Pre-stack basis pursuit seismic inversion for brittleness of shale

Brittleness of rock plays a significant role in exploration and development of shale gas reservoirs. Young＇s modulus and Poisson＇s ratio are the key param- eters for evaluating the rock brittleness in shale gas exploration because their combination relationship can quantitatively characterize the rock brittleness. The high- value anomaly of Young＇s modulus and the low-value anomaly of Poisson＇s ratio represent high brittleness of shale. The technique of pre-stack amplitude variation with angle inversion allows geoscientists to estimate Young＇s modulus and Poisson＇s ratio from seismic data. A model constrained basis pursuit inversion method is proposed for stably estimating Young＇s modulus and Poisson＇s ratio. Test results of synthetic gather data show that Young＇s modulus and Poisson＇s ratio can be estimated reasonably. With the novel method, the inverted Young＇s modulus and Poisson＇s ratio of real field data focus the layer boundaries better, which is helpful for us to evaluate the brittleness of shale gas reservoirs. The results of brittleness evaluation show a good agreement with the results of well interpretation.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

Simultaneous measurement of vibration amplitude and rotation angle based on a single-channel laser self-mixing interferometer

Based on a single-channel laser self-mixing interferometcr, we present a new silnultaneous measurement of the vibration amplitude and tile rotation angle of objects that both affect the power spectrum containing two peaks of the interferometer signals. The fitted results indicate that the curve of the peak frequency versus the vibration amplitude follows a linear distribution, and the curve of the difference of the two-peak power values versus the angle follows a Gaussian distribution. A vibration amplitude with an error less than 3.0% and a rotation angle with an error less than 11.7% are calculated from the fitted results.