AVAz inversion using adaptive shaping regularization
The existence of high-angle fractures leads to azimuthal anisotropy of the underground rock.The variation of the reflection coefficient with azimuth in transversely isotropic media with a horizontal symmetry axis can be approximately expressed in the form of the Fourier series.The Fourier coefficients depend on the background medium and crack parameters,and the phases of the Fourier coefficients depend on the fracture symmetry axis directions.In the conventional Fourier analysis,the Fourier coefficients are calculated by summing the azimuthal seismic data at each time sample or depth sample,which can be easily influenced by random noise.In order to improve the robustness and stability of Fourier coefficient estimation,an AVAz(Amplitude Variation with Azimuth)inversion method based on shaping regularization is proposed,following the conventional Fourier analysis.The conventional shaping operator is invariant with time or depth,we propose an adaptive shaping operator based on the azimuthal anisotropic intensity.The damping factor is calculated using the second-order Fourier coefficients from conventional Fourier analysis.The adaptive shaping operator is constructed by combining the first-order difference matrix and the damping factor,to achieve the purpose of adjusting the shape of the shaping operator automatically.Theoretical tests show that the proposed AVAz inversion method with adaptive shaping regularization can effectively improve the stability of the second-order Fourier coefficient prediction.The field case demonstrates the effectiveness of the AVAz inversion with adaptive shaping regularization in fracture prediction,and the fracture prediction results are consistent with the logging data.
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