Understanding Extreme Geohazards: The Science of the Disaster Risk Management Cycle European Science Foundation Conference November 28 to December 1, 2011, Sant Feliu de Guixols, Spain

Modeling of seismic waves in layered media and the inversion for the seismic tensor

Dmytro Malytskyy
Carpathian Branch of Subbotin Institute of Geophysics (CB IGPH), Lviv, Ukraine, dmytro@cb-igph.lviv.ua

This paper is organized as follows. After a discussion of the differential equations for wave propagation in the horizontally stratified medium and of the initial and boundary conditions, we derive the displacements on the free surface of the layered medium for plane waves when a point source is located on the s-th imaginary boundary at the depth (physical parameters of the layers s and (s+1) are put to be identical). Then, the source will be represented as a single force of arbitrary orientation and a general moment tensor point source. Further, “a primary field” for a point source will be introduced. Method for the solution of the direct seismic problem is considered based on the matrix method of Thomson-Haskell. The tensor represents a superposition of three single couples without moment along the x, y, z-axes and three double couples in xy, xz, yz-planes. Further, we give the results for the field of displacements on the free surface. The results of this direct problem we use in the inversion of source parameters. The inverse method relies on inverting for components of the moment tensor and a determination of an earthquake source-time function.