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

New velocity data in addition to literature data derived from sonic log, seismic, and laboratory measurements are analyzed for clastic silicate rocks. These data demonstrate simple systematic relationships between compressional and shear wave velocities. For water-saturated clastic silicate rocks, shear wave veloci­ ty is approximately linearly related to compressional wave velocity and the compressional-to-shear velocity ratio decreases with increasing compressional velocity. Laboratory data for dry sandstones indicate a nearly constant compressional-to-shear velocity ratio with rigidity approximately equal to bulk modulus. Ideal models for regular packings of spheres and cracked solids exhibit behavior similar to the observed water­ saturated and dry trends. For dry rigidity equal to dry bulk modulus, Gassmann's equations predict velocities in close agreement with data from the water-saturated

http://luminageo.us/papers/Castagna,%20Batzle,%20Eastwood%20(1985)%20Relationship%20Compresional-Shear%20wave%20velocities.pdf

Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks

The shear‐wave (S-wave) velocity of near‐surface materials (soil, rocks, pavement) and its effect on seismic‐wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh‐wave phase velocity of a layered‐earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion‐curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high‐frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high‐frequency range when using the Levenberg‐Marquardt and singular‐value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg‐Marquardt method. Synthetic examples demonstrated calculation efficiency and stability ...

/pdf/estimation-of-near-surface-shear-wave-velocity-by-inversion-29l31bs7zn.pdf

Estimation of near‐surface shear‐wave velocity by inversion of Rayleigh waves

A compilation of compressional-wave ( V p) and shear-wave ( V s) velocities and densities for a wide variety of common lithologies is used to define new nonlinear, multivalued, and quantitative relations between these properties for the Earth's crust. Wireline borehole logs, vertical seismic profiles, laboratory measurements, and seismic tomography models provide a diverse dataset for deriving empirical relations between crustal V p and V s. The proposed V s as a function of V p relations fit V s and V p borehole logs in Quaternary alluvium and Salinian granites as well as laboratory measurements over a 7-km/sec-wide range in V p. The relations derived here are very close to those used to develop a regional 3D velocity model for southern California, based on pre-1970 data, and thus provide support for that model. These data, and these relations, show a rapid increase in V s as V p increases to 3.5 km/sec leading to higher shear-wave velocities in young sedimentary deposits than commonly assumed. These relations, appropriate for active continental margins where earthquakes are prone to occur, suggests that amplification of strong ground motions by shallow geologic deposits may not be as large as predicted by some earlier models.

Empirical relations between elastic wavespeeds and density in the Earth's crust

Offset-Dependent Reflectivity–Theory and Practice of AVO Analysis

A method of seismic data processing is described in which a particular wavelet is selected from a plurality of wavelets as being most characteristic of a received seismic signal. A subtracted signal can be determined by subtracting a weighted signal of the particular wavelet from the received signal. From the subtracted signal, an additional particular wavelet can be chosen. The process of subtracting a signal and determining an additional particular one of the plurality of wavelets can be repeated until a criterion is met. The method can be repeated at several depths. The resultant spectral analysis can be used to determine, for example, an absorption coefficient.

Instantaneous spectral analysis

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the timefrequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

http://luminageo.us/papers/Sinha,%20Routh,%20Anno,%20Castagna%20(2005)%20SD%20of%20seismic%20data%20with%20CWT.pdf

Spectral decomposition of seismic data with continuous-wavelet transform

Shear-wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude-versus-offset analyses and multicomponent seismic interpretations. Measured shear-wave velocity logs are, however, often unavailable. We developed a general method to predict shear-wave velocity in porous rocks. If reliable compressional-wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear-wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional- and shear-wave velocities for water-saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first-order applicability of the Biot–Gassmann theory to real rocks. We verified these concepts with laboratory measurements and full waveform sonic logs. Shear-wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations.

John P. Castagna

Papers

Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks

Offset-Dependent Reflectivity–Theory and Practice of AVO Analysis

Instantaneous spectral analysis

Spectral decomposition of seismic data with continuous-wavelet transform

Shear-wave velocity estimation in porous rocks: theoretical formulation, preliminary verification and applications