Download or read book Iterative Seismic Data Interpolation Using Plane wave Shaping written by Ryan Louis Swindeman and published by . This book was released on 2015 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geophysical applications often require finding an appropriate solution to an ill-posed inverse problem. An example application is interpolating irregular or sparse data to a regular grid. This data regularization problem must be addressed appropriately before many data processing techniques can begin. In this thesis, I investigate plane-wave shaping in two and three dimensions as a data regularization algorithm, which can be used for the interpolation of seismic data and images. I use plane-wave shaping to interpolate several synthetic and field datasets and test its accuracy in image reconstruction. Because plane-wave shaping adheres to the direction of the local slopes of an image, the image-guided interpolation scheme attempts to preserve information of geologic structures. I apply several alternative interpolation schemes - formulated as an inverse problem with a convolutional operator to constrain the model space - namely: plane-wave destruction, plane-wave construction, and prediction-error filters. Investigating their iterative convergence rates, I find that plane-wave shaping converges to a solution in fewer iterations than the alternative techniques. I find that the only required parameter for this method, the smoothing radius, is best chosen to be approximately the same size as the holes for missing-data problems. The optional parameter for edge padding is best selected as approximately half of the smoothing radius. Applications of this research project include potential applications in well-log interpolation, seismic tomography, and 5-D seismic data interpolation.
Download or read book Sequential Seismic Inversion Using Plane wave Synthesis written by Jun Ji and published by . This book was released on 1995 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seismic Data Interpolation with Shaping Inversion to Zero Offset and Least squares Flattening written by Ben Watson Gremillion and published by . This book was released on 2019 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Insufficient data often require regularized solutions to inverse problems in geophysics. In other words, we wish to find a model that best matches the data and obeys expected model behavior. Inadequate midpoint sampling is one insufficient data example where large trace intervals can lead to spatial aliasing in seismic data. Inversion to zero offset (IZO) is a solution to this problem that relates zero-offset traces with nonzero-offset traces to find a well sampled model that best matches the inadequately sampled data. IZO can significantly reduce spatial aliasing in stacked seismic data and is typically constrained by the widely known Tikhonov regularization. However, selecting parameters for traditional regularization techniques can be difficult, and the opposing roles of error minimization and model constraint can lead to slow convergence. Shaping regularization is an alternative method that explicitly maps the estimated model to the space of admissible models and, in some cases, can lead to faster convergence. In the first part of this thesis, I present a technique, called shaping IZO, that incorporates inversion to zero offset into the shaping regularization inversion scheme. I show that shaping IZO can reduce spatial aliasing and improve the resolution of stacked seismic data using synthetic and field examples. My results prove that shaping IZO is a viable alternative to traditional IZO. Insufficient data can also create large areas of missing traces in seismic surveys. In extreme cases, only 2D lines might be available where 3D data are desired. Interpolating over such large areas can be beneficial for later seismic data processing and interpretation but doing so is a challenge. Previous methods, such as interpolation with projection onto convex sets algorithms, prediction error filters, and local slopes have struggled with the sparse and irregular inputs of 2D-to-3D interpolation. In the second part of this thesis, I present interpolation by least-squares flattening as a way to estimate a 3D seismic volume from 2D seismic lines. Interpolation by least-squares flattening first finds the shifts that best align corresponding reflectors of the input traces by incorporating dynamic time warping into a least-squares inversion scheme. After applying these shifts to align reflectors in the input traces, the method then interpolates the flattened reflectors and their associated shifts to a regular 3D grid. Finally, the interpolated shifts are used to unflatten the interpolated reflectors, yielding a 3D volume estimate. I apply interpolation by least-squares flattening to decimated versions of the Teapot Dome land dataset to validate the technique and compare it to other forms of interpolation. My results show that interpolation by least-squares flattening is an effective method to interpolate sparse, irregular traces to a 3D volume
Download or read book Functional Analysis and Numerical Mathematics written by Lothar Collatz and published by Academic Press. This book was released on 2014-05-12 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.
Download or read book Least Squares Inversion of Field Seismic Data for an Elastic 1 D Earth written by Warren Theodore Wood and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastic 1-D inversion of seismic reflection data is successfully applied to common midpoint field data of varying offset ranges. The inversion, actually iterative forward modeling, operates on plane wave seismic data and yields P-wave velocity, (V [subscript p]), density, and S-wave velocity, (V [subscript s]) for each of many (typically hundreds) equal time thickness layers. The problem is viewed in terms of a multi-dimensional optimization problem where the error function is defined as the square of model and data misfit. The error is minimized by the Newton method which requires slope (sensitivity of each datum to each model parameter) and curvature (full Hessian) of the error function at each of several iterations. The algorithm is tested on realistic synthetic data, and when applied to conventional common midpoint data is very helpful in determining the nature of a bottom simulating reflector in the Carolina Trough off shore South Carolina. The algorithm is also applied to deep water data acquired in the Nankai Trough offshore Japan as part of a tectonic study of the accretionary prism. Here the waveform inversion results from 8 very wide aperture expanding spread profiles (ESPs), and 610 conventionally acquired common midpoint gathers are used to generate sediment property cross sections across the accretionary wedge deformation front, highlighting the vertical and lateral sediment property changes.
Download or read book Geophysical Inverse Theory and Regularization Problems written by Michael S. Zhdanov and published by Elsevier. This book was released on 2002-04-24 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology. The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. This text is the first to treat many kinds of inversion and imaging techniques in a unified mathematical manner.The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods. The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration.This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on inversion theory.
Download or read book Petroleum Abstracts written by and published by . This book was released on 1996 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics of Multidimensional Seismic Imaging Migration and Inversion written by N. Bleistein and published by Springer Science & Business Media. This book was released on 2000-12-15 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seismic Inversion written by Gerard T. Schuster and published by SEG Books. This book was released on 2017-07-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theory and practice of inverting seismic data for the subsurface rock properties of the earth. The primary application is for inverting reflection and/or transmission data from engineering or exploration surveys, but the methods described also can be used for earthquake studies. Seismic Inversion will be of benefit to scientists and advanced students in engineering, earth sciences, and physics. It is desirable that the reader has some familiarity with certain aspects of numerical computation, such as finite-difference solutions to partial differential equations, numerical linear algebra, and the basic physics of wave propagation. For those not familiar with the terminology and methods of seismic exploration, a brief introduction is provided. To truly understand the nuances of seismic inversion, we have to actively practice what we preach (or teach). Therefore, computational labs are provided for most of the chapters, and some field data labs are given as well.
Download or read book Moving Boundary Problems in Multi physics Coupling Processes written by Leilei Chen and published by Frontiers Media SA. This book was released on 2023-07-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Earth Soundings Analysis written by Jon F. Claerbout and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The first work describes the analysis of echo soundings in seismic prospecting. The progress reports describe activities of the Stanford Exploration Project regarding seismic echo soundings.
Download or read book Surface Wave Methods for Near Surface Site Characterization written by Sebastiano Foti and published by CRC Press. This book was released on 2014-08-21 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a Greater Understanding of How and Why Surface Wave Testing Works Using examples and case studies directly drawn from the authors’ experience, Surface Wave Methods for Near-Surface Site Characterization addresses both the experimental and theoretical aspects of surface wave propagation in both forward and inverse modeling. This book accents the key facets associated with surface wave testing for near-surface site characterization. It clearly outlines the basic principles, the theoretical framework and the practical implementation of surface wave analysis. In addition, it also describes in detail the equipment and measuring devices, acquisition techniques, signal processing, forward and inverse modeling theories, and testing protocols that form the basis of modern surface wave techniques. Review Examples of Typical Applications for This Geophysical Technique Divided into eight chapters, the book explains surface wave testing principles from data measurement to interpretation. It effectively integrates several examples and case studies illustrating how different ground conditions and geological settings may influence the interpretation of data measurements. The authors accurately describe each phase of testing in addition to the guidelines for correctly performing and interpreting results. They present variants of the test within a consistent framework to facilitate comparisons, and include an in-depth discussion of the uncertainties arising at each stage of surface wave testing. Provides a comprehensive and in-depth treatment of all the steps involved in surface wave testing Discusses surface wave methods and their applications in various geotechnical conditions and geological settings Explains how surface wave measurements can be used to estimate both stiffness and dissipative properties of the ground Addresses the issue of uncertainty, which is often an overlooked problem in surface wave testing Includes examples with comparative analysis using different processing techniques and inversion algorithms Outlines advanced applications of surface wave testing such as joint inversion, underwater investigation, and Love wave analysis Written for geotechnical engineers, engineering seismologists, geophysicists, and researchers, Surface Wave Methods for Near-Surface Site Characterization offers practical guidance, and presents a thorough understanding of the basic concepts.
Download or read book A Practical Understanding of Pre and Poststack Migrations Poststack written by John C. Bancroft and published by . This book was released on 1999 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seismic Wave Propagation in Stratified Media written by Brian Kennett and published by ANU E Press. This book was released on 2009-05-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic Wave Propagation in Stratified Media presents a systematic treatment of the interaction of seismic waves with Earth structure. The theoretical development is physically based and is closely tied to the nature of the seismograms observed across a wide range of distance scales - from a few kilometres as in shallow reflection work for geophysical prospecting, to many thousands of kilometres for major earthquakes. A unified framework is presented for all classes of seismic phenomena, for both body waves and surface waves. Since its first publication in 1983 this book has been an important resource for understanding the way in which seismic waves can be understood in terms of reflection and transmission properties of Earth models, and how complete theoretical seismograms can be calculated. The methods allow the development of specific approximations that allow concentration on different seismic arrivals and hence provide a direct tie to seismic observations.
Download or read book Fundamentals of Seismic Wave Propagation written by Chris Chapman and published by Cambridge University Press. This book was released on 2004-07-29 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Seismic Wave Propagation, published in 2004, presents a comprehensive introduction to the propagation of high-frequency body-waves in elastodynamics. The theory of seismic wave propagation in acoustic, elastic and anisotropic media is developed to allow seismic waves to be modelled in complex, realistic three-dimensional Earth models. This book provides a consistent and thorough development of modelling methods widely used in elastic wave propagation ranging from the whole Earth, through regional and crustal seismology, exploration seismics to borehole seismics, sonics and ultrasonics. Particular emphasis is placed on developing a consistent notation and approach throughout, which highlights similarities and allows more complicated methods and extensions to be developed without difficulty. This book is intended as a text for graduate courses in theoretical seismology, and as a reference for all academic and industrial seismologists using numerical modelling methods. Exercises and suggestions for further reading are included in each chapter.
Download or read book Seismic Interferometry written by Gerard Thomas Schuster and published by Cambridge University Press. This book was released on 2009-05-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the theory and practice of seismic interferometry for academic researchers, oil industry professionals and advanced students.
