spatial dependence of the radiation. A number of important results were obtained, including: (1) A new radiating boundary condition allowing a nonuniform prestress, useful for repeated ruptures, was developed; (2) Having to assume only a physics of the tractions on the fault, the full spectra of radiated waves for events with a wide range of sizes were generated; (3) Characterizing the spectral content of the radiation, a nonlinear magnitude dependence of a second corner frequency was found, and shown to be related to fundamental source parameters; (4) Strong directivity effects for large events were exhibited in spectral ratios. With renewed support, continued research on this subject is being carried out, with a focus on three specifc projects: The first project involves further exploration of magnitude and spatial dependence of directivity effects. Initial results have shown striking amplification of acceleration spectra away from the epicentral region in large events. Further exploration of these effects includes time domain complements of the frequency domain measurements already made. This work will further develop a new theoretical tool for exploring an issue with potentially large hazard and earthquake engineering implications. The second project involves the extension of measurements made in two-dimensional models of radiated energy spectra to three-dimensional models. A further generalization of a new radiating boundary condition is being developed in two dimensions, both extending it to higher dimensions and to continuous loading, allows direct measurements at long times. This allows quantitative physical predictions of the magnitude dependence of radiated energy spectra. The third project involves the application of a new measurement developed in the models to earthquake data. The measurement takes advantage of a natural averaging measure through summing of energy spectra to convert to average acceleration spectra. In the models, the period of the peak average acceleration spectra was shown to reflect fundamental source parameters. Measurements of the magnitude dependence of this quantity in earthquakes are being carried out.