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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. --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Mathematical models

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The lAG International Symposium on Gravity, Geoid, and Space Missions 2004 (GGSM2004) was lield in the beautiful city of Porto, Portugal, from 30 August to 3 September 2004. This symposium encompassed the themes of Commission 2 (Gravity Field) of the newly structured lAG, as well as interdisciplinary topics related to geoid and gravity modeling, with special attention given to the current and planned gravi- dedicated satellite missions. The symposium also followed in the tradition of mid-term meetings that were held between the quadrennial joint meetings of the International Geoid and Gravity Commissions. The previous mid-term meetings were the International Symposia on Gravity, Geoid, and Marine Geodesy (Tokyo, 1996), and Gravity, Geoid, and Geodynamics (Banff, 2000). GGSM2004 aimed to bring together scientists from different areas in the geosciences, working with gravity and geoid related problems, both from the theoretical and practical points of view. Topics of interest included the integration of heterogeneous data and contributions from satellite and airborne techniques to the study of the spatial and temporal variations of the gravity field. In addition to the special focus on the CHAMP, GRACE, and GOCE satellite missions, attention was also directed toward projects addressing topographic and ice field mapping using SAR, LIDAR, and laser altimetry, as well as missions and studies related to planetary geodesy.

Gravity --- Geological modeling --- Inversion (Geophysics) --- Geodynamics --- Measurement --- Earth --- Figure --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Prospecting --- Modeling, Geological --- Models and modelmaking --- Geophysical methods --- Mathematical models --- Physical geography. --- Geophysics/Geodesy. --- Geography --- Geophysics. --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Earth (Planet)

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This is the first study to present simultaneously both deconvolution and inversion, two powerful tools of data analysis. Featured within this volume are various geophysical convolution models and a treatment of deconvolution for a time-varying signal. The single channel time-varying deconvolution is shown equivalent to the multichannel time-invariant deconvolution, thus a formalism and associated algorithms can handle both. Inverse theory as well as various inversion schemes are presented on the basis of a relationship between a small perturbation to the model and its effects on the observatio

Seismic reflection method --- Inversion (Geophysics) --- Prospecting --- Deconvolution. --- Geophysical methods --- Mathematics. --- Exploration (Prospecting) --- Mines and mineral resources --- Mine examination --- Mine valuation --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Deconvolution in seismic reflection --- Mathematical models --- Data processing

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Geophysical Inverse Theory and Applications, Second Edition, 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. It's the first book of its kind to treat many kinds of inversion and imaging techni

Earth sciences -- Mathematics. --- Geodynamics. --- Geophysics. --- Inversion (Geophysics). --- Cosmic Physics --- Physics --- Physical Sciences & Mathematics --- Inversion (Geophysics) --- Geophysics --- Functional analysis. --- Measurement. --- Functional analysis --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Geological physics --- Terrestrial physics --- Earth sciences --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Prospecting --- Measurement --- Geophysical methods --- Mathematical models

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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 t

Inversion (Geophysics) --- Geophysics --- Functional analysis. --- Mathematical optimization. --- Measurement. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Inverse method (Geophysics) --- Inverse problem (Geophysics) --- Inverse theory (Geophysics) --- Inversion models (Geophysics) --- Models, Inversion (Geophysics) --- Prospecting --- Geophysical methods --- Mathematical models --- Earth Sciences --- General and Others