Abstract 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.

Abstract We begin the study of seismic tomography with image reconstruction methods based on ray theory. We assume that the source produces seismic wave energy with wavelengths much smaller than the size of the inhomogeneities encountered in the medium. Only when this assumption is obeyed can the propagation of the seismic wave energy be properly modeled by rays. Otherwise, the seismic diffraction tomography in Chapter 3 must be applied to solve the problem. Two groups of image reconstruction methods exist for doing seismic ray tomography. The transform methods in Section 2.2 comprise the first group. Applications of transform methods have their roots in astronomical and medical imaging problems. They are very limiting as far as seismic imaging problems are concerned since straight raypath propagation and full-scan aperture are generally assumed. However, the transform methods make an excellent introduction to the principles of tomography because of their simplicity and serve as a bridge between applications of tomography in other fields with applications in seismology. Also, the development of seismic diffraction tomography has a close relationship with the transform methods. The series expansion methods in Section 2.3 comprise the second group of image reconstruction methods. Out of all the methods presented in this book the series expansion methods presently see the most use in seismic tomography. Therefore, a large part of Chapter 2 is spent addressing the series expansion methods. Before proceeding further one should have a good grasp of the Fourier transform concepts to understand the material in Section 2.2.

Abstract 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

Abstract The purpose of this chapter is two-fold. First, through case studies, we illustrate the procedures for implementing the theory presented in Chapters 2 and 3 . Second, the case studies highlight some of the benefits of using seismic tomography in the oil industry. The first two case studies utilize crosswell seismic data in conjunction with the simultaneous iterative reconstruction technique (SIRT) presented in Chapter 2 on seismic ray tomography. The first case study addresses the production problem of monitoring the progress of a steam-flood enhanced oil recovery (EOR) program. The second case study involves more of a development problem in which the structural interpretation of a fault-controlled reservoir must be better understood for in-fill drilling. The third case study uses the seismic diffraction tomography presented in Chapter 3 to image two salt sills using marine surface seismic data. We selected this problem to illustrate the seismic diffraction tomography methodology and limitations rather than to solve an exploration problem.

Abstract 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.