Abstract Assessing residual moveout after migration is a useful way to undertake velocity analysis in surface seismic data. In this paper, we apply this concept to walk-away vertical seismic profile (VSP) data. Because of the non-symmetric source and receiver geometry, it is hard to detect the depth residual moveout in conventional common image gathers (CIGs) for VSP data. In this case, we changed the horizontal axis from horizontal offsets from the common image point (CIP) to be receiver depths. We derive a residual moveout function for migrated common receiver gathers assuming a constant velocity model having a single horizontal reflector. We then extend this tool to a layered medium using a layer stripping, V rms approach, which allows us to obtain interval velocities of the model layers. It has better results than the classic depth residual moveout. This is further applied to more complex, laterally varying velocity models with good results. This is valid since with VSP data we are generally imaging within a small (compared to surface seismic) distance away from the borehole and our analysis method allows us to estimate velocity perturbations away from the trial migration velocity model.

Abstract What the geoscientist might really like to do is cut the Earth along a line, down some thousands of metres, and have a look at the rocks, and their pore fluids, in place. While this rather invasive technique is not yet popular, analogous methods are. Seismic tomography is a means of making a picture of a slice of the earth using seismic data (the word tomography being derived from the Greek τoμoσ which means section or slice). Seismic techniques have long been used to create subsurface pictures. The medical community has also been greatly assisted by computed tomography (CAT or CT scanning) for some time (e.g., Kak, 1979; Coulam et al., 1981; Seeram, 1982). However, it is only recently that seismic tomography (ST) has been developed for hydrocarbon exploration. Although some of the methods used in exploration geophysics for a number of years can be classified as tomographic, ST provides a general unifying concept of geophysical parameter estimation and imaging. More recent acquisition geometries (e.g., crosswell) and diverse data sets (well log, borehole seismic and surface seismic) can also be processed and integrated via ST methods. The current interest in and promise of ST in geophysical exploration is made possible by a number of factors including cross-fertilization from other sciences, advances in seismic field data acquisition, imaging theory and computing speed. Tomographyi s a type of inversep roblem. That is, measurements are first made of some energy which has propagated through a medium. The

Abstract The tomographic problem may be stated again as, From projections (sums of some interior value) measured outside of an object find the interior distribution of values inside the object. So we first need to gather the appropriate data, then make an image via a suitable inversion technique. As discussed in the previous chapter, there are many forms of tomographic data which can be acquired, depending on the problem to be solved. Most data types are the result of some form of energy transmitted from a source to a receiver. In more complex cases, some kind of scattering may intervene between the source and receiver. In the exploration seismic case, the traveltime or amplitude of seismic waves (waves say of 5 Hz up to 20 kHz) is measured. This amplitude or traveltime is considered to be a projection or sum of some value (amplitude attenuation, slowness or scatterer strength) along the path travelled by the energy. A schematic diagram for a projection or travel path sum is shown below. A projection is the sum of an object's parameters( or function's values) alonga given line or energy transit path. A sum or integral of this type is also known as a Radon transform. For a more detailed treatment of the Radon transform, see Helgason (1980), Deans (1983), or Natterer (1986). The Radon transform is defined below with symbol references to Figure 2.1. Note that this transform is also known as a slant stack( for clear geometric reasons)and is equivalent to theτ-p

Abstract In this chapter, we will consider cases from a number of geologic settings, where various survey geometries and tomographic reconstructions are used to assist in solving geophysical problems. Many of the studies to date have been based on seismic traveltime inversion as a way to find seismic velocity. These velocity maps can be used as stand-alone geologic models or can provide velocity control for further processes. Other studies have used the reflection amplitudes to create subsurface sections. Again, various source and receiver geometries are customarily used: borehole-to-borehole, surface-to-borehole, and surface-to-surface. Of course, the greater the degree of angular coverage around the rock mass of interest, the greater will be the reliability of the reconstructed image. The first geophysical tomographic geometry to be considered here is the crosswell configuration. In this case, a source is suspended in one borehole and the receiver(s) records the resultant energy in an adjacent borehole. By making numerous measurements from various source-receiver positions, the velocity, or attenuation of the intervening rock can be calculated from the directly arriving energy. This type of survey and analysis has found usage in areas from nuclear waste site characterization to in situ steam flood monitoring. When crosswell surveying though, many other events are recorded in addition to the direct arrivals. To increase coverage and information extracted from a crosswell survey, some investigators have used reflected and scattered events. We will also discuss reflection analysis in some detail. Next considered is the case of using surface seismic data in conjunction with Vertical

Abstract In the course of these notes, we have considered tomography as practiced in disciplines ranging from diagnostic medicine to whole Earth geophysics. The concept of recovering material properties form their line integrals is seen to be broadly applicable and quite powerful. In medicine and some other realms of non-destructive testing, tomography has become a standard and well-accepted technique. In geophysics, partially due to the incompleteness of our surveys and relative novelty of the method, tomography is still developing in a critical environment. There are realms in which tomographic concepts are directly applicable, such as petrophysical scanning and crosswell surveying; some other specialties require generalization or reinterpretation of fundamental tomographic definitions (eg., reflection tomography or the generalized inverse Radon transform). CT core scanning will quite possibly become a very standard core analysis method, given current interest and results. MRI core scans may become similarly useful. Insofar as crosswell studies are performed, tomographic techniques again are providing and will likely continue to provide an important acquisition and analysis methodology. ST will certainly play a further role in VSP and surface seismic studies; perhaps dominantly as a velocity analysis method. The migration/inversion problem is elegantly cast in a tomographic form and may be solved in a tomographic manner. The recent levels of interest and studies to date suggest that the geophysical world provides numerous problems that are amenable to a tomographic solution.

Abstract This publication encompasses seismic tomography from the earliest work to current exploration and development imaging. Applications and case histories are presented.