地层构造约束的稳定最小平方成像条件研究(英文)

A stabilized least-squares imaging condition with structure constraints

传统的炮集偏移采用Claerbout提出的互相关型成像条件,然而互相关型成像条件不能保持反射振幅。反褶积型成像条件可以改善成像振幅和照明补偿,但存在不稳定问题。最小平方成像条件计算所有炮集上、下行波场的互相关,求和后再与下行波场的照明总能量相除,因此比传统的成像条件稳定,然而在照明很弱且照明不均衡的区域,其成像效果不理想。针对成像条件稳定性和照明均衡问题,在最小平方成像条件的基础上,本文提出了一种地层构造约束的稳定最小平方成像条件。在反问题正则化理论框架下,采用平面波重建算子约束的偏移成像结果沿构造同相轴方向光滑,提高了成像条件计算的稳定行,均衡了成像振幅。水平层状模型和Sigsbee2A模型的算例均表明了本方法的有效性,与阻尼最小平方成像条件相比,构造约束的稳定最小平方成像条件提高了偏移成像的稳定性和成像振幅的均衡性,成像结果同相轴更加连续,改善了照明不足和照明不均衡,压制了假象和噪声,有利于深层构造的保幅成像。

Conventional shot-gather migration uses a cross-correlation imaging condition proposed by Clarebout （1971）, which cannot preserve imaging amplitudes. The deconvolution imaging condition can improve the imaging amplitude and compensate for illumination. However, the deconvolution imaging condition introduces instability issues. The least-squares imaging condition first computes the sum of the cross-correlation of the forward and backward wavefields over all frequencies and sources, and then divides the result by the total energy of the forward wavefield. Therefore, the least-squares imaging condition is more stable than the classic imaging condition. However, the least-squares imaging condition cannot provide accurate results in areas where the illumination is very poor and unbalanced. To stabilize the least-squares imaging condition and balance the imaging amplitude, we propose a novel imaging condition with structure constraints that is based on the least-squares imaging condition. Our novel imaging condition uses a plane wave construction that constrains the imaging result to be smooth along geological structure boundaries in the inversion frame. The proposed imaging condition improves the stability of the imaging condition and balances the imaging amplitude. The proposed condition is applied to two examples, the horizontal layered model and the Sigsbee 2A model. These tests show that, in comparison to the damped least-squares imaging condition, the stabilized least-squares imaging condition with structure constraints improves illumination stability and balance, makes events more consecutive, adjusts the amplitude of the depth layers where the illumination is poor and unbalanced, suppresses imaging artifacts, and is conducive to amplitude preserving imaging of deep layers.