Anisotropy and mis-ties in seismic data: A modelling study

Abstract

We investigate the possibility that anisotropy may cause misties between borehole and surface seismic data owing to non-hyperbolic moveout. Our results are based on a simple 2-D model consisting of a homogeneous layer overlying a reflector at 3000 m. Three cases are studied, (i) the homogeneous layer is isotropic, (ii) it is elliptically anisotropic, and (iii) it has non-elliptical anisotropy, all with a vertical velocity of 3000 m/s resulting in a zero-offset TWT to the reflector of 2 s. For this model, travel times at the surface as a function of offset can be computed exactly and then convolved with a source wavelet to generate synthetic CDP gathers. Conventional velocity analysis is carried out on the CDPs, and the synthetics are then stacked using the velocity which gives the most coherent signal. For the isotropic case the synthetics stack exactly at a velocity of 3000 m/s, as expected, and no mis-tie exists. The same is true for the elliptical case, except that the optimum stacking velocity is the horizontal velocity of 3550 m/s and not the vertical velocity, in agreement with theory. For the non-elliptical case it is difficult to choose the optimum stacking velocity and mis-ties of up to 10 ms can easily appear on the stacked section depending upon the choice of velocity. The non-elliptical velocity function we chose is somewhat extreme, but still considered to be only weakly to moderately anisotropic. We demonstrate that velocity as a function of propagation angle generally deviates significantly from the elliptical assumption, using published data of other workers. Given these observations, we conclude that weak non-elliptical anisotropy may play a role in mis-ties on the order of a few ms up to 10 ms between borehole and surface seismic data.