introduction

The presence of anisotropy in the subsurface is now widely recognized, and the importance of handling it in the processing stage for improved imaging is gaining momentum. However, the feasibility of using inverted anisotropic parameters to understand the underlying lithology is yet to be evaluated. This paper tackles this important issue; specifically we will attempt to use inverted anisotropic parameters estimated using surface seismic data to discriminate between sands and shales.

Alkhalifah and Tsvankin (1995) demonstrated that, for transversely isotropic (TI) media with vertical symmetry axis (VTI media), just two parameters are sufficient for performing all time-related processing such as NMO correction (including non-hyperbolic moveout correction, if necessary), DMO correction, and prestack and poststack time migration. Taking V_h to be the P-wave velocity in the horizontal direction, one of these two parameters, $\eta$, is given by  

$$\eta \equiv 0.5 \left( \frac{V_h^2}{V_{{\rm nmo}}^2(0)}-1 \right)=\frac{\epsilon-\delta}{1+2 \delta} \, ,$$ (1)

and the other, the short-spread normal moveout (NMO) velocity for a horizontal reflector, is given by  

$$V_{{\rm nmo}}(0)=V_{P0} \sqrt{1+2 \delta} \, ,$$ (2)

where V_P0 is the P-wave vertical velocity, and $\epsilon$ and $\delta$ are Thomsen's (1986) dimensionless anisotropy parameters.

These two parameters can also be characterized directly in terms of the conventional elastic coefficients c_ij as follows

$$\eta = \frac{c_{11} (c_{33}-c_{44})}{2c_{13}(c_{13}+2c_{44})+2c_{33}c_{44}} - \frac{1}{2},$$

and

$$V_{{\rm nmo}}(0) = \sqrt{\frac{c_{13}(c_{13}+2c_{44})+c_{33}c_{44}}{ (c_{33} - c_{44})}}.$$

The fact that we cannot uniquely determine the elastic coefficients from $\eta$ and $V_{{\rm nmo}}(0)$ does not matter, because time-related processing depends on just $V_{{\rm nmo}}(0)$ and $\eta$.

Alkhalifah and Tsvankin (1995) further show that these two parameters, $\eta$ and $V_{{\rm nmo}}(0)$, can be obtained solely from surface seismic P-wave data, using estimates of stacking velocity for reflections from interfaces having two distinct dips. The inversion technique discussed by Alkhalifah and Tsvankin, however, is designed for a homogeneous medium above the reflector, while realistic subsurface models are, at a minimum, vertically inhomogeneous. Later, Alkhalifah (1997a) modified their inversion to handle vertically inhomogeneous media. Here, $\eta$, whose departure from zero indicates anisotropy, is the key parameter that we will use for the lithology discrimination.

Using data from offshore Africa, Alkhalifah (1997a) showed that anisotropic processing yields improved images over that obtained from isotropic processing. Reflections from dipping faults that were attenuated in the isotropically-processed data appeared in the anisotropic one. Reflections from horizontal events also benefitted from the non-hyperbolic correction imbedded in the anisotropic processing.

Here, we show that the importance of anisotropy processing is not confined to data from offshore Africa. Imnage of data from offshore Trinidad can also be improved with processing that takes the anisotropy of the subsurface into account. Unlike the shale-dominated subsurface in offshore Angola, the subsurface in Trinidad is made up of alternating sequences of sand and shale. However, significant improvement in imaging using anisotropic processing is demonstrated in Trinidad. In addition, the inversion of the anisotropic data makes it possible to evaluate the feasibility of distinguishing between shale-dominated layers and sand-dominated layers, due to the physical property that shales have inherent anisotropy while sands do not.