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No description available.

Science Dept, Education College, King Abdul-Aziz University, Madinah, Saudi Arabia.

This thesis covers seismic signal analysis and inversion. It can be divided into two parts. The first part includes principal component analysis (PCA) and singular spectrum analysis (SSA). The objectives of these two eigen-analyses are extracting weak signals and designing optimal spatial sampling interval. The other part is on least squares inverse problems with a L1 norm constraint. The study covers seismic reflectivity inversion in which L1 regularization provides us a sparse solution of reflectivity series, and seismic reverse time migration in which L1 regularization generates high-resolution images. PCA is a well-known eigenvector-based multivariate analysis technique which decomposes a data set into principal components, in order to maximize the information content in the recorded data with fewer dimensions. PCA can be described from two viewpoints, one of which is derived by maximizing the variance of the principal components, and the other draws a connection between the representation of data variance and the representation of data themself by using Singular Value Decomposition (SVD). Each approach has a unique motivation, and thus comparison of these two approaches provides further understanding of the PCA theory. While dominant components contain primary energy of the original seismic data, remaining may be used to reconstruct weak signals, which reflect the geometrical properties of fractures, pores and fluid properties in the reservoirs. When PCA is conducted on time-domain data, Singular Spectrum Analysis (SSA) technology is applied to frequency-domain data, to analyse signal characters related to spatial sampling. For a given frequency, this technique transforms the spatial acquisition data into a Hankel matrix. Ideally, the rank of this matrix is the total number of plane waves within the selected spatial window. However, the existence of noise and absence of seismic traces may increase the rank of Hankel matrix. Thus deflation could be an effective way for noise attenuation and trace exploration. In this thesis, SSA is conducted on seismic data, to find an optimal spatial sampling interval. Seismic reflectivity inversion is a deconvolution process which compresses the seismic wavelet and retrieves the reflectivity series from seismic records. It is a key technique for further inversion, as seismic reflectivity series are required to retrieve impedance and other elastic parameters. Sparseness is an important feature of the reflectivity series. Under the sparseness assumption, the location of a reflectivity indicates the position of an impedance contrast interface, and the amplitude indicates the reflection energy. When using L1 regulation as sparseness constraint, inverse problem becomes nonlinear. Therefore, it is presented as a Basis Pursuit Denosing (BPDN) or Least Absolute Shrinkage and Selection Operator (LASSO) optimal problem and solved by spectral projected gradient (SPG) algorithm. Migration is a key technique to image Earth’s subsurface structures by moving dipping reflections to their true subsurface locations and collapsing diffractions. Reverse time migration (RTM) is a depth migration method which constructs wavefields along the time axis. RTM extrapolates wavefields using a two-way wave equation in the time-space domain, and uses the adjoint operator, instead of the inverse operator, to migrate the record. To improve the signal-to-noise ratio and the resolution of RTM images, RTM may be implemented as a least-squares inverse problem with L1 norm constraint. In this way, the advantages of RTM itself, least-squares RTM, and L1 regularization are utilized to obtain a high-resolution, two-way wave equation-based depth migration image.

No description available.

Full Waveform Inversion (FWI) is a highly promising but far from robust and stable optimisation for computing the subsurface velocity model from seismic data acquired with long offsets and low frequencies. Mathematically, it solves the non-linear problem of matching model-predicted data to observed data with an iterative localised minimisation of the misfit. Therefore it is necessarily restricted by the need for an accurate starting model. In this thesis, we look at being able to relax the constraints on the starting model in FWI, obtain lower wavenumber updates from FWI, and in the process distinguish between adequate and inadequate starting models. Our approach here is to precede the conventional Born-based iterations with Rytov-based iterations which isolate discrete frequency phase. Here the misfit function being minimised is the norm of the phase residual which measures the difference in phase between observed and predicted data. Our treatment of the phase residual differs from previous work in two specific ways: i) we define the time-weighted phase residual, ii) we unwrap the residual thereby accounting for errors greater than half a cycle or 'cycle-skipped'. Previous work did (i) using the Laplace-Fourier domain i.e. using an exponential function. Here we use a more versatile time window which prepares the residual for (ii). Previous work in the context of FWI did not attempt (ii) at all. We find it is the combination of (i) and (ii) that provides the solution we are looking for. In this thesis we formulate the theory for inverting the time-weighted phase residual. We find this mismatch measure meets the requirement of being able to distinguish between adequate and inadequate starting models. Finally, we demonstrate that an 'unwrapped' solution deals with the latter. The unwrapped solution is shown to correctly invert cycle-skipped data and successfully update longer wavelengths than possible with conventional inversion when wide-angle data is available. This leads to a multi-scale approach which ends with conventional inversion but begins with phase-unwrapped inversion at the lowest useable frequency. It finds the global minimum solution to the full wavefield inverse problem down to a depth governed by the offset range of the survey using only a simple starting model.

Recent work has shown that the fractures, which control productivity and fluid flow in some reservoirs, can cause the rockmass to be anisotropic to shear-wave propagation. The aim of this thesis is to extract information about fracture orientation and density from shear-waves recorded in producing formations. I examine VSP data from two areas (where productivity is fracture related): the Lost Hills field, California; and from three sites along the Austin Chalk trend, Texas. I use anisotropy estimation techniques to determine instrument polarities and the anisotropy parameters at each site. I produce anisotropic models for both areas. I am not able to resolve reservoir anisotropy using transmitted shear-waves. To determine reservoir anisotropy, I adapt reflected amplitude techniques and apply them to the Austin Chalk VSP data. At all four sites I find that the leading split shear-wave is polarized parallel to known fracture and stress directions. The polarization direction of the rockmass changes with depth in the Lost Hills anticline leading to multiply split shear-waves. Application of estimation techniques in the presence of multiple splitting has lead to incorrect interpretations of this data set in recent publications. I modelled the multioffset data from the BP test site, Texas, with a combination of vertical aligned cracks and horizontal thin layer anisotropy. This study demonstrates that analysis of shearwave anisotropy can be used to determine fracture orientation for use in oil recovery projects. Reflected amplitude studies show that the Austin Chalk in the Burleson County VSP, which contains a producing reservoir, is anisotropic, whereas the Austin Chalk at the other two sites, which do not contain reservoirs, is isotropic. I conclude that analysis of reflected shear-wave amplitudes represents an important tool for identifying fractured reservoirs. Also, reflection studies can be used in cases where the reservoir is too thin for delays to build up in transmitted shear-waves.

Complex short-period teleseismic P-waveforms (consisting of the direct P wave and surface reflections pP and sP) are observed from many earthquake sources. It is often not possible to easily interpret these waveforms in terms of those three phases. This is necessary to obtain accurate earthquake depths and P and S wave radiation patterns. This thesis examines the contribution made by various factors to P-wave seismogram complexity using both synthetic and real data. First, using a number of synthetic waveforms it is confirmed that long duration sources can contribute significantly to the complexity of short-period waveforms. However, it is highlighted that by using broadband recordings much of this complexity can be accounted for, and attributed to the limited passband of the short-period recording system. In addition, S-to-P mode conversions at near-source structure can also contribute significantly to the complexity of the short-period waveform. Second, the causes of differences in the complexity of the short-period waveforms from the 1987 Whittier Narrows and the 1991 Sierra Madre earthquakes are examined. Originally these earthquakes were thought to be separated by a distance approximately the size of the first Fresnel Zone, and hence should, in theory, have indistinguishable near-source structure, when seen at teleseismic distances. Using relative amplitudes, the published CMT focal mechanism for these events is confirmed . In the case of Sierra Madre earthquake it was also possible to positively identify the one surface reflection, visible on the shortperiod seismogram, as pP. Even with complex waveforms the relative amplitude method can be used to place constraints on the focal mechanism of the Whittier Narrows earthquake. Using forward modelling, with a simple kinematic source model, synthetic seismograms are matched to the observed broadband seismograms for both earthquakes. Using this simple source model, the variation in the source duration, caused by the difference in source rupture areas between the two earthquakes, is sufficient to account for the first-order variations in complexity seen. To second order, the near-source structure is sufficiently different even at the limit of resolution of the data, to contribute to some extent to the observed complexity variation, most likely due to the large thickness of sediment west of the Sierra Madre Fault. Third, a suite of seismograms from the 29 October 1995 Caspian Sea earthquake is examined. Using relative amplitudes, the surface reflection on these seismograms is correctly identified and the actual depth estimated to be 48 km. From this it is shown that an arrival mis-identified by the Prototype International Data Center as a surface reflection is most likely to be be a mode conversion at an interface 80 km beneath the source. Forward modelling of the broadband and short-period waveforms shows that these mode-conversions are enhanced by the downward propagating line rupture, and are best seen when the position of the stations are at a node in the P-wave radiation pattern. This produces an apparently complex waveform. Visible S waves from this earthquake at European stations show the very low attenuation in the mantle path and this may contribute to the greater than usual complexity observed for this event. Finally several earthquakes that appear to show seismogram complexity that cannot be explained using a simple kinematic source model or path effects are examined. By modifying an existing finite-difference fault modelling code I present a possible dynamic source model that may provide one explanation for this additional complexity. This model includes real source physics (friction law, rupture criteria) and material heterogeneities. It produces complex farfield pulse shapes that vary with fault length, material heterogeneity, initial state of stress and attenuation.

Full-waveform inversion (FWI) is a technique that seeks to find a high-resolution high-fidelity model of the Earth's subsurface that is capable of matching individual seismic waveforms, within an original raw field dataset, trace by trace. The method begins from a best-guess starting model, which is then iteratively improved using a sequence of linearized local inversions to solve a fully non-linear problem. In principle, FWI can be used to recover any physical property that has an influence upon the seismic wavefield, but in practice the technique has been used predominantly to recover P-wave velocity, and this is the route that is followed here. Full-waveform tomographic techniques seek to determine a highly resolved quantitative model of the sub-surface that will ultimately be able to explain the entire seismic wavefield including those phases that conventional processing and migration seek to remove such as refracted arrivals. Although the underlying theory of FWI is well established, its practical application to 3D land data, and especially to seismic data that have been acquired using vibrators, in a form that is effective and robust, is still a subject of intense research. In this study, 2D and 3D FWI techniques have been applied to a vibrator dataset from onshore Oman. Both the raw dataset and the subsurface model cause difficulties for FWI. In particular, the data are noisy, have weak early arrivals, are strongly elastic, and especially are lacking in low-frequency content. The Earth model appears to contain shallow low-velocity layers, and these compromise the use of first-arrival travel-time tomography for the generation of a starting velocity model. The 2D results show good recovery of the shallow part of the velocity models. The results show a low-velocity layer that extends across the velocity model, but lacking in a high-resolution image due to the absence of the third dimension. The seismograms of the final inversion models give a good comparison with the field data and produce a reasonably high correlation coefficient compared to the starting model. An inversion scheme has been developed in this study in which only data from the shorter offsets are initially inverted since these represent the subset of the data that is not cycle skipped. The offset range is then gradually extended as the model improves. The final 3D model contains a strongly developed low-velocity layer in the shallow section. The results from this inversion appear to match p-wave logs from a shallow drill hole, better flatten the gathers, and better stack and migrate the reflection data. The inversion scheme is generic, and should have applications to other similar difficult datasets.