Theory of interval traveltime parameter estimation in layered anisotropic media

Comparison of interval parameter estimation

Next, we test the accuracy of the proposed interval parameter estimation formulas (equations 30 and 34) in Model 2 (Table 2) representing a stack of aligned orthorhombic layers. The exact reflection traveltime computed by ray tracing is shown in Figure 3a and its nonhyperbolic part (Figure 3b) is the difference between the exact value subtracted by the hyperbolic part controlled by NMO velocities. The inverted interval parameters from known effective parameters are shown in Table 3 and match the true results with the accuracy of floating-point precision.

Sample	$2 t_{0}$	$a_{11}$	$a_{22}$	$a_{1111}$	$a_{1122}$	$a_{2222}$
	0.2052	0.1993	0.1446	-0.6983	-0.4917	-0.2249
		0.2052	0.1993	0.1446	-0.6983	-0.4917
	0.3	0.1389	0.1010	-0.1276	-0.1788	-0.042
		0.5052	0.1584	0.1151	-0.0646	-0.0774
	0.2010	0.1713	0.1254	-0.7136	-0.0392	-0.2779
		0.7062	0.1619	0.1179	-0.0389	-0.0318

Table 3. Inverted interval parameters (red and bold) for Model 2 given the exact effectve parameters (black) at the bottom of all layers based on equations 30 and 34. The resultant parameters are close to the true result within floating-point precision.

Theory of interval traveltime parameter estimation in layered anisotropic media