Introduction A direct correlation of lithology to stacked and mi- grated seismic data, although an attractive goal, is usually an elusive one. In extreme cases, such as hard limestone formations encased in clastics, lithologic information may be obvious in the seismic amplitudes. For subsur- face formations characterized by small velocity changes between different lithologies, however, such a correlation may not be possible. Similarly, acoustic logs themselves are poor indicators or differentiators of lithology, unless they are combined with other logs such as density or po- rosity logs. One main reason for this is that reservoir rocks such as sandstone, limestone, and shale each exhibit large acoustic-velocity ranges that may overlap significantly. In addition, this limited information is available only at the location of a well, and seismic data are looked upon to provide it elsewhere. Although the goal of direct cor- relation from seismic to lithology seems simple, serious thought suggests that it could be a complicated exercise. The seismic response of subsurface rocks depends on the contrasts in compressional- and shear-wave velocities and densities. Those contrasts in turn depend on the rock’s lithology, porosity, pore-fluid content, and pressure, all of which affect seismic-wave propagation (e.g., Gregory, 1977; Castagna et al., 1993). That dependence requires knowledge about variations in the elastic properties of rock frames, their mineral constituents, and pore fluids, as well as a model for the interactions among them. Rock physics provides the link between the physical properties of rocks and their seismic response, and that link estab- lishes the P-wave velocity (V P ), S-wave velocity (V S ), and density ( ρ) of the subsurface rocks, along with their re- lationships to the rocks’ elastic moduli (bulk modulus κ and shear modulus μ), porosity, pore fluid, temperature, pressure, and the like. Velocities, densities, and many other physical prop- erties can be measured directly in the laboratory from rock samples taken from boreholes. Such measurements are not available everywhere and may not be directly ap- plicable to in-situ conditions, so empirical relations de- rived from experiments and well logs are usually applied. Those empirical relations are based on certain data and therefore have assumptions that must be fulfilled before the relations can be applied in a meaningful way. In this chapter, we discuss estimation of rock properties and how they are used to predict a rock’s pore-fluid properties and saturation. Seismic velocities and density Velocity estimation The P- and S-wave velocities for homogeneous, non- porous, and isotropic rocks are given, in terms of the elastic constants, by the well-known equations 1 and 2 of Chapter 1 –– that is, in terms of the bulk modulus and the shear modulus: V V P S and = + = κ μ ρ μ ρ 4 3 . Both of these equations are derived by assuming the prop- agation of elastic waves in isotropic elastic media. How- ever, porous media, and therefore porous rocks, are not strictly elastic. For our purposes, we will assume that these equations are applicable, at least to the first order. The ratio V P /V S is an important diagnostic value in seismic determination of lithology, and it can be written as V V P S = + 2 4 3 κ μ . (1) Chapter 2: Rock-physics Foundation for AVO Analysis John P. Castagna 1 , Satinder Chopra 2 , and Firas Al-Jarrah 1 1 University of Houston, Houston, Texas, U.S.A. Email: [email protected]; fi[email protected]. 2 Arcis Seismic Solutions, TGS, Calgary, Alberta, Canada. Email: [email protected]. 15 Downloaded 12/28/17 to 205.196.179.237. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
Chapter 2: Rock-physics Foundation for AVO Analysis
Jun 23, 2023
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