Introduction This investigation was undertaken to evaluate the processing flows needed to obtain vertical and radial post-stack-migrated seismic sections from a heavy-oil reservoir in eastern Alberta. Converted-wave seismic processing flows have been previously investigated and documented by Harrison (1992) and Isaac (1996). Of particular importance to converted-wave processing is the analysis of receiver statics. Isaac (1996) and Cary and Eaton (1993) showed that S-wave receiver statics can be extremely large and variable compared to P-wave receiver statics. It is not uncommon to have S-wave receiver statics on the order of ±200 ms, whereas P-wave receiver statics are commonly small, typically less than 20 ms. Velocity analysis is an integral component of converted-wave processing. There has been extensive research relating to nonhyperbolic moveout, valid for weak anisotropy. In many cases, for short to medium offset P-P data, hyperbolic normal moveout (NMO) is an adequate approximation for moveout used in velocity estimations (Al-Chalabi, 1973; Tsvankin and Thomsen, 1994; Alkhalifah, 1997). For P-S data, the hyperbolic NMO correction is valid only for short offsets (Iverson et al., 1989). Furthermore, Castagna and Chen (2000) found that conventional processing software assumes hyperbolic moveout and may produce false structure and false responses below anisotropic regions because of improper removal of NMO. It has been found that the overlying rock in some heavy-oil areas exhibits high values of anisotropy. Newrick and Lawton (2003) found that at Pikes Peak, Saskatchewan, the Thomsen parameters of anisotropy have values of ϵ=0.12±0.02 and δ=0.30±0.06 , from data using a multioffset vertical seismic profile. If the Jackfish area is similar, there is a need to explore the results based on nonhyperbolic NMO as opposed to the standard hyperbolic NMO calculations.

Abstract Although least-squares inversion is a useful tool in data analysis, nonuniqueness is an inevitable problem. This problem can be analyzed by considering the sensi-tivity of a model response to the parameter estimates. Such sensitivity methods produce extremal solutions which barely satisfy some resolution (or stability) criteria. Two closely related methods for producing such solutions are the “Edgehog” and “Most Squares” methods due to Jackson (1973 , 1976 ) These techniques, which evaluate the “degree of non-uniqueness” in a least-squares inversion, require only the information computed in a singular value decomposition (SVD) solution. While the “edgehog” and “most squares” techniques are mathematically similar, the “most squares” estimate is the simpler to compute. Both methods show that the credibility of an inversion depends on both the specified error criterion as well as on the properties of the Jacobian matrix associated with the least-squares solution. The similar performance of these two closely related methods is demonstrated with the traveltime inversion of both synthetic and real vertical seismic profiles (VSPs). The sensitivity analysis of this inversion problem provides a quantitative measure of solution reliability.

Abstract The propagation of energy via waves is a familiar phenomenon in our everyday life. The particular waves to be studied here are seismic waves which are intentionally created to image the interior of the earth Aki (1980), Claerbout (1985), , and (Telford), 1976. . Our three dimensional earth consists of more than the geological structures we are accustomed to thinking about, much of the earth is fluid or fluid like. Here the principal fluids of interest are hydrocarbons. The other essential uid to consider is water. The fluid-like materials include the many gases trapped in earth, gases like carbon dioxide, helium, and natural gas. Actually, we may not be aware of the less visible subsurface structure but all of the surface geology you can observe in some form exists under the surface and more. To find accumulations of petroleum requires an intimate knowledge of the subsurface geology, the history of the material source and the structure of the subsurface. A reservoir requires porosity, a sealing mechanism, and a hydrocarbon source. The storage capacity is dependent on the porosity, the seal prevents leakage of the hydrocarbons, and the source generates the hydrocarbons. Note, the source rocks are not always the same as the reservoir rocks. To produce hydrocarbons the reservoir must be found and be capable of producing fluids. The interconnections of the porous spaces, the permeability, permits flow of the gases and liquids. Tightly connected porous spaces are difficult producers, but well connected spaces have good permeability and are productive. The oil exploration process finds possible drilling locations and the actual drilling of a well is used to test the geological hypothesis of hydrocarbon existence.

Abstract The propagation of seismic waves in an inhomogeneous media is mathematically represented by the wave equation. This section describes the spatial dimensions of the model, the finite difference approximation, and the computational aspects of the seismic modeling problem. The spatial derivative has three forms. In one dimension the wave equation is expressed in Equation 2.2. The media velocity C is a constant for homogeneous models and varies for inhomogeneous models. The two dimensional wave equation is Equation 2.3, and the three dimensional is Equation 2.4. The time derivative in two dimensions can be augmented to include the 2.5D amplitude corrections Liner 1991 as shown in Equation 2.5. A significant new result is the 2.5D stability condition which exhibits a time dependent nature unlike the 2D and 3D stability conditions which are constant, Bording (1992). The applications of acoustic wave equations include exploding reflector modeling and reverse time migration, Bording (1994). Shot record modeling, exploding reflector modeling, and reverse time migration algorithms Bording (1993) and (1994) have been developed using these wave equations. Given a source function, derivative approximations, and appropriate boundary conditions, it is possible to model waves. Figure 2.1 is an example of a propagating wave in a four layer model. The model is a rectangular box with the source placed at the center. The model velocity is different for each layer. The top layer has velocity of 2000 m/s, the next layer is 2400 m/s and the remaining layers alternate between 2000 and 2400. An example of the boundary condition method is presented in Section 2.5.

Abstract Before describing the methodology and performance of reverse-time migration, it should be stated that it is only one of about four accurate depth migration methods. As described by Whitmore et al. (1988), these four methods include phase-shift plus interpolation migration Gazdag, (1978), frequency-space migration Berkhout, (1985), Kirchhoff migration Schneider, (1978), and finite-difference reverse-time migration McMechan, (1983). (The first two of these methods are employed in the frequency domain, while the latter two use the time domain.) Faster, but less general, time migration algorithms include the frequency-wavenumber migration due to Stolt (1978), and the various paraxial approximation codes described by Claerbout (1985). Additionally, the Hale-McClellan algorithm described by Hale (1991) represents an economical method 3-D poststack depth migration. We focus on finite-difference reverse-time migration for two reasons. First of all, it directly uses the technology described in the first two chapters. Secondly, it is probably the most general of the depth migration codes, albeit the most expensive. However, with the advent of high performance computing and parallel processing, it appears that the computing costs will not be prohibitive – even for three-dimensional problems. The beauty of reverse-time migration is that it can be a very general method for seismic imaging. This method uses the finite-difference wave equation modeling as a means of migrating seismic data. As we will see in this chapter and later chapters, reverse-time migration can be used to image highly complex geological structures. Migration is the data processing technique which positions seismic reflections in their correct subsurface location. Recorded seismic traces are generally plotted at a horizontal position which is at the mid-point between sources and receivers. For layered media, this common-mid-point (CMP) is generally the correct location for the reflection's common-depth-point (CDP) or common-reflection-point(CRP). In areas where we are dealing with reflections from dipping formations, the CMP is not the correct location for the reflecting point. A correction for the positioning of the reflector can be supplied by migration.

Abstract Most of the original applications of reverse-time migration were on CMP (common midpoint) stacked data. The method found use in oil exploration near steeply dipping salt intrusions (Whitmore and Lines, 1986; Lines et al., 1995; Mufti et al., 1996) and overthrust fold belts (Whitmore, 1983; Bording et al., 1987; Lines, 1993; and Wu et al., 1996). To the extent that the CMP stacked data represent the zero-offset sections of an exploding reflector, model studies (eg. Bording et al., 1987) show that reverse-time migration can do an excellent job. CMP stacking encounters its worst problems in representing CRP (common reflection point) data whenever geological structures deviate most from at layer geometries. With the fact that CMP does not equal CRP for such geometries, one might wonder why stacking would work at all. However, fortunately for geophysicists, CMP stacking is reasonably robust for mildly complex structures, as shown by Kelly et al. (1982). Another method of alleviating the problems of steep dip in processing is the use of DMO (dip-moveout). Ideally the use of NMO (normal moveout) corrections used with DMO corrections and CMP stacking allows poststack migration to perform as well as prestack migration at considerably less expense. The benefits and advantages of using DMO are summarized by Hale (1991). The most general (and most expensive) imaging technique which is available in the migration tool box is the process of prestack depth migration. The use of this powerful method necessitates the use of accurate velocity models. In fact, as we will see in the next chapter, prestack reverse-time depth migration will be used as a velocity analysis tool.