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

From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time To enhance the resolution of the seismic reflection method, we must investigate these variations in more detail. We present quantitative results of theoretical studies on propagation of plane waves for normal incidence, through perfectly elastic multilayered media. As wavelet shapes, we use zero-phase cosine wavelets modulated by a Gaussian envelope and the corresponding complex wavelets. A finite set of such wavelets, for an appropriate sampling of the frequency domain, may be taken as the basic wavelets for a Gabor expansion of any signal or trace in a two-dimensional (2-D) domain (time and frequency). We can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals. These results appear as complex 2-D functions of time and frequency, i.e., as “instantaneous frequency spectra. ’ ’ Choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces. For this purpose, we developed a Gabor expansion involving basic wavelets with a constant time duration/mean period ratio. For layered media, as found in sedimentary basins,

Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media

The authors introduce a directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information. The passband regions of the component filters are wedge-shaped and thus provide directional information. It is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed. The authors discuss the theory for directional decomposition and reconstruction. In addition, implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered. >

A filter bank for the directional decomposition of images: theory and design

Multifold ground coverage by seismic techniques such as the common reflection point method provides a multiplicity of wave travel path information which allows direct determination of root‐mean‐square velocities associated with such paths. Hyperbolic searches for semblance among appropriately gathered arrays of traces form the basis upon which velocities are estimated. Measured semblances are presented as a velocity spectral display. Interpretation of this information can give velocities with meaningful accuracy for primary as well as multiple events. In addition, the velocity data can help correctly label events. This paper outlines the fundamental principles for calculating velocity spectra displays. Examples are included which demonstrate the depth and detail of geological information which may be obtained from the interpretation of such displays.

Velocity spectra-digital computer derivation and applications of velocity functions

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

Multicomponent seismic data provide the potential to better characterize the subsurface than do P-wave data alone. Converted waves (C-waves) and pure shear waves can be used to validate bright spot reflections, provide Poisson's ratio estimates, provide reflection images where the P-wave reflectivity contrast is small, image through gas clouds where the P-wave signal is attenuated/scattered, and detect/characterize fractures through shear-wave splitting.

An introduction—Multicomponent

A principal problem in seismic exploration is the heterogeneous partially reflecting medium that makes up the transmission zone to the target reflectors of interest. Multiple reflection between the free surface and the shallower reflectors produces additive noise that interferes with our view of the bedding plane geometry and rock properties in the target zone. Residual multiple energy on the interpreter's record section display can easily be mistaken for signal. Because the magnitude of multiples is dependent on reflectivity products, and because subsurface reflectivities are normally small, the importance of multiples is highly variable. The complementary combination of predictive deconvolution and common depth point stack is routinely used for the reduction of multiple reflections. Predictive deconvolution achieves a temporal prediction and subtraction of that class of short-period multiples that is most predictable, and common depth point stack reduces that class of multiples distinguishable from primaries on the basis of local horizontal phase velocity in the x, t observational space. Each of these methods can be justified in terms of a simplified one-dimensional model of the earth. However, a major reason for their success is that they are employed with an empirical, statistical approach. As a result, these two processes are particularly robust and forgiving and respond imperfectly, but often constructively, to real-world deviations from the simplified models. Both processes are capable of distorting or destroying the desired signal, and their noise-reduction effectiveness is dependent on the manner of application. Quality control methods are imperfect, and there is an element of human artistry in seismic data processing. Predictive deconvolution employs a one-dimensional (t) filter designed on a purely statistical basis. Seismic data represent observations in (x 1 , x 2 , t), a four-dimensional space, and multiple reflections are deterministically predictable (in principle) from the shallower primary reflection data. Common depth point stack operates in (x 1 , t) as an array steered for the arrival of the roughly spherical target reflection wavefront. Multidimensional filter design aimed at coherent noise rejection, based on the nonrandom noise structure in (x 1 , t) is often used in problem areas. More effective reduction of multiple reflections is one of many potentially useful improvements in the seismic method.

Multiple reflections as an additive noise limitation in seismic reflection work

Offset‐dependent line‐intersection displays can be of significant direct interpretive value. On our data set from a proprietary location, use of these displays permits a refined structural interpretation and improves the usefulness of amplitude and amplitude‐versus‐offset displays for direct hydrocarbon detection. The degree of data reproducibility at each intersection may be exposed as a function of offset through the use of prestack and partial‐range stack splice and difference displays. At a set of marine line intersections, after only cursory processing, the range of residual amplitudes found by subtracting strike traces from dip traces is from −20 dB to +6 dB relative to the input. The average is about −8 dB. The poorest line intersection ties occur below the edges of deep bright spots, where velocity anomalies leading to time mis‐ties greater than 10 ms can occur. Shallow near‐surface velocity anomalies, out‐of‐plane arrivals including fault plane reflections, and, occasionally, water reverberation ...

Offset-dependent mis-tie analysis at seismic line intersections

The finite length of seismic arrays results in smeared estimates of the plane‐wave decomposition of the recorded wave field. The smearing is a fundamental property of plane‐wave decomposition; it can be reduced but not eliminated. If not accounted for, this smearing can have a significant effect upon the waveform inversion of plane‐wave seismograms. This paper illustrates the effects of limited spatial aperture on the plane‐wave decomposition and demonstrates that these truncation artifacts can be described by a linear ray parameter‐dependent filter. Experiments with synthetic data indicate that including the effects of limited aperture in the forward model of an iterative inversion produces a stable inversion result without significantly reducing the information content of the data. The method is illustrated with synthetic data derived for an earth consisting of elastic, isotropic, flat layers.

Accounting for limited spatial aperture in the waveform inversion of rho -tau seismograms

Summary Nine-component 3-D seismic reflection data are acquired using orthogonal shear-wave sources and orthogonal horizontal geophone components. Shear-wave sources are usually oriented inline and crossline to the receiver lines, as are the horizontal geophones. These coordinates are referred to as the field coordinates. Field coordinates implicitly mix SH, SV, and P-waves. Shear-wave data processing and interpretation is simplified if the prestack data are azimuthally rotated to a radial-transverse coordinate system. The radial component contains predominantly SV and P-wave modes, while the transverse data are predominantly SH. The SH data are simplified in that SH waves convert only to SH upon reflection and transmission (in a flat layered earth), unlike SV propagation which is coupled with P. There are distinct differences between SV and SH waves in terms of of the surface waves generated (Rayleigh versus Love). SH systems exhibit SH head waves, while SV systems have P head waves followed by P-SV-P head waves, etc., having very different slopes and intercepts than do those for SH. Normal moveout and amplitude-versus-offset are different for SH and SV waves, and the SV data contain P-waves and converted waves. Field coordinates mix all of these components together in variable proportions, confusing attempts at processing and interpretation.

http://www.beg.utexas.edu/egl/egl_pubs/radialtransverse.pdf

Milo M. Backus

Papers

An introduction—Multicomponent

Multiple reflections as an additive noise limitation in seismic reflection work

Offset-dependent mis-tie analysis at seismic line intersections

Accounting for limited spatial aperture in the waveform inversion of rho -tau seismograms

Radial-Transverse (SV-SH) Coordinates for 9-C 3-D Seismic Reflection Data Analysis