Migration/inversion: think image point coordinates, process in acquisition surface coordinates
Migration/inversion: think image point coordinates, process in acquisition surface coordinates
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DOI：
10.1088/0266-5611/21/5/013
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发表时间：
2005-09
期刊：
影响因子：
2.1
通讯作者：
N. Bleistein;Yu Zhang;Sheng Xu;Guanquan Zhang;S. Gray
中科院分区：
文献类型：
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作者：
N. Bleistein;Yu Zhang;Sheng Xu;Guanquan Zhang;S. Gray
我们陈述了地震偏移/反演过程的一般原则：考虑图像点坐标;在表面坐标中计算。该原理允许从源到反射器到接收器的能量的多个行进路径的自然分离。此外，Beylkin行列式（处理参数与采集表面坐标之间的变换的雅可比行列式）特别简单，与标准单到达基尔霍夫中的共偏移距Beylkin行列式形成鲜明对比。这种处理方法的一个特点是将克希霍夫算子的反褶积结构或波动方程偏移的反褶积成像算子转化为褶积算子，即用伴随绿色函数的乘法代替绿色函数的除法。从图像点坐标到表面坐标的这种变换也适用于最近开发的标准基尔霍夫反演方法的扩展。标准方法在积分过程中使用绿色函数，并且倾向于产生比替代方法（例如在反演公式中使用绿色函数的高斯光束表示的方法）更多的成像伪影。这些方法指向需要一个真正的振幅基尔霍夫技术，使用更一般的绿色的功能：高斯光束，真正的振幅单向绿色的功能，或从双向波动方程的绿色的功能。在这里，我们提出了一个推导的真振幅基尔霍夫，使用这些更一般的绿色的功能。当这种反演被重新转换为对所有源和接收器的积分时，公式出奇地简单。
We state a general principle for seismic migration/inversion processes: think image point coordinates; compute in surface coordinates. This principle allows the natural separation of multiple travel paths of energy from a source to a reflector to a receiver. Further, the Beylkin determinant (Jacobian of transformation between processing parameters and acquisition surface coordinates) is particularly simple in stark contrast to the common-offset Beylkin determinant in standard single arrival Kirchhoff . A feature of this type of processing is that it changes the deconvolution structure of Kirchhoff operators or the deconvolution imaging operator of wave equation migration into convolution operators; that is, division by Green's functions is replaced by multiplications by adjoint Green's functions. This transformation from image point coordinates to surface coordinates is also applied to a recently developed extension of the standard Kirchhoff inversion method. The standard method uses Green's functions in the integration process and tends to produce more imaging artefacts than alternatives, such as methods using Gaussian beam representations of Green's functions in the inversion formula. These methods point to the need for a true-amplitude Kirchhoff technique that uses more general Green's functions: Gaussian beams, true-amplitude one-way Green's functions, or Green's functions from the two-way wave equation. Here, we present a derivation of a true-amplitude Kirchhoff that uses these more general Green's functions. When this inversion is recast as an integral over all sources and receivers, the formula is surprisingly simple.