RELATIONSHIPS OF TSUNAMI GENERATION AND AN EARTHQUAKE SOURCE

Abstract

This paper presents a theory of tsunami generation and propagation on a spherically symmetric, self-gravitating, elastic Earth in terms of normal modes. We predict the character of newborn tsunamis at regional far field distances from a simply parameterized moment tensor point source with step function time history. Tsunami eigenfunctions are shown to penetrate the Earth from tens of kilometers at 2, 000 second period to tens of meters at 20 second period. This behavior explains why the longest tsunami periods are the only ones influenced by crust and mantle structure and why they are preferentially excited by submarine earthquakes. We find that large tsunamis need sizable parent earthquakes because over 96% of their energy is concentrated in the ocean. This makes the entire solid Earth virtually a node for tsunami generation. The excitation of tsunami modes is strongly dependent upon the moment, mechanism and depth of faulting. Calculated tsunami energy, E_T, can vary by a factor of 100 for sources of equal moment within 30 kilometers of the sea floor. Maximum E_T for dip slip and strike slip faulting with moment M₀=10²⁰N·m is 1.5×10¹³ and 1.1×10¹² joules. With mechanism and depth fixed, this source model predicts that E_T is proportional to M₀². The ratio of tsunami to radiated seismic energy is less than 1% for all but the largest events. We believe that this theory coupled with a seismic source recovery technique could be a realistic basis for the forecasting of potentially dangerous tsunamis in real time.