No abstract

We present an automatic algorithm to implement nonhyperbolic velocity analysis in VTI media. The approach is based on the use of nonhyperbolic traveltime equations that are accurate at large offsets and in anisotropic media. This is combined with an efficient parameterization to allow appropriate search for the moveout parameters (zero-offset traveltime, moveout velocity, and effective anellipticity). The raw coherency curve obtained at each CMP gather is used to filter out noisy picks and detects automatically the reflected energy with the respective parameters which makes the procedure automatic avoiding thus the tedious task of interpreting velocity spectra and picking the moveout parameters. Dix-type inversion formulae are used to retrieve interval parameters from the picked values to be used for later processing.

To: "Automatic nonhyperbolic velocity analysis, " Brahim Abbad, Bjørn Ursin, and Didier Rappin, Geophysics, 74, no. 2, U1-U12.There was a misprint in equation (11) in the paper, a multiplication by 4 is required in the denominator of the fi rst term instead of 2 and another division by the number of traces N is needed for the second term (semblance coeffi cient).The correct equation becomes then (11) This makes the bootstrapped differential semblance (BDS) coeffi cient ranges between 0 and 1. We apologize for the error and wish to thank Andrew J. Carter, Statoil, for making us aware of this mistake.

We formulated two coherency measures, based on the bootstrapped differential semblance (BDS) estimator, that offered higher resolution in parameter tracking than did standard normalized differential semblance. Bootstrapping is a statistical resampling procedure used to infer estimates of standard errors and confidence intervals from data samples for which the statistical properties are unattainable via simple means, or when the probability density function is unkown or difficult to estimate. The first proposed estimator was based on a deterministic sorting of original offset traces by alternating near and far offsets to achieve maximized time shifts between adjacent traces. The near offsets were indexed with odd integers, while the even integers were used to index far offsets that were located at a constant index increment from the previous trace. The second was the product of several BDS terms, with the first term being the deterministic BDS defined above. The other terms were generated by random sorting of traces that alternated near and far offsets in an unpredictible manner. The proposed estimators could be applied in building velocity (and anellipticity) spectra for time-domain velocity analysis, depth-domain residual velocity update, or to any parameter-fitting algorithm involving discrete multichannel data. The gain in resolution provided by the suggested estimators over the differential semblance coefficient was illustrated on a number of synthetic and field data examples.