Sensitivity Analysis of P-Wave Polarization Direction and Velocity Gradient Inversion

Abstract

Velocity gradient is an important parameter for interpreting tomographic velocity field and identifying geological boundaries. It is usually translated from the results of seismic travel-time tomography. Recent researches show seismic polarization direction appears to be a promising data source for obtaining velocity gradient field directly. However, what remains unclear is the sensitivity of polarization direction to velocity gradient, which causes difficulty for correctly inverting polarization direction data. To clarify this problem, the sensitivity of velocity gradient parameters on polarization direction is discussed in this paper. It was found that the sensitivity of polarization direction is related to the spatial position of the model parameter. The further the parameter position is from the sensor, the lower the sensitivity is. Such nonuniform distribution of sensitivity may cause distortion of inversion results with incomplete projection data. Based on this analysis, adjustment factors are introducing to the polarization direction inversion algorithm for correctly inverting polarization direction data. Numerical tests are conducted to verify our theoretical analysis and inversion algorithm. Test results show that our theoretical analysis is accurate in both homogeneous velocity field and near velocity interfaces. The inversion method with the adjustment factor can more accurately recover the velocity gradient, offering a promising approach for geological boundary imaging.

Keywords

• velocity gradient
• polarization direction
• sensitivity
• inversion