Envelope synthesis of short‐period seismograms in 3‐D random media for a point shear dislocation source based on the forward scattering approximation: Application to small strike‐slip earthquakes in southwestern Japan

摘要

Even though high‐frequency seismograms of local earthquakes are complex because of the excitation of scattered waves caused by random lithospheric heterogeneities, their envelopes are well reproduced by the forward scattering approximation on the basis of stochastic characterization of random media. We present a method to synthesize three‐component vector wave envelopes for a point shear dislocation source by way of the stochastic raypath method using the Markov approximation for the parabolic wave equation. Because of multiple forward scattering, the directionality of the synthesized envelope shows a smoothed quadrant pattern compared to the original radiation pattern; the scattered or diffracted energy appears even in the direction of the null axis and on the nodal planes. The quadrant pattern becomes smooth as hypocentral distance increases. To examine the availability of the synthesized envelope, we analyze seismograms of two small strike‐slip earthquakes that occurred in southwestern Japan. First, we estimate the statistical parameters characterizing the randomness and the intrinsic absorptions in frequencies 2–4, 4–8, and 8–16 Hz assuming a von Karman‐type random medium, and then we examine the directionality of the envelope. The maximum energy density of the envelope shows a quadrant pattern for both P and S waves with a 45 degree shift. The directionality appears in the frequencies up to 16 Hz and at distances up to 200 km. The directionality also appears on the S wave envelope duration. The observed directionality is well explained by the synthesized envelope, but it is still difficult to explain the partition of energy into three components by the synthesized envelopes.