A new theory is presented to study the scattered elastic wave energy propagation in a random isotropic scattering medium. It is based on a scattered elastic wave energy equation that extends the work of Zeng et al. (1991) on multiple scattering by considering S to P and P to S wave scattering conversions. We obtain a complete solution of the scattered elastic wave energy equation by solving the equation in the frequency/wave-number domain. Using a discrete wave-number sum technique combined with a modified repeated averaging and the FFT method, we compute numerically the complete solution. By considering that the scattering conversion from P- to S-wave energy is about (α/β)4 times greater than that from S to P waves (Aki, 1992), we found that the P-wave scattering field was converted quickly to the S-wave scattering field, leading to the conclusion that coda waves generated from both P- and S-wave sources are actually dominated by scattered S waves. We also compared our result with that obtained under the acoustic wave assumption. The acoustic wave assumption for seismic coda works quite well for the scattered S-wave field but fails for the scattered P-wave field. Our scattered elastic wave energy equation provides a theoretical foundation for studying the scattered wave field generated by a P-wave source such as an explosion. The scattered elastic wave energy equation can be easily generalized to an inhomogeneous random scattering medium by considering variable scattering and absorption coefficients and elastic wave velocities in the earth.

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