正则化形式的稳定粘声逆时偏移成像方法

Stable and regularized visco-acoustic reverse time migration

在粘声介质逆时偏移成像方法中,只要改变振幅衰减项的符号就可以从理论上进行衰减补偿,但是由于振幅补偿时间算子的补偿比例随着波数增加而呈自然指数级增长,因而使得高频成分伴随高频噪声被过度补偿,影响了最终成像结果的精度。基于预测校正策略,提出了一种正则化形式的稳定传播的粘声逆时偏移成像方法,推导出了一阶形式的稳定粘声补偿波动方程,用于震源波场与检波点波场的补偿延拓,该方程同时考虑了因地层吸收而导致的振幅衰减与相位频散的特性。分别利用水平层状模型以及局部Marmousi模型进行了方法测试,结果表明,提出的方法不仅可以有效补偿因地层吸收而衰减的能量,对成像结果的频带特征也有良好的展宽与恢复。相对于不考虑粘性特征的逆时偏移结果,该方法的成像结果中深层构造的刻画更加清晰;与采用仅考虑振幅衰减补偿方程的成像结果相比,该方法的成像结果中同相轴的位置更加准确,其深层构造的分辨率与可信度也有了进一步提升。

For visco-acoustic reverse time migration,a compensation for the attenuation can be performed theoretically by changing the sign of the amplitude attenuation term.However,as the proportion of time operator of the amplitude compensation increases exponentially with the increase of the wave number,the high-frequency component will be overcompensated along with the high-frequency noise,causing an instability in the propagation of wavefields,thereby affecting the final(compensated)imaging result.Based on a predictor–corrector strategy,a regularized reverse time migration imaging method with stable propagation was proposed,and a first-order stable compensation wave equation was derived,which may be used for extrapolating both source and receiver wavefields.The equation takes into account the characteristics of the amplitude attenuation and phase dispersion caused by the absorption of the underground medium.A horizontal layer model and a local Marmousi model were tested.The results showed that the proposed method can not only effectively compensate for the energy attenuation caused by underground adsorption but is also capable of broadening and recovering the frequency band characteristics of the imaging results.Compared with the results obtained by reverse time migration without considering the viscous characteristics,the proposed method provided a clearer image of the deep underground structure.Compared with the results obtained through the compensation equation considering only the amplitude attenuation,the position of the structure was identified more accurately,demonstrating that the proposed method can further improve the resolution and reliability of underground imaging.