Multiple anisotropic parameter inversion for a tti earth model

Abstract

A method for determining values of anisotropic model parameters of a Tilted Transversely Isotropic (TTI) Earth model, the anisotropic parameters including P-wave velocity (Vp 0 ) along a tilted symmetry axis, the Thomsen anisotropy parameters δ and ε (or η=(ε−δ)/(1+2δ)) representative of variations of wave velocities as a function of wave propagation angle from the symmetry axis, the method including acquiring input data for a geological volume of interest; determining a theoretical relationship between the input data and the anisotropic model parameters; and calculating the values of the anisotropic model parameters at each of a plurality of subsurface locations in the geological volume of interest based on the theoretical relationships and the input data using workflows involving iterative or sequential combinations of processes including input data preprocessing, conventional tomographic inversion, three dimensional tomographic inversion based on a tilted transversely isotropic model, and three dimensional pre-stack depth migration using a tilted transversely isotropic model.

1 . A computer implemented method for determining values of anisotropic model parameters of a Tilted Transversely Isotropic (TTI) Earth model, the anisotropic parameters including P-wave velocity (Vp 0 ) along a tilted symmetry axis, the Thomsen anisotropy parameters δ and δ (or η=(ε−δ)/(1+2δ)) representative of variations of wave velocities as a function of wave propagation angle from the symmetry axis, the method comprising:
 acquiring input data for a geological volume of interest;   determining a theoretical relationship between the input data and the anisotropic model parameters; and   calculating the values of the anisotropic model parameters at each of a plurality of subsurface locations in the geological volume of interest based on the theoretical relationships and the input data using workflows involving iterative or sequential combinations of processes including input data preprocessing, conventional tomographic inversion, three dimensional tomographic inversion based on a tilted transversely isotropic model, and three dimensional pre-stack depth migration using a tilted transversely isotropic model, thereby providing an accurate model of geological features present in the geological volume of interest.   
     
     
         2 . The method of  claim 1 , wherein the iterative or sequential combinations of processes includes interpretive picking. 
     
     
         3 . The method of  claim 1 , wherein the tomographic inversion is recursive and iterative, and uses three dimensional tilted transversely isotropic ray tracing to model three dimensional wave propagation. 
     
     
         4 . The method of  claim 1 , wherein the input data include surface seismic data, vertical seismic profile data, checkshot data, VSP data, well log data, interpretational data, regional trend, a priori data, or any combination of the foregoing. 
     
     
         5 . The method of  claim 4 , wherein the interpretational data include picks of horizon positions and shapes. 
     
     
         6 . The method of  claim 1 , further comprising creating an initial TTI model using the input data, the initial TTI model being created by estimating subsurface reflector structural dips and obtaining TTI symmetry axes in the geological volume of interest. 
     
     
         7 . The method of  claim 1 , further comprising normalizing the input data prior to performing the inversion. 
     
     
         8 . The method of  claim 1 , wherein the input data includes seismic data, the method further comprising, prior to performing the three dimensional TTI tomographic inversion, migrating the seismic data using 3D TTI prestack depth migration algorithm, sorting the migrated seismic data according to their subsurface location and their migration offset/angle into common-image-point (CIP) gathers, and selecting and quantifying residual moveouts in the common-image-point gathers domain. 
     
     
         9 . The method of  claim 1 , wherein the values of the anisotropic model parameters at each of the plurality of subsurface locations are calculated using three dimensional TTI tomographic inversions, simultaneously, or separately in a sequential manner, using various combinations of inversions with full sets or subsets of the input data and full sets or subsets of output data. 
     
     
         10 . The method of  claim 9 , wherein the output data includes Vp 0 , δ and η and/or ε. 
     
     
         11 . The method of  claim 1  further comprising performing a TTI pre-stack depth migration process using a TTI model with Vp 0 , δ and η. 
     
     
         12 . The method of  claim 1 , wherein the calculation includes calculating values of the anisotropic parameters by iteratively selecting values of Vp 0 , δ and η until (a) seismic image positions of subsurface structures in the geological volume of interest tie their spatial positions recognized in drilled wells and (b) residual moveouts in common-imaging-point gathers are minimum at every point in the model. 
     
     
         13 . The method of  claim 12 , wherein the subsurface structures include rock boundaries. 
     
     
         14 . A computer implemented method for determining values of anisotropic model parameters of a three dimensional TTI earth model, the anisotropic parameters including P-wave velocity (Vp 0 ) along a tilted symmetry axis, the Thomsen anisotropy parameters δ, ε (or η=(ε−δ)/(1+2δ)) representative of variation of wave velocities as a function of wave propagation angle from the symmetry axis, the method comprising:
 a. obtaining an initial TTI earth model that substantially flattens common-imaging-point gathers and substantially ties seismic data to well data, the initial migration velocity model including initial values Vp 0 , δ, ε (or η) at each of a plurality of subsurface locations in a geological volume of interest;   b. inputting checkshot data, or VSP data, or both checkshot and VSP data at well locations into a three dimensional tomographic inversion to determine updated values of Vp 0  near the well locations, the values of Vp 0  being updated by a correction ΔVp 0 , wherein Vp 0 =Vp 0 +ΔVp 0 ;   c. determining an incremental improvement Δδ to δ(initial) using the relative change Δδ=(ΔVp 0 )/Vp 0 ;   d. extrapolating the relative change Δδ from near-well locations to the entire three dimensional TTI earth model at each of the plurality of subsurface locations, taking into account geological consistency and regularization, to determine updated values of δ, wherein δ=δ+Δδ;   e. determining updated values of Vp 0 =Vp 0 (1−Δδ) using the extrapolated three dimensional Δδ at each of the plurality of subsurface locations and obtaining the three dimensional extended incremental update ΔVp 0 =−Δδ Vp 0 ;   f. inputting near-to-mid-offset/angle residual moveout information in the common-imaging-point gathers obtained with an improved migration velocity model that is defined with the updated values of Vp 0  and δ into a TTI tomographic inversion process to further provide updated values of δ at each of the plurality of subsurface locations; and   g. inputting near-to-far-offset/angle residual moveout information in the common-imaging-point gathers obtained with the improved model the TTI tomographic inversion process to provide updated values of η at each of the plurality of subsurface locations.   
     
     
         15 . The method of  claim 14 , further comprising iteratively repeating (a), (b), (c), (d), (e), (f) and (g), wherein the improved parameters of the TTI model determined at the end of an iteration corresponds to the initial parameters of the TTI model at the next iteration. 
     
     
         16 . A computer product having machine executable instructions, the instructions being executable by a machine to perform a tomographic inversion method for determining values of anisotropic parameters of a TTI earth model, the anisotropic parameters including P-wave velocity (Vp 0 ) along a tilted symmetry axis, the Thomsen anisotropy parameters δ and ε (or η=(ε−δ)/(1+2δ)) representative of variation of wave velocities as a function of wave propagation angle from the symmetry axis, the method comprising:
 determining a relationship between input data and the anisotropic parameters, the input data being acquired for a geological volume of interest; and   calculating the values of the anisotropic parameters at each of a plurality of subsurface locations in the geological volume of interest based on the relationship and the input data using workflows involving iterative or sequential combinations of processes including input data preprocessing, three dimensional tomographic inversion, and three dimensional TTI pre-stack depth migration.