Aaron Stanton

Least Squares Wave Equation Migration of Elastic Data

Least squares migration compensates for the effects of missing data, noise, and illumination by imposing various constraints on an image while ensuring the model fits the observed data. Multicomponent seismic data are well suited for least squares migration as they generally suffer from many of the same complications as single component data. This article extends least squares wave equation migration to two component elastic data in isotropic media. Forward and adjoint operators are written using Helmholtz recomposition/decomposition operators implemented in the Fourier domain, while extrapolation is carried out using a split-step operator. Poynting vectors calculated using source and receiver side P-wave potentials are used to calculate angle gathers. We regularize the inversion by dip filtering in the angle domain to reduce the effect of source/receiver sampling, noise, and PP/PS crosstalk artifacts.

Multicomponent seismic data reconstruction using the quaternion Fourier transform and POCS

The quaternion Fourier transform is used to obtain a Fourier domain representation of a multicomponent seismic record. Projection Onto Convex Sets (POCS) is used as a means to reconstruct all three components at once. The results of this process are compared with standard component-by-component reconstruction. The algorithm is applied to 2D and 3D 3C synthetic data but it could be easily extended to a higher number of dimensions and components.

Five-dimensional Vector Data Interpolation

Five dimensional interpolation and denoising of multicomponent seismic data is carried out using the quaternions and Projection Onto Convex Sets (POCS). The method is able to reconstruct up to four components of data simultaneously. A real data example is shown for a converted wave dataset acquired over a heavy oil reservoir in the Western Canadian Sedimentary Basin that displays the effects of shear wave splitting. Vector reconstruction is compared with traditional component-by-component reconstruction and is shown to give an improved reconstruction result while preserving the vector relationship between components.