THREE-DIMENSIONAL FINITE ELEMENT MODELLING OF ELASTIC WAVES
TENG YU-CHIUNG(Aldridgc Laboratory of Applied Geophysics, Columbia University, Nctv York, U. S. A.)ZHANG ZHI-LI(Institute of Geophysics, State Seismological Bureau, Beijing)
In this paper, the three-dimensional iinite element algorithm for solving transient elastic wave propagation problems and the existing practical difficulties are discussed. An algorithm, the combination of finite element in space with lumped mass matrix representation and a modified explicit central difference time integration, may overcome partially the difficulties of requiring an enormously large computer incore storage and a large amount of computing time. For a structure with 30×30×30 hexahedron elements, the present algorithm can reduce the computer in-core storage down to 1/5000 time of the conventional algorithm of "block-by-block". The nodal-point-oriented approach, which particalarly suits for the computation on the parallel computer systems is used. We also adopt an effective excitation method (EE method) in the entire marching process. With this EE method, the region of excitation motion expands with increasing in time yteps, and the computing time can be further reduced. As a demonstrative example, a three-dimensional wedge shaped structure with two kinds of medium has been considered. The forcing function is taken as the first derivative of the Gaussian function. For some profiles of this wedge problem, the snapshot view of wave patterns and the .synthetic seismogram for the calculated displacement fields are also presented.