On tsunami nucleation II. An instantaneous modulated line source

Physics

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Scientific paper

Tsunami generation on a spherically-symmetric, self-gravitating and elastic Earth is investigated using normal mode summations and moment tensor line sources. Wave cancellation in a line source of length L substantially eliminates tsunamis whose horizontal wavenumber component along the fault exceeds 3π/L. This results in a preferential beaming of tsunami radiation perpendicular to the fault strike. Beaming from a source of fixed length occurs in the same fashion irrespective of.slip mechanism. Tsunami radiation patterns from finite sources are thus more uniform than those from point sources. The largest far field sea waves from any long shallow fault are likely to be found within 20° azimuth of the perpendicular bisecting great circle. Although line sources subordinate distinctions in radiation patterns, focal mechanism is still a critical element in determining the extent of tsunami excitation. The ratio of maximum tsunami amplitude from strike and dip slips of equal moment are 1:10 for faults 400 km in length. Finite faulting weakens strike-slip tsunamis relative to dip-slip tsunamis because the beaming and natural radiation directions of strike slips are severely misaligned. Using an empirical relation linking source process time, fault length and moment, I predict tsunami energies in the range 1010-1017 J for earthquake moments spanning 2 × 1018 < M0 < 2 × 1023 Nm. These energies are one half to one thousandth of that obtained from equivalent point sources. For all mechanisms, tsunami energy is roughly proportional to M01.5. At a 1000 km distance, maximum tsunami amplitudes in the open ocean vary from 8 cm to 10 m for events with magnitudes between 7.5 and 9.5. These values are in accord with measurements from 14 historical earthquakes. Although beaming from line sources does not amplify far field wave heights calculated from equivalent point sources, the adoption of finite fault models in tsunami forecasting schemes is desirable. I speculate that the estimation of finite source parameters by indirect means, and not by formal waveform inversion, could be sufficiently accurate in real time forecasting applications.

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