Boots – shoes – and leggings
Patent
1995-12-05
1998-04-07
McElheny, Jr., Donald E.
Boots, shoes, and leggings
G06F 1900
Patent
active
057372209
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
This invention relates to a method of determining elastic parameters of earth strata, and more specifically to an improved method of determining elastic parameters in an anisotropic medium such as a Transversely Isotropic medium ("TI medium").
BACKGROUND
In geologic exploration and particularly in the exploration for underground hydrocarbon deposits, it is useful to obtain a measure of the elastic parameters of earth strata, either for the direct goal of understanding the behavior of the earth formations subject to mechanical stresses and strains, or as an intermediate step in improving seismic measurement and processing methods.
The elastic moduli of earth formations are directly related to, and useful for characterizing, rock strength, porosity, lithology, and pore fluids.
The elastic moduli of earth strata are also directly related to the acoustic propagation characteristics of the earth, and along with density constitute primary parameters of earth strata in seismology. The elastic moduli are related to the speed of propagation for elastic waves which may vary as a function of direction of propagation and direction of polarization. Waves with polarization direction approximately aligned with propagation direction are referred to as quasi P waves (qP). Waves with polarization direction approximately orthogonal to propagation direction are quasi shear waves (qS). The elastic moduli may be expressed as matrix elements c.sub.ij where i.ltoreq.6, j.ltoreq.6. The number of independent elastic parameters c.sub.ij can vary between two parameters in the case of an isotropic medium and 21 parameters for an arbitrary elastic medium.
The earth is comprised of many layers of geologic strata, and it is common to use a horizontally layered medium as a basic model of the earth, wherein each layer is attributed with elastic parameters corresponding to measured parameters such as the density and the propagation velocities for P, SV and SH waves. When anisotropy is encountered, it has been found to be particularly useful to model the earth as a TI elastic medium.
A TI medium is transversely isotropic with respect to some symmetry axis. Using the vertical axis as the symmetry axis, it is referred to as a "TIV medium", whereas if the horizontal axis is used as a symmetry axis, it is sometimes referred to as a "TIH medium". In either case, a TI medium is characterised by its density .rho. together with five independent elastic moduli relating stress and strain. In condensed subscript notation, with rotational symmetry around the 3-axis, the moduli are {c.sub.11,c.sub.13,c.sub.33,c.sub.55,c.sub.66 }. The density-normalised moduli, A.sub.ij =c.sub.ij /.rho., have dimensions of velocity.sup.2 and are related to elastic propagation in the medium as follows. Any plane harmonic wave propagating in the medium, having a phase slowness vector (p.sub.1,p.sub.3) lying, for example, in the 1-3 plane must have displacement either in the 1-3 plane (the qP or qSV case) or normal to it (the SH case). In either case, the squared phase slowness vector (X,Z)=(p.sub.1.sup.2,p.sub.3.sup.2) must satisfy the appropriate Christoffel relation. In the SH case that is +A.sub.55)X-(A.sub.11 +A.sub.55)Z+1=0 (2) parameters as follows: waves with vertical polarization (SV) where the earth strata of interest exhibit primarily horizontal layering, the TIV medium provides a good model for seismic purposes. If additional parallel vertical fractures are imposed in addition to the layering, another form called a Fractured TIV or "FTIV medium" is created, which has especially relevant and useful parallels with the hydrocarbon bearing earth formations of interest to seismic exploration. A FTIV medium has eight independent elastic parameters c.sub.ij. Both TI and FTIV media fall into the broader category of orthorhombic media, which are defined as having three mutually orthogonal planes of mirror symmetry. A general orthorhombic medium has nine independent elastic parameters c.sub.ij.
In laboratory studies the acoustic slowness measurem
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Hyden Martin D.
Jeffery Brigitte L.
McElheny Jr. Donald E.
Schlumberger Technology Corporation
Smith Keith G. W.
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