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# [SSS26-08] Stochastic excitation of seismic waves by an intense Hurricane: Seismic excitation proportional to the cube of pressure

Keywords:Stochastic excitation, Hurricane, Atmosphere-Solid Earth interaction

Surface pressure is the excitation source of seismic signals; it has short correlation length (~1 km or less) whereas excited surface waves (0.01-0.02 Hz) have horizontal wavelengths of 100-300km. The source is also spread over some areas. Under such conditions, we must model the source by a stochastic pressure source that is spread over the surface of the Earth. In terms of parameters, this source is then characterized by two parameters, the pressure power spectral density S

_{p}and its correlation length L but both parameters can vary in space. We derived a relation between the observed power spectral density (PSD) of seismic velocity S

_{v}and the PSD of surface pressure Sp by the normal mode theory.

For a low frequency range 0.01-0.02 Hz, seismic and pressure amplitudes show, at least to first order, axisymmetric variations and also decreasing trends with distance from the center of a hurricane. Taking the center of a hurricane at the origin and assuming axisymmetry, we can write down an integral relation between Sv and Sp as

S

_{v}(x) = K(x, y) L

^{2}S

_{p}(y) dy

where x and y are distances from the center of a hurricane. K(x,y) is the excitation kernel for a source at y and a seismic observation at x and was computed for an Earth model PREM.

From data, we have Sv and Sp in the integrand. We first noted that a constant L cannot make the two observed quantities compatible. Therefore, we introduced the y dependence in L

^{2}where the correlation length varied with distance and solved for it . With such spatially varying L(y), the two data can be made compatible. The important point is that we also found a correlation between this L (solution) and surface pressure Sp. In fact there is a good linear relationship that can be expressed as L=c Sp where c is a constant. This is equivalent to saying that L

^{2}S

_{p}in the integrand is c

^{2}S

_{p}

^{3}.

This relation implies that the excitation of seismic ground motion becomes proportional to the cube of pressure. Near the center of a hurricane, pressure variations generally increase, but seismic-excitation becomes even more efficient near the center because of this nonlinear relation.