Rayleigh waves at a continental boundary by the finite element method

Abstract

The finite element method in two dimensions must be modified for the study of Rayleigh waves in an oceanic model as follows. Horizontal displacements within finite elements of water must be found from vertical displacements and the condition of irrotational motion. This method leads to a discontinuity in horizontal displacement at the ocean bottom. It gave phase velocities of Rayleigh waves in the region of the Pacific ocean-bottom seismometer which agreed to within 0.2 per cent with those found by the method of Haskell and Dorman. It also gave the variation with depth of the horizontal and vertical amplitudes of the propagating Rayleigh modes. For fundamental Rayleigh-mode motion at a period of 21.33 sec incident on either side of a model of the region between the Pacific ocean-bottom seismometer and Berkeley, 96 per cent of the incident energy is transmitted as the fundamental Rayleigh mode. This result is quite different from that for the propagation of the fundamental Love mode. At a period of 21.33 sec, the fundamental Rayleigh mode has a horizontal amplitude at the ocean bottom of only a little over one-half that of the fundamental Rayleigh mode in the region of Berkeley, even for Rayleigh waves approaching from the west. This corresponds to a difference of 0.2 in estimates of surface-wave magnitude.