Migration of scattered teleseismic body waves

Summary The retrieval of near‐receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three‐component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green’s function. The high‐frequency approximation further simplifies the problem by enabling (1) the use of an earth‐flattened, 1‐D reference model, (2) a reduction in computations to 2‐D through the assumption of 2.5‐D experimental geometry, and (3) band‐diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free‐surface transfer operator to individual station records and a Karhunen–Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave‐type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free‐surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo‐spectral synthetic seismograms demonstrates an application of the methodology.