Constrained Anisotropy Estimation For PSDM Velocity Model Building And Refinement
Authors: Ferla Maurizio , Cibin Patrizia , Gentile Erika , Battistutti Emanuela , Johan Leutscher 
Published: March 2015

Abstract
In this study a new stable and geologically plausible anisotropic inversion methodology is proposed for building and refining the velocity model for pre-stack depth migration workflow (PSDM). We describe an unconventional constrained inversion technique for the evaluation of the interval Thomsen anisotropic parameters e and d.
The main feature of this algorithm is the prevention of non-realistic and highly oscillating values which can be often obtained applying conventional unconstrained Dix transform methods, for small variations of the stacking or effective values. The new proposed approach is especially designed for robust anisotropy estimation, in terms of the anellipticity parameter ?, which is fundamental for the vertical and lateral accurate positioning of seismic events, calibrated to the sonic well logs. The estimation of the anisotropic interval parameters is based on a combination of credible, internal, analytical trend function and a least-squares fit, matching the input RMS values.
The constrained inversion is a minimization problem: this approach reconstructs the interval values from the effective ones in a least-squares sense, generating instantaneous velocity and interval ?int, with geological sense and honoring the stacking estimates. An explicit Dix solution inverts the vertical functions without control on the results, whereas least-squares find a global solution. The PSDM iterations show evident advantages for the proper anisotropy introduction. The benefits and the improvements respect to the standard methodologies are visible on the showed real dataset application in terms of a better focusing, correct positioning and enhanced imaging, increasing the quality and consistency of the results. The work has been completed evaluating the improvements gained by taking anisotropy into account, comparing the results with the isotropic scenario and with the standard methodologies.

Introduction
The proposed study in this paper describes an unconventional methodology to convert the effective anisotropic values Vnmoeff and ?eff into interval ones. The instantaneous values, velocity (Vnmoint) and ?int, are then used to estimate the two Thomsen's dimensionless anisotropic parameters e and d and considered as input for building and refining the velocity model for anisotropic pre-stack depth migration (PSDM). The standard approaches estimate the interval anisotropic parameters from picked stacking values. The stacking velocities (Vnmoeff) and the fourth order ?eff are assumed to be explained by a root-mean-squares (RMS) averaging of the interval parameters. A conventional method uses an explicit solution for the inversion of the RMS integral.
However, this approach could easily produce wildly unrealistic values from small variations in the stack vertical profile, in presence of irregular picking, multiples and noisy seismic data.
The derived constrained inversion estimates non-oscillatory and geologically plausible instantaneous parameters from conventional stacking values using a combination of credible, internal, analytical trend function and a least-squares fit. The inversion results match the transformed input RMS parameters in a least-squares sense