Parametric reconstruction of multidimensional seismic records

Abstract

Logistic and economic constraints often dictate the spatial sampling of a seismic survey. The process of acquisition records a finite number of spatial samples of the continuous wave field. The latter leads to a regular or irregular distribution of seismograms. Seismic reconstruction methods are used to recover non-acquired data and to synthesize a dense distribution of sources and receivers that mimics a properly sampled survey. This dissertation examines the seismic sampling problem and proposes algorithms for efficient multidimensional seismic data reconstruction. In particular, I address the problem of reconstructing irregularly sampled data using multidimensional linear prediction filters. The methodology entails a strategy that consists of two steps. First, the unaliased part of the wave field is reconstructed via Fourier reconstruction (Minimum Weighted Norm Interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter permits the the recovery of aliased data with Multi-Step Auto-Regressive (MSAR) algorithm. The recovered prediction filters are used to reconstruct the complete data in either the f-x domain (MSAR-X) or the f-k domain (MSAR-K). The thesis also presents the use of Exponentially Weighted Recursive Least Squares (EWRLS) to estimate adaptive prediction filters for f-x seismic interpolation. Adaptive prediction filters are able to model signals where the dominant wavenumbers are varying in space. This concept leads to a f-x interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms with spatially variant dips.