November 1998 | Volume 23 Issue 09 | View Issue
Velocity panels are picked routinely in the geophysical industry and, not that infrequently, non-hyperbolic moveout is observed, even on flat plains data. Events which are over-corrected at large offsets are commonly ignored, for example, by far-offset muting. These far-offset events frequently contain useful signal energy and could potentially contribute to a better stack, if only they could be corrected properly, and the mute opened up. Signal enhancement should be expected, not only from the increase in fold, but also because of a more refined velocity analysis, better multiple attenuation, and better statistics for solving statics.
In this study a specific real example of non-hyperbolic moveout observed with flat reflectors is investigated (Fig. 1A). First an overview of some underlying theory is given. This is followed by a description of the velocity analysis used, and finally real data results are shown.
Observation and Elimination
The first response on observing non-hyperbolic moveout was to suspect a breakdown of the Dix-approximation at far offsets. However, ray traced NMO correction (Harrison, 1989) based on original stacking velocities accounted for less than a quarter of the observed departure from true hyperbolic moveout. Mark Harrison successfully applied ray traced NMO correction to non-hyperbolic moveout caused by a strong velocity inversion. Even after his best effort there remained overcorrected events above the velocity inversion in his data set.
Next, for the data shown in Fig.1A, lateral velocity variation, topography, structure and irregular geometry were considered and ruled out. What, then, could cause the observed non-hyperbolic moveout? Two more possible mechanisms come to mind: firstly a vertical velocity gradient [V(z)], or secondly anisotropy, could be causes. The MO correction procedure leading to Fig. 1A assumes blocky interval velocities and will break down if velocity gradients are too strong. A nearby well-log (within 3 km, Fig. 1B) indeed shows a negative velocity grad ien t in the formation immediately above the Second-White-Specks reflector [2WS] which exhibits non-hyperbolic moveout. Ray traced NMO correction, this time incorporating a V(z) velocity model based on the well-log information, does not account for more than about a quarter of the departure from hyperbolic moveout. Fig. 2 shows a residual moveout comparison for travel times picked from the common offset gather in Fig. 1C and moveout corrected firstly with the Dix velocity equation, secondly, by ray tracing and thirdly, by a V(z) plus ray tracing combination. Thus far residual moveout seems indestructible!
VTI-Type Anisotropy
Anisotropy is investigated next, the simp lifying assumption of vertical anisotropy is made (VTI-med ium, transverse isotropy with vertical symmetry axis). Fig. 3 shows 3D common offset gathers from the same area. Plotted are four different azimuth ranges as indicated by the sector diagrams, sectors contributing traces to a limited azimuth range are shown in black. In this area at least, VTI type anisotropy seems predominant. A procedure presented by Vladimir Crechka and Ilya Tsvankin at the 1997 SEC meeting is utilized in order to estimate the parameters of anisotropy:
EQUATION 01
where Vnmo is the familiar vertical moveout velocity,
and Vhrz is a horizontal velocity parameter.
For Vhrz = Vnmo, the last term vanishes and equation (1) is reduced to the Dix approximation, no anisotropy exists. Equation (1) applies to the single layer model.
Crechka and Tsvankin d erive equations for the layered media case tha t can be employed to compu te horizontal and vertical interval velocities. If the only objective is to flatten non-hyperbolic moveout curves, equation (1) is sufficient. The horizontal velocity Vhrz makes little difference at small offsets, but its influence increases with offset to the point where it appears to dominate Vnmo. With equation (1), Vhrz and Vnmo are obtained by least square error fitting of moveout curves picked from the data in Fig. 1C. The residual moveout comparisons in Fig. 2 (all for the layer 7 – layer 8 boundary, which is the 2WS reflector, for layer numbering see Fig. 5) show that there is little, if any, residual moveout under the anisotropy assumption. The reciprocal-square-error of the moveout- curve-fit is d isplayed in Fig. 4. Vertical moveout velocity Vnmo increases to the left and horizontal velocity Vhrz increases downward in this trace-like display, the two-dimensional maximum designates the least square error point.