Numerical Modeling And Migration Of Receiver Function For Inhomogeneous Media

The modeling and interpretation of receiver function for lateral inhomogeneous media is a potential study field for the physics of the Earth interior.In this paper, deconvolution and linearized inversion of receiver function are improved; multi-channel deconvolution and wavelet inversion are developed for receiver function. The elastic wave motion equation is applied in the simulation and migration of receiver function in lateral inhomogeneous media, multi-grid algorithm is introduced in numerical modeling of elastic wave motion equation, and phase-delay boundary condition is also provided to absorb boundary reflection. Numerical test shows that the method presented in this paper can be applied in the lateral inhomogeneity study of the Earth Interior.Deconvolution and inversion of receiver function is a basic problem for receiver function study. Multi-channel deconvolution, based on multi-channel signal analysis, is presented to recover receiver function from three-component teleseismic P waveforms clustered within certain backazimuth and epicenter distance, to increase the resolution of receiver function. Wavelet inversion is also introduced to broadband receiver function, to solve for nonuniqueness cased by linear approximation of nonlinear problem, and broadband receiver function is decomposed into multi-resolution versions, and the inversion result for the low-resolution version is iteratively taken as the initial model for the high-resolution, and gradually obtain the inversion model for broadband receiver function.Three finite-difference methods, i.e., stagger grid, implicit and explicit algorithms, are analyzed in detail. Multi-grid algorithm is firstly introduced in elastic wave simulation, to solve for the stability problem inherent in stagger grid and implicit algorithm, also for the efficiency problem inherent in explicit algorithm, and the precision, stability and efficiency for simulation of elastic wave arc increased by multi-grid method.Phase-delay method is provided to effectively absorb boundary reflection and increase efficiency for wave motion simulation, based on phase delay and amplitude decaying features along wave propagation.Receiver function is simulated for inhomogeneous media, as a special case for elastic wave modeling with nearly vertical incidence plane P wave as initial condition, and provide the base for inversion and migration of receiver function in inhomogeneous media.Prestack migration method, based on wave motion equation, is also developed for receiver function, and compared with ray method. Both P-to-S conversion wave and direct P phase contained in receiver function are migrated and imaged by reverse-time migration for data gather including all receiver functions recorded in allseismological stations for one event, and imaging profile is finally obtained by stacking for all events. Numerical migration for typical models show that, in contrast to ray method, prestack wave motion migration can correctly image inhomogeneous media, and suppress multiple reflection wave effectively.Prestack migration method presented in this paper should be developed to apply in observational teleseismic P waveform data, to study the inhomogeneity of crust and upper mantle.