Deformable layer tomography and application to the Vinton Dome

Summary The tomographic approach of velocity-depth model building attempts to invert for velocity as a function of space location. For common geologic features such as weathering zones, stratigraphic beddings, and salt bodies, it makes more sense to characterize their velocities by deformed layers. The deformable layer tomography (DLT) focuses on constraining the geometry of velocity interfaces, or velocity contours. The goal is to have a more realistic model parameterization using a minimum number of solution variables. The DLT utilizes the knowledge of velocity range that is known in most applications. In this paper the DLT will be illustrated using synthetic tests in crosswell and tomostatics applications. An on-going DLT project for 3-D prestack depth migration in the Vinton Dome, southwest Louisiana, is described. It is postulated that the long-wavelength component of the velocity field can be mapped using the first arrivals of the surface 3-D seismic data. Introduction The velocity-depth model building is a key for prestack depth migration in complex areas mainly due to the dependency of wave propagation on the velocity field. Building velocity model by seismic tomography offers the advantage of a global constraining of the solution using all data available (e.g., Bishop et al., 1985; Farra and Madariaga, 1988; Kosloff et al., 1996). A central issue for tomography is how to parameterize the velocity model. There are two general model parameterization approaches. The first may be called the ‘finite-difference’ (FD) approach, which divides the model space into a framework of regular grids or cells, each has a constant velocity or constant velocity gradient. Most tomographic studies have followed this approach to invert for velocity values on the grids or cells. The second may be called the ‘finite-element’ (FE) approach, which characterizes the model space with some volumetric elements or layers following geologic beddings or recognized reflection horizons. Each element may have a constant velocity value, or a constant velocity gradient, or a generalized velocity function. Regardless of the details, the fundamental concept of both the FD and FE approaches is to determine the velocity field as a function of the spatial position. A variant of the FE model parameterization, here referred as the deformable layer tomography (DLT), is investigated here. Rather than determining the velocities of the model elements, we are mainly interested in the determination of the geometric shape of the elements, with or without determining their velocity values at the same time. In other words, the focus of the DLT is on determining the geometry of velocity contours. This approach of directly inverting for the geometry of velocity contours stemmed from the following observations. First, priori to most velocity model building efforts the range of velocity values can be determined from well logs, check-shots, and geologic data. The main unknown is the spatial distribution of the velocity values. Second, though the FE approach of model parameterization usually offers much fewer model variables than that of the FD approach, the precised geometry of velocity elements, corresponding to the geologic units, is unknown most times. However, a rough estimation of the structure of velocity elements can often be drawn from previous geologic and geophysical data, though there is a large uncertainty in the position of these elements. Finally, the post-inversion smoothing and contouring, as commonly done after most velocity model building efforts, is not a deterministic process. Such smoothing is often necessary before the final migration in order to remedy the short-wavelength velocity error, though smoothing will decrease the data fitting, or partially undo the velocity model building effort. This paper discusses the idea of the DLT method. Several synthetic examples will be shown, including comparison with the grid tomography. Finally, the applicability of the DLT to a 3-D seismic data over the Vinton Dome, Louisiana, will be discussed.