Using PKiKP coda to determine inner core structure: 1. Synthesis of coda envelopes using single‐scattering theories

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Previous seismic studies have reported evidence of scattered seismic energy coming from the inner core (IC). This implies that the IC has lateral variations in structure or composition with a scale length of tens of kilometers. In the present study, we focus on synthesizing the coda following precritical PKiKP and try to determine the location of the heterogeneities that produce this coda, using previously reported observations as a guide. Using a single‐scattering approximation and ray theory, we generate synthetic PKiKP coda envelopes from six distinctive places inside the Earth: within the lower mantle on the source and receiver side, along the core‐mantle boundary on the source and receiver side, along the inner core boundary, and within the inner core. We use two approaches to generate synthetic coda from topography on a boundary surface and one that is appropriate for volumetric scattering. In our computations we calculate the arrival time, ray parameter, and amplitude of the seismic waves and take into account errors in the back azimuth, as well as source and receiver effects. We find that previously reported “spindle”‐shaped or growing coda can only be produced from volumetric heterogeneities located in the shallowest 350 km of the IC; however, strong trade‐offs between the different parameters describing the volumetric heterogeneities (i.e., characteristic wavelengths, RMS velocity or impedance contrast, and total volume) preclude the determination of a unique model. Additionally, we find that reasonable models of topography at the core‐mantle boundary can produce large variations of the PKiKP amplitude due to focusing and defocusing effects. Therefore complexity at the inner core boundary is not necessarily required to account for dramatic amplitude variations in the direct PKiKP amplitudes.