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

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

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave-equation traveltime inversion (WT), seismograms are computed by any full-wave forward modeling method (we use a finite-difference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a least squares sense. A gradient optimization method is used and the formula for the Frechet derivative (perturbation of traveltimes with respect to velocity) is derived directly from the wave equation. No traveltime picking or ray tracing is necessary, and there are no high frequency assumptions about the data. Body wave, diffraction, reflection and head wave traveltimes can be incorporated into the inversion. In the high-frequency limit, WT inversion reduces to ray-based traveltime tomography. It can also be shown that WT inversion is approximately equivalent to full-wave inversion when the starting velocity model is 'close' to the actual model.Numerical simulations show that WT inversion succeeds for models with up to 80 percent velocity contrasts compared to the failure of full-wave inversion for some models with no more than 10 percent velocity contrast. We also show that the WT method succeeds in inverting a layered velocity model where a shooting ray-tracing method fails to compute the correct first arrival times. The disadvantage of the WT method is that it appears to provide less model resolution compared to full-wave inversion, but this problem can be remedied by a hybrid traveltime + full-wave inversion method (Luo and Schuster, 1989).

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Wave-equation traveltime inversion

Preface 1. Introduction to rock physics 2. Rock physics interpretation of texture, lithology and compaction 3. Statistical rock physics: combining rock physics, information theory, and statistics to reduce uncertainty 4. Common techniques for quantitative seismic interpretation 5. Case studies: lithology and pore-fluid prediction from seismic data 6. Workflows and guide lines 7. Hands-on References Index.

Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk

A multiplicity of factors influence seismic reflection coefficients and the observed gravity of typical sedimentary rocks. Rock velocity and density depend upon the mineral composition and the granular nature of the rock matrix, cementation, porosity, fluid content, and environmental pressure. Depth of burial and geologic age also have an effect. Lithology and porosity can be related empirically to velocity by the time‐average equation. This equation is most reliable when the rock is under substantial pressure, is saturated with brine, and contains well‐cemented grains. For very low porosity rocks under large pressures, the mineral composition can be related to velocity by the theories of Voigt and Reuss. One effect of pressure variation on velocity results from the opening or closing of microcracks. For porous sedimentary rocks, only the difference between overburden and fluid pressure affects the microcrack system. Existing theory does not take into account the effect of microcrack closure on the elasti...

L. W. Gardner

Papers

Formation velocity and density—the diagnostic basics for stratigraphic traps