摘要：A spherical source, one of the simplest seismic sources, has been represented in various ways in the literature.These representations include a spherical source with outward radial expansion (S1), a spherical crack source with outward and inward crack wall motions along the spherical surface (S2), an isotropic source represented by three mutually perpendicular vector dipoles (S3) or three mutually perpendicular tensile cracks (S4), and a spherical source undergoing a transformational expansion (S5).We systematically examined these sources and their static displacement fields to clarify how these representations are mutually related.We also considered the sources in a bimaterial medium, in which the source material is different from the surrounding medium, as a model of a magma or hydrothermal reservoir.Our examinations show that the source volume change of a spherical source (S1) (actual volume) can be uniquely determined from the seismic moment of an isotropic source (S3) regardless of our assumption of the source medium and that the actual volume of S1 is related to the seismic moment of S3 through the equivalence of the displacement fields due to these two sources.The seismic moment of S3 is also related through another equation to the source volume change of three tensile cracks (S4), which is equal to the source volume changes defined in S2 and S5.This relation has different forms, depending on the source medium and source process.This study provides a unified view for quantifying a spherical source using the seismic moment of an isotropic source determined from waveform inversion analysis.
