Seismic Diffraction Tomography
Published:January 01, 1994
Seismic diffraction tomography is useful for reconstructing images of subsurface inhomogeneities which fall into two categories. The first category includes inhomogeneities that are smaller in size than the seismic wavelength and have a large velocity contrast with respect to the surrounding medium. Imaging these inhomogeneities with the seismic ray tomography methods presented in Chapter 2 is generally out of the question. The second category includes inhomogeneities that are much larger in size than the seismic wavelength and have a very small velocity contrast with the surrounding medium. Although seismic ray tomography is valid for imaging these inhomogeneities, it works best when the velocity contrasts are large. Note that both categories of inhomogeneity are capable of producing measurable scattered wavefields of similar power. The large velocity contrast of the first category inhomogeneity offsets its small size while the large size of the second category inhomogeneity makes up for its small velocity contrast.
The outline for this chapter closely parallels that of Chapter 2. First, in Section 3.2 we review acoustic wave scattering theory and derive two independent linear relationships between data functions representing scattered energy and the model function M(r). The model function M(r) used in this chapter is a measure of the velocity perturbation caused by an inhomogeneity at vector position r from a constant background velocity. Second, using either of the linear relationships between a data function and the model function M(r), the generalized projection slice theorem is derived in Section 3.3 which serves as
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Fundamentals of Seismic Tomography
We define tomography as an imaging technique which generates a cross-sectional picture (a tomogram) of an object by utilizing the object's response to the nondestructive, probing energy of an external source. Seismic tomography makes use of sources that generate seismic waves which probe a geological target of interest.
Figure 1(a) is an example configuration for crosswell seismic tomography. A seismic source is placed in one well and a seismic receiver system in a nearby well. Seismic waves generated at a source position (solid dot) probe a target containing a heavy oil reservoir situated between the two wells. The reservoir's response to the seismic energy is recorded by detectors (open circles) deployed at different depths in the receiver well. The reservoir is probed in many directions by recording seismic energy with the same receiver configuration for different source locations. Thus, we obtain a network of seismic raypaths which travel through the reservoir.
The measured response of the reservoir to the seismic wave is called the projection data. Tomography image reconstruction methods operate on the projection data to create a tomogram such as the one in Figure 1(b). In this case we used projection data consisting of direct-arrival traveltimes and seismic ray tomography to obtain a P-wave velocity tomogram. Generally, different colors or shades of gray in a tomogram represent lithology with different properties. The high P-wave velocities (dark gray/black) in the tomogram in Figure 1(b) are associated with reservoir rock of high oil saturation.
Seismic tomography has a solid theoretical foundation. Many seismic tomography techniques have close ties to more familiar seismic imaging methods such as traveltime inversion, Kirchhoff migration, and Born inversion. For example, seismic ray tomography used to determine lithologic velocity is essentially a form of traveltime inversion and seismic diffraction tomography is closely related to Born inversion and seismic migration. Thus, seismic tomography may actually be more familiar to you at this point than you might think since it is just another aspect of the subsurface imaging techniquesg eophysicistsh ave been using for years.