Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical problems in geophysical investigations of solid Earth

Most techniques used in seismological practice have been performed under assumption that surface waves propagate along great circle arcs between the epicenter and the recording station. However, the results of tomographic studies show that lateral variations of surface wave phase velocities may amount to ~ 10%. Such variations should result in deviation of the wave paths from great circle arcs and in corresponding anomalies of geometrical spreading (focusing effect). We performed numerical modeling (ray tracing and dynamic ray tracing) of these effects on the basis of recent global phase velocity maps for fundamental Rayleigh mode obtained by tomographic inversion in the period range from 60 to 150 seconds.

The aim for such a modeling is to investigate where the standard procedures for surface wave processing based on the ray theory are valid, and to obtain quantitative characteristics of the effects of rays focusing. These characteristics should be taken into account in different applications: seismic source study, magnitude measurements, Q estimation. Neglect of anomalies of geometrical spreading, as well as stronger effects, such as caustics and multipathing, may lead to false estimates.

Similarity of predicted and observed focusing effects was analyzed statistically on the material of real seismic records. Records of the earthquakes in wide magnitude range and with epicenters in different seismic regions were used for the analysis (about 2500 measurements). Synthetic and observed Rayleigh wave amplitude spectra are found to be more similar if the focusing effect is taken into account: correction of spectra for predicted focusing effect significantly improves the fit of synthetics to observations. So, the maps of lateral variations of surface wave phase velocities obtained from travel time observations can be used for calculation of dynamic characteristics of surface waves.

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