The inversion of shear wave anisotropy with cross- dipole logs has played an increasingly important role in the booming development of shale gas plays.It has been widely employed for the detection of aligned natural fractures around the borehole,the evaluation of the engineering efficiency of hydraulic fracturing and the estimation of in-situ stress distribution.In the last decade,the waveform inversion methods employing a fast simulated annealing algorithm to solve the derived non-linear optimal objective function have been developed and widely applied,based on the waveform similarity of the split fast and slow shear waves.Although these methods overcome the ambiguity in determining the fast shear wave azimuth,they have to make erroneous judgments of fast and slow shear wave azimuth in weak anisotropy formations.In addition, we have found that due to the influence of logging tool eccentricity,source frequency,well borehole conditions and the formation properties,the raw cross-dipole data gathered from the field are often mixed with leaky P wave and other noises that may severely degrade the reliability of the anisotropy inversion. In this paper,we introduce an algorithm that has made several improvements to the solution of above problems.This algorithm employs a self-adaptive and shift invariant multi-scale analysis tool,dual-tree complex wavelet transform to decompose the original signal into multiple time-frequency domains that extracts the flexural wave and depress the leaky P wave,as well as noises that could not be wiped off the band-pass filter.Subsequently,a modified very fast simulated annealing method with variable metric search and independent initial temperature is applied to find the solution more efficiently and to enhance the stability of the anisotropy inversion. Applications of the algorithm to a set of synthetic cross dipole data by 3D finite difference modeling and to the field data obtained from a Chinese oil field are presented in this paper to demonstrate the validity of our method.These results have revealed that the modified very fast simulated annealing algorithm combined with wavelet de-noising could yield a more stable anisotropy azimuth with less erroneous judgments in weak anisotropy formations and a higher efficiency and stability than conventional inversion methods.
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