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The amplitudes of high-frequency seismic waves generated by local and/or regional earthquakes vary from site to site, even at similar hypocentral distances. It had been suggested that, in addition to local site effects (e.g., variable attenuation and amplification in surficial layers), complex wave propagation in inhomogeneous crustal media is responsible for this observation. To quantitatively investigate this effect, we performed observational, theoretical, and numerical studies on the characteristics of seismic amplitude fluctuations in inhomogeneous crust. Our observations of P-wave amplitude for small to moderately sized crustal earthquakes revealed that fluctuations in P-wave amplitude increase with increasing frequency and hypocentral distance, with large fluctuations showing up to ten-times difference between the largest and the smallest P-wave amplitudes. Based on our theoretical investigation, we developed an equation to evaluate the amplitude fluctuations of time-harmonic waves that radiated isotropically from a point source and propagated spherically in acoustic von Kármán-type random media. Our equation predicted relationships between amplitude fluctuations and observational parameters (e.g., wave frequency and hypocentral distance). Our numerical investigation, which was based on the finite difference method, enabled us to investigate the characteristics of wave propagation in both acoustic and elastic random inhomogeneous media using a variety of source time functions. The numerical simulations indicate that amplitude fluctuation characteristics differ a little between medium types (i.e., acoustic or elastic) or source time function durations. These results confirm the applicability of our analytical equation to practical seismic data analysis.

Application of scattering theory to P-wave amplitude fluctuations in the crust