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.
An in situ estimation of anisotropic elastic moduli for a submarine shale
Direct arrival times and slownesses from wide-aperture walkaway vertical seismic profile data acquired in a layered anisotropic medium can be processed to give a direct estimate of the phase slowness surface associated with the medium at the depth of the receivers. This slowness surface can, in turn, be fit by an estimated transversely isotropic medium with a vertical symmetry axis (a "TIV" medium). While the method requires that the medium between the receivers and the surface be horizontally stratified, no further measurement or knowledge of that medium is required. When applied to data acquired in a compacting shale sequence (here termed the "Petronas shale") encountered by a well in the South China Sea, the method yields an estimated TIV medium that fits the data extremely well over 180 o of propagation angles sampled by 201 source positions. The medium is strongly anisotropic. The anisotropy is significantly anelliptic and implies that the quasi-shear mode should be triplicated for off-axis propagation. Estimated density-normalized moduli (in units of km2/s 2) for the Petronas shale are All = 6.99 -+ 0.21, A33 = 5.53 _ 0.17, A55 = 0.91 _+ 0.05, and A13 - 2.64 _+ 0.26. Densities in the logged zone just below the survey lie in the range between 2200 and 2400 kg/m 3 with an average value close to 2300 kg/m3.
AVO Analysis Using the VSP
A multioffset VSP geometry and 3-component processing flow have been developed to obtain true reflection coefficients from 3-component VSP data with the purpose of using the reflection coefficients for AVO analysis. The geometry and processing flow have been tested on synthetic data and found to recover the true reflection coefficients for a range of incidence angles. A muhioffset field VSP survey was acquired for the analysis of the AVO response of a gas-bearing carbonate. 3component processing of the data resulted in a good correlation between real and modeled P-P and P-S reflection coefficients. Single interface AVO analysis was found to be inadequate in describing the AVO behavior of the reflections from the top and the base of the gas-bearing carbonate zone, and full multilayer modeling was found to match the real data well.