线性同相轴波场分离的高分辨率τ-p变换法

基于最小二乘τ-p变换和τ-p域模型稀疏分布的假设，本文给出高分辨率τ-p变换的推导及其模型空间域的离散采样公式，同时给出了保振幅线性同相轴波场分离的算法流程.在求解本文给出的高分辨率τ-p正变换时，由于待求解的矩阵不具备最小平方法所具有的Toeplitz结构，故采用Cholesky分解法进行计算.本文模拟了井间地震和阵列声波测井中的Stoneley上下行波的分离算法过程，高分辨率正反τ-p变换且滤波所得结果显示本文算法误差小和保振幅的特点.对于在τ-p域距离很近或时间域同相轴近于水平的线性波场，高分辨率算法的聚焦作用使得所分离波场畸变小，体现本文算法精度高的优点.理论模型试算表明本文给出的高分辨率τ-p变换线性波场分离算法具有稳定性、精度高和保振幅的特点.

High resolution τ-p transform in linear events wavefield separation

The formula derivation of high resolution τ-p transform was given in this paper based on the assumption of sparse distribution of model space in linear Radon domain, and also the high fidelity algorithm of the Linear events wavefield separation. Cholesky decomposition algorithm was adopted to solve the high resolution forward τ-p transform because the Toeplitz structure of the 2D matrix in least square method is destroyed. The wavefield separation of up and down-going wave separation is modeled in array sonic logging and the crosswell seismic data. The method presented in this paper has the advantage of small error or high fidelity for the forward τ-p transform. The focusing of high resolution make the wavefield’s distortion smaller when the two events is very closer to each other or when some events are horizontal in x-t domain which the traditional least square method cannot separate them efficiently. Stability, high accuracy and high fidelity of the high resolution τ-p transform were demonstrated by the synthetic linear wavefield examples in this paper.