本研究是將疊前三維三分量彈性波中的反射P波與S波分離的技術，由平坦地形擴展至複雜地形，做為應用於實測資料的準備。針對地形起伏大到難以用靜態修正來處理的變化，採取對高低起伏地形不做靜態修正，而直接以散量與旋量的計算，完全的分離出P波與S波，是本研究的目的與特色。假設地球介質是均向性的，在複雜地形地表接收的疊前三維三分量彈性波，準備一個模擬地形且垂直方向有速度變化的三維彈性計算模型。波動傳播是以有限差分法模擬彈性波動方程式計算的。在每一個有限差分計算格點，供給P波速度及S波速度。
本研究是以位移向量有限差分法，假設正方形格點，將三維三分量彈性波資料，由接收位置向下傳播至計算模型中，在傳播過程中，在地表以下某一深度，沿著平行於地表的一個面（稱為分解面），計算散量（純量）和旋量（三分量的向量），並留下記錄，得到分離的P波與S波。
接著進行的逆時移位，是直接將分離的P波與S波以反時間序列傳播至介質，並在反射點成像的移位法。將彈性波計算模型分割成一個P波速度計算模型和一個S波速度計算模型，將散量（只含P波）以純量波動方程式、P波速度計算，向下傳播至P波速度計算模型中，並依據成像時間記錄該位置的P波振幅，得到複雜地形的P波逆時移位地層影像；將散量的x、y和z分量，以純量波動方程式、S波速度計算，分別由分解面向下傳播至S波速度計算模型中，並依據成像時間記錄該位置的S波振幅，得到複雜地形的S波逆時移位地層影像。

We expand the algorithm that separates the P- and S-waves in three-dimension (3-D), three-component (3-C) elastic seismic data into topographic area, as part the study toward applying the algorithm on real data. Assume that the earth medium is isotropic. For a 3-D, 3-C elastic seismic data, we prepare a three-dimensional vertically homogeneous elastic computational model that simulate the medium with topographic surface. Finite difference simulation of the elastic wave equation is used to calculate wave propagation. Each finite difference grid point is provided with a P-velocity and an S-velocity.
Finite-difference simulating displacement elastic wave equation are used to compute wave propagations, uses squared finite-difference grid. The 3-D, 3-C elastic data is downward extrapolated from the receiver locations into the elastic computational model using elastic wave equation. During downward extrapolation, divergence (a scalar) and curl (a three-component vector) of the displacement are computed and recorded on a decomposition surface that is concurrent to the earth’s surface and is a few grid increments below.
And then go on to proceed Reverse-Time Migration, The elastic computation model is then split into one P-velocity computational model and an S-velocity computational model. The divergence (contains P-waves only) is downward extrapolated into the P-velocity computational model using the scalar wave equation, and according to the time of formation of image, note down the amplitude of P wave. The x-, x- and z-components of the curl (contains S-waves only) are downward extrapolated into the S-velocity computational model using the scalar wave equation, and according to the time of formation of
image, note down the amplitude of S wave.

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