Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

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The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

The Rock Physics Handbook

Preface 1. Introduction 2. The elastodynamics and its simple solutions 3. Seismic rays and travel times 4. Dynamic ray tracing. Paraxial ray methods 5. Ray amplitudes 6. Ray synthetic seismograms Appendix. Fourier transform, Hilbert transform and analytical signals References Index.

Seismic Ray Theory

Prestack migration and/or inversion may be implemented in either the time or the frequency domain. In the frequency domain, it is possible to discretize the frequencies with a much larger sampling interval than that dictated by the sampling theorem and still obtain an imaging result that does not suffer from aliasing (wrap around) in the depth domain. The selection of input frequencies can be reduced when a range of offsets is available; this creates a redundancy of information in the wavenumber coverage of the target. In order to optimize the use of this information, we define a new discretization strategy that depends on the maximum effective offset present in the surface seismic survey: the larger the range of offsets, the fewer frequencies are required. The strategy, exact in a homogeneous 1D earth, selects frequencies by making use of the well-known effect of image stretch in normal-moveout (NMO) correction and in migration (usually considered detrimental for the imaging). The strategy is also useful in more general earth models: we apply it to the 2D Marmousi model and recover a continuous range of wavenumbers using only three input frequencies. The Marmousi inversion result accurately predicts all other data frequencies, demonstrating the redundancy of the data.

Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies

A least-squares migration algorithm is presented that reduces the migration artifacts (i.e., recording footprint noise) arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. We tested the performance of the least-squares migration on synthetic and field data in the cases of limited recording aperture, coarse sampling, and acquisition gaps in the data. Numerical results show that the least-squares migrated sections are typically more focused than are the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution. Regularization helps attenuate migration artifacts and provides a sharper, better frequency distribution of estimated reflectivity. The least-squares migrated sections can be used to predict the missing data traces and interpolate and extrapolate them according to the governing modeling equations. Several field data examples are presented. A ground-penetrating radar data example demonstrates the suppression of the recording footprint noise due to a limited aperture, a large gap, and an undersampled receiver line. In addition, better fault resolution was achieved after applying least-squares migration to a poststack marine data set. And a reverse vertical seismic profiling example shows that the recording footprint noise due to a coarse receiver interval can be suppressed by least-squares migration.

Least-squares migration of incomplete reflection data

The common‐reflection‐surface stack provides a zero‐offset simulation from seismic multicoverage reflection data. Whereas conventional reflection imaging methods (e.g. the NMO/dip moveout/stack or prestack migration) require a sufficiently accurate macrovelocity model to yield appropriate results, the common‐reflection‐surface (CRS) stack does not depend on a macrovelocity model. We apply the CRS stack to a 2-D synthetic seismic multicoverage dataset. We show that it not only provides a high‐quality simulated zero‐offset section but also three important kinematic wavefield attribute sections, which can be used to derive the 2-D macrovelocity model. We compare the multicoverage‐data‐derived attributes with the model‐derived attributes computed by forward modeling. We thus confirm the validity of the theory and of the data‐derived attributes. For 2-D acquisition, the CRS stack leads to a stacking surface depending on three search parameters. The optimum stacking surface needs to be determined for each point...

Common‐reflection‐surface stack: Image and attributes

Recently Bortfeld (1982) gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero‐offset reflection from the common datum point traveltime measurements of the event. To underline the significance and consequences of this method, a derivation and discussion of geometrical spreading factors is now given for two‐ and three‐dimensional earth models with curved reflecting boundaries. The spreading factors can be used easily to transform primary reflections in a zero‐offset seismic section to true amplitude reflections. These permit an estimation of interface reflection coefficients, either directly or in connection with a true amplitude migration. A seismic section with true amplitude reflections can be described by one physical experiment: the tuned reflector model. Hence the application of the wave equation (in connection with a migration after stack) is justified on such a seismic section. Also the geometrical spreading factors that are deri...

Computing true amplitude reflections in a laterally inhomogeneous earth

Compressional primary nonzero offset reflections can be imaged into three‐dimensional (3-D) time or depth‐migrated reflections so that the migrated wavefield amplitudes are a measure of angle‐dependent reflection coefficients. Various migration/inversion algorithms involving weighted diffraction stacks recently proposed are based on Born or Kirchhoff approximations. Here a 3-D Kirchhoff‐type prestack migration approach is proposed where the primary reflections of the wavefields to be imaged are a priori described by the zero‐order ray approximation. As a result, the principal issue in the attempt to recover angle‐dependent reflection coefficients becomes the removal of the geometrical spreading factor of the primary reflections. The weight function that achieves this aim is independent of the unknown reflector and correctly accounts for the recovery of the source pulse in the migrated image irrespective of the source‐receiver configurations employed and the caustics occurring in the wavefield. Our weight ...

http://repositorio.unicamp.br/jspui/bitstream/REPOSIP/52640/1/WOSA1993LT27300005.pdf

Peter Hubral

Papers

Common‐reflection‐surface stack: Image and attributes

Computing true amplitude reflections in a laterally inhomogeneous earth

3-D true‐amplitude finite‐offset migration

Foundations of Anisotropy for Exploration Seismics

Common-reflection-surface stack : a real data example