Direct traveltime inversion of VSP data for elliptical anisotropy in layered media
This paper presents an exact method for inversion of VSP data for anisotropic parameters that uses traveltimes directly, rather than phase slownesses computed from traveltime differences. There is a tradeoff in the present traveltime-based method compared with the slowness-based method. In our method we have to assume some function representing the vertical velocity variation, something that is not necessary in the phase-slowness method. There is, however, a higher numerical accuracy in the direct traveltime method. This is due partly to our using observed traveltimes directly in the computations rather than taking differences between values of comparable size, which greatly magnifies the relative errors. Error analysis shows that there also are other intrinsic reasons why our technique has less error. A numerical example representing a typical VSP yielded errors from the phase-slowness method (requiring two sources and two receivers) that were about 18 times larger than for a single determination by the direct traveltime method. Furthermore, in cases where the VSP has been acquired with a single source offset, e.g., for some offshore wells, the traveltime method will yield results, whereas the slowness method will not. INTRODUCTION In the last decade or two there has been a greatly increased recognition that significant seismic anisotropy is rather common in sedimentary rocks. It has also been shown that neglecting even a seemingly modest degree of anisotropy can lead to significant degradation in processed seismic images (e.g., Winterstein, 1986; Wright, 1987; Larner, 1993; Tsvankin, 1996; Chen and Castagna, 2000) or to significant errors in vertical or lateral positioning of subsurface features (e.g. Banik, 1984, 1987; Isaac and Lawton, 1999; Vestrum et al., 1999). Gaiser (1990) determined how to estimate the anisotropic parameters of a transversely isotropic medium from VSP data using vertical and horizontal phaseslowness measurements. Miller and Spencer (1994) and Miller et al. (1994) presented methods for inverting phase slowness estimates from walkaway VSPs for anisotropy parameters. Using a similar method, Leaney et al. (1999) have inverted multiazimuthal multioffset VSP P-wave data over a marine carbonate reservoir to determine azimuthal anisotropy in the carbonate and transverse isotropy in the overlying shale. Leslie and Lawton (1999) present a method for inverting refraction seismic data for the anisotropic parameters of steeply dipping strata. Tsvankin and Thomsen (1994) and Alkhalifah and Tsvankin (1995) deal with the problem of inverting for longer spreads, beyond the near-vertical elliptic-anisotropic approximation, in order to recover velocity fields for processing. * Authors listed in alphabetical order.
Implementation of Symmetric Nonstationary Phase-Shift Wavefield Extrapolator on an Alpha Cluster
Highly accurate seismic depth imaging (migration) is required by the oil/gas exploration industry in regions of complex geology. Fourier-domain depth-imaging techniques provide the needed accuracy although the cost of computation can be large when lateral velocity variation is rapid. Parallel computers provide an efficient solution to overcome the computational barrier of Fourier-domain imaging techniques. In this paper, a new Fourier-domain imaging technique, based on nonstationary filtering and wavefield extrapolation theories, is described. The amount of compuration required for an example 2D synthetic seismic data set is analyzed. The parallel version of the algorithm is implemented using C++ and Fortran 90 on an Alpha cluster workstation. The Message Passing Interface (MPI) library was used for data distribution and collection. The algorithm, found to be accurate but slow on serial machines, can achieve a speed acceptable for most industrial applications.
What is Enlightenment
Enlightenment is man's emergence from his self-imposed nonage. Nonage is the inability to use one's own understanding without another's guidance. This nonage is self-imposed if its cause lies not in lack of understanding but in indecision and lack of courage to use one's own mind without another's guidance. Dare to know! (Sapere aude.) "Have the courage to use your own understanding," is therefore the motto of the enlightenment.