We present an explicit inverse approach using a Hessian matrix for least-squares migration (LSM) with Q compensation. The scheme is developed by incorporating an effective Q-based solution of the viscoacoustic wave equation into a blockwise approximation to the Hessian in LSM, which is implemented after the so-called deabsorption prestack time migration (PSTM). The effective Q model used fully accounts for frequency-dependent traveltime and amplitude at the same imaging location. We can extract the effective Q parameters by scanning during previous deabsorption PSTM. This avoids the challenging task of building the Q model. The blockwise Hessian matrix approach decomposes the full Hessian matrix into a series of computationally tractable small-sized matrices using a localised approach. We derive the explicit formula of the offset-dependent Hessian matrix using an analytical Green's function obtained from deabsorption PSTM. In this way, we can approximate a reflectivity imaging for the targeted zone by a spatial deconvolution of the migrated result with an explicit inverse. The resulting scheme broadens the frequency-band of imaging by deabsorption, and improves the subsurface illumination and spatial resolution through the inverse Hessian. A high-resolution, true-amplitude migrated gather can then be obtained. Synthetic and field data sets demonstrate the proposed blockwise LS-QPSTM.

中文翻译：

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块状Hessian矩阵的粘声最小二乘迁移：一种有效的Q方法

我们提出了一种使用Hessian矩阵进行Q补偿的最小二乘迁移（LSM）的显式逆方法。该方案是通过将粘声波方程的基于Q的有效解合并到LSM中Hessian的逐块近似中来开发的，该近似是在所谓的脱吸收叠前时间偏移（PSTM）之后实施的。使用的有效Q模型完全说明了在同一成像位置上与频率有关的行进时间和幅度。我们可以通过在先前的解吸PSTM中进行扫描来提取有效的Q参数。这避免了构建Q模型的艰巨任务。逐块Hessian矩阵方法使用局部化方法将完整的Hessian矩阵分解为一系列可计算处理的小型矩阵。我们使用从解吸PSTM获得的解析格林函数推导了依赖于偏移量的Hessian矩阵的显式公式。通过这种方式，我们可以通过对反演结果进行空间反褶积来近似估计目标区域的反射率成像。所得方案通过反吸收拓宽了成像的频带，并通过逆黑森州改善了地下照明和空间分辨率。然后可以获得高分辨率，真振幅偏移的道集。综合和现场数据集证明了拟议的块状LS-QPSTM。所得方案通过反吸收拓宽了成像的频带，并通过逆黑森州改善了地下照明和空间分辨率。然后可以获得高分辨率，真振幅偏移的道集。综合和现场数据集证明了拟议的块状LS-QPSTM。所得方案通过反吸收拓宽了成像的频带，并通过逆黑森州改善了地下照明和空间分辨率。然后可以获得高分辨率，真振幅偏移的道集。综合和现场数据集证明了拟议的块状LS-QPSTM。