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Petroleum reserves --- Inversion (Geophysics) --- Mathematical models.
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This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.
Petroleum reserves --- Inversion (Geophysics) --- Mathematical models.
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Mathematical optimization --- Functional analysis --- Geophysics --- Inversion (Geophysics)
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This book examines different classical and modern aspects of geophysical data processing and inversion with emphasis on the processing of seismic records in applied seismology. Chapter 1 introduces basic concepts including: probability theory (expectation operator and ensemble statistics), elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection t
Inversion (Geophysics) --- Prospecting --- Geophysical methods --- Mathematical models.
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This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data. These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets. Solutions to the exercises are available on a website at http://publishing.cambridge.org/resources/0521819652
Earth sciences --- Time-series analysis. --- Inversion (Geophysics) --- Mathematics.
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In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology. Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.
Inversion (Geophysics) --- Geophysics --- Functional analysis. --- Mathematical optimization. --- Measurement.
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Gravity --- Inversion (Geophysics) --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Prospecting --- Gravimetry --- Measurement --- Geophysical methods --- Mathematical models
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This book examines different classical and modern aspects of geophysical data processing and inversion with emphasis on the processing of seismic records in applied seismology. Chapter 1 introduces basic concepts including: probability theory (expectation operator and ensemble statistics), elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection t
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The ultimate aim of the oil exploration industry is to determine the distribution of rock types and underground fluids. At this stage, we can actually determine the distribution of several underground physical properties with a certain accuracy. The challenge for the rock physicist is to translate those physical properties (P-velocity, S-velocity, density) into rock types and fluids (gas-, or oil-, or water-bearing sand, shale). If performed correctly, dry holes can be avoided and millions of dollars can be saved. Ultimately, an integrated approach is required. This book deals with a series of topics in rock physics, including elasticity, pore pressure, incompressibility of rocks and the Gassmann equation, fluid substitution, forward modelling and empirical equations, rock physics applications to AVO studies and inversion studies, and the Differential Effective Medium (DEM) method. It is generally addressed to the practitioner (geophysicist, geologist), and in some instances, detailed instructions are furnished to perform a particular task. Some chapters, on the other hand, are theoretical and more mathematical, and are expected to be of interest to both practitioners and students alike. Other chapters include innovative ideas that could, for instance, be tested by oil companies that have substantial amounts of data at their disposal.
Amplitude variation with offset analysis. --- Inversion (Geophysics) --- Inversion (géophysique) --- Seismology --- Sismologie --- Mathematics. --- Mathématiques.
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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. This book is written for scientists and advanced students in engineering, earth sciences, and physics. The reader should have 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 (e.g., Snell's law and ray tracing). For those not familiar with the terminology and methods of seismic exploration, a brief introduction is provided in the Appendix of Chapter 1. Computational labs are provided for most of the chapters, and some field data labs are given as well. Matlab and Fortran labs at the end of some chapters are used to deepen the reader's understanding of the concepts and their implementation. Such exercises are introduced early and geophysical applications are presented in every chapter. For the non-geophysicist, geophysical concepts are introduced with intuitive arguments, and their description by rigorous theory is deferred to later chapters.--
Seismic traveltime inversion. --- Seismic reflection method --- Seismic tomography. --- Inversion (Geophysics) --- Seismology --- Deconvolution. --- Mathematics.
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