特征波反演成像理论框架

地震波反演成像的核心问题是将解一个非线性(较)强的反问题转化为提一个更凸的反问题并进行求解。存在强非线性性的主要原因是实测数据与要反演的模型参数之间的关系远非线性,其次是由于包含模型参数的控制方程不能很好地预测实际数据。因此,提出了特征波反演(characteristic wave inversion,CWI)成像的理论框架,基本思想是:不追求对实测波场全部波现象的模拟,而是模拟其中的部分特征波场;不一定追求波形逼近,但要尽可能利用到达时(相位)的逼近。相对于全波形反演(full waveform inversion,FWI),特征波反演由四个基本步骤组成:①特征波场(characteristic wave field,CWF)的提取;②波动理论的透射波层析成像;③波动理论的一次反射波层析成像;④最小二乘叠前深度偏移成像。特征波场提取是其中重要的环节,包含三重含义:①波现象的分解(譬如,矢量波分解成标量波以及一次波和多次波分解);②时空局部的、单震相的、带方向的带限波场的分解;③同相轴上地震子波的分解(譬如,提取子波的达到时、相位等)。特征波场提取基于压缩感知的框架进行,其它三个线性化的参数反演环节,首先考虑的是针对地下介质参数层状分布时的反射波反演成像,然后再考虑针对散射和绕射波的反演成像。数据域特征波反演在估计低波数速度信息时仅依赖同相轴上子波的到达时或/和相位信息,需尽量排除振幅对到达时和相位估计的影响。像域中的背景速度反演仅适宜基于到达时的反演,基于像的幅值的反演在理论上是不合理的。高波数参数估计时,首先进行方位角度反射系数的估计,在此基础上进行散射强度的估计。CWI技术系列是推进经典FWI走向实用化的正确途径,初步数值试验结果证明了上述判断。

The core of seismic wave inversion imaging is to translate solving a strong nonlinear inverse problem to a further convex inverse problem.The reason of strong nonlinearity in inverse problem lies in the far from linear relation between the real data and the model parameters and the forward problem cannot accurately predict the full wave field.Therefore,we put forward the theoretical framework of characteristic wave inversion (CWI).Its basic idea is not to seek predicting the whole wave phenomena in the real data,but to aspire for interpreting characteristic wave field.Comparing with the full waveform inversion (FWI),CWI is consisted of four basic steps:characteristic wave field (CWF) extracting;wave equation based transmitted wave tomography;wave equation based reflection wave tomography;least square prestack depth migration.CWI is an inversion-imaging framework based on the characteristic wave phenomena in the real data.CWF extraction is the key step,which has three levels meaning:decomposing of the wave phenomena (such as vector wave filed is decomposed into scalar wave field,primaries and multiples are decomposed);decomposing of the temporally and spatially local,single seismic phase,directional and bandlimited wave field from real data;decomposing of the wavelet on the events into the travletime,phase and something else.The compressive sensing method is used in CWF extraction.Wave equation based transmitted wave tomography is based on the first arrival and early arrival traveltime.The inversion imaging based on the disturbance wave field firstly deal with the reflection wave from the layered strata,and then the scattered wave and diffracted wave.The background velocity estimation in the data domain mainly depends on the traveltime and phase,and the effect of the amplitude of the wavelet on the traveltime and phase measuring is removed as possible.The traveltime or phase information can be only used in the background velocity estimation in the imaging domain;it is not suitable for using the amplitude information.For the parameter disturbance estimation,the azimuth/opening-angle reflectivity estimation should be firstly implemented,and then the scattering strength is estimated.Characteristic Wave Inversion Imaging is a realistic procedure to push the classical FWI into the practical application.The numerical experimentation proves the statements.

国家自然科学基金项目(41374117)和国家油气重大专项(2011ZX05005-005-008HZ,2011ZX05006-002,2011ZX05023)联合资助。