Adaptive waveform inversion: theory

Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error

Design &implementation of complex-valued FIR digital filters with application to migration of seismic data

One-dimensional (I-D) and two-dimensional (2-D) frequency-space seismic migration FIR digital filter coefficients are of complex values when such filters require special space domain as well as wavenumber domain characteristics. In this thesis, such FIR digital filters are designed using Vector Space Projection Methods (VSPMs), which can satisfy the desired predefined filters' properties, for 2-D and three-dimensional (3-D) seismic data sets, respectively. More precisely, the pure and the relaxed projection algorithms, which are part of the VSPM theory, are derived. Simulation results show that the relaxed version of the pure algorithm can introduce significant savings in terms of the number of iterations required. Also, due to some undesirable background artifacts on migrated sections, a modified version of the pure algorithm was used to eliminate such effects. This modification has also led to a significant reduction in the number of computations when compared to both the pure and relaxed algorithms. We further propose a generalization of the l-D (real/complex-valued) pure algorithm to multi-dimensional (m-D) complex-valued FIR digital filters, where the resulting frequency responses possess an approximate equiripple nature. Superior designs are obtained when compared with other previously reported methods. In addition, we also propose a new scheme for implementing the predesigned 2-D migration FIR filters. This realization is based on Singular Value Decomposition (SVD). Unlike the existing realization methods which are used for this geophysical application, this cheap realization via SVD, compared with the true 2-D convolution, results in satisfactory wavenumber responses. Finally, an application to seismic migration of 2-D and 3-D synthetic sections is shown to confirm our theoretical conclusions. The proposed resulting migration FIR filters are applied also to the challenging SEGIEAGE Salt model data. The migrated section (image) outperformed images obtained using other FIR filters and with other standard migration techniques where difficult structures contained in such a challenging model are imaged clearly

Geophysical data registration using modified plane-wave destruction filters

I propose a method to efficiently measure local shifts, slopes, and scaling functions between seismic traces using modified plane-wave destruction filters. Plane-wave destruction can efficiently measure shifts of less than a few samples, making this algorithm particularly effective for detecting small shifts. When shifts are large, amplitude-adjusted plane-wave destruction can also be used to refine shift estimates obtained by other methods. Amplitude-adjusted plane-wave destruction separates estimation of local shifts and amplitude weights, allowing the time-shift to be measured more accurately. This algorithm has clear applications to geophysical data registration problems, including time-lapse image registration, multicomponent image registration, automatic gather flattening, automatic seismic-well ties, and image merging. The effectiveness of this algorithm in predicting shifts associated with fluid migration, wave mode conversions, and anisotropy and amplitude gradients associated with amplitude variations with offset or angle is demonstrated by applying the algorithm to a synthetic trace, a time-lapse field data example from the Cranfield CO₂ sequestration project, a multicomponent field data example from West Texas, and the Mobil AVO prestack seismic data. Finding correspondence between different parts of the same dataset falls into the same category of problems as local shift estimation. Computation of structure-oriented amplitude gradients for attribute-assisted interpretation requires the estimation of local slopes by correlating reflections between neighboring seismic traces in an image. One of the major challenges of interpreting seismic images is the delineation of reflection discontinuities that are related to geologic features, such as faults, channels, salt boundaries, and unconformities. Visually prominent reflection features often overshadow these subtle discontinuous features which are critical to understanding the structural and depositional environment of the subsurface. For this reason, precise manual interpretation of these reflection discontinuities in seismic images can be tedious and time-consuming, especially when data quality is poor. Discontinuity enhancement attributes are commonly used to facilitate the interpretation process by enhancing edges in seismic images and providing a quantitative measure of the significance of discontinuous features. These attributes require careful pre-processing to maintain geologic features and suppress acquisition and processing artifacts which may be artificially detected as a geologic edge. The plane-wave Sobel filter cascades plane-wave destruction filters with plane-wave shaping in the transverse direction to compute an enhanced discontinuity attribute. The plane-wave Sobel attribute can be applied directly to a seismic image to efficiently and effectively enhance discontinuous features, or to a coherence image to create a sharper and more detailed image. I demonstrate the effectiveness of this method by applying it to two field data sets from offshore New Zealand and offshore Nova Scotia with several faults and channel features and compare the results to other coherence attributes.Geological Science

Digital Signal Processing

Contains a research summary and reports on fifteen research projects.National Science Foundation FellowshipJoint Services Electronics Program (Contract DAAG29-78-C-0020)National Science Foundation (Grant ENG76-24117)U.S. Navy - Office of Naval Research (Contract N00014-75-C-0951)National Science Foundation (Grant ENG76-24117)Schlumberger-Doll Research Center FellowshipHertz Foundation FellowshipNational Aeronautics and Space Administration (Grant NSG-5157)U.S. Navy - Office of Naval Research (Contract N00014-77-C-0196

Directional seismic source signature deconvolution

Marine seismic source arrays are directional. Source directivity is used to attenuate coherent noise, but primary reflected data may be degraded. Source directivity is ignored in a standard processing sequence, so directional source signature deconvolution may be required. In the frequency-wavenumber (f-k) directional deconvolution method, a filter is calculated from far-field source signatures and is applied to the f-k transform of common-receiver gathers. Reflections on common-receiver gathers are often spatially aliased, and this causes practical problems with the technique. Directional deconvolution may also be performed in combination with prestack migration because the prestack Kirchhoff summation migration operator is a function of source take-off angle. The constant-offset section is deconvolved separately with a full range of filters for source signatures radiated in different directions; then the migration summation operator sums across the deconvolved sections, selecting the section which has been deconvolved for the correct source signature at each point. Physical model data, which were acquired over simple models using a directional source, are used to evaluate directional deconvolution assuming constant velocity. Reflector continuity and resolution are improved by using directional deconvolution. Directional deconvolution combined with prestack migration is extended to media in which the velocity varies with depth, and is applied to two datasets from the Southern North Sea. The second dataset, which has shallow steeply dipping reflectors, is improved by using directional deconvolution. Directional deconvolution may be combined with a Kirchhoff migration technique which assumes a linear velocity-depth model. Results are superior to conventional Kirchhoff migration because ray bending is honoured. Directional deconvolution cannot synthesise fully point-source equivalent data from data acquired with a source array without excessive noise amplification. Source arrays with a short in-line dimension should be used where possible. For data which have been acquired with a long source array, directional deconvolution is desirable