沉积盆地横向变密度模式重力异常快速正演方法及其在反演中的应用

Effi cient modeling of the gravity anomaly caused by a sedimentary basin with lateral variable density contrast and its application in basement relief estimation

提高反演的效率是沉积盆地基底重力反演面临的一个重要问题,其中重力异常正演计算的耗时是不可忽视的一个方面。本文提出了一种快速计算盆地基底重力异常的混合计算方案,在以任一计算点为中心的区域R内采用垂直棱柱体公式计算重力异常,而在区域外采用垂直线元公式计算,从而得到整个沉积盆地基底起伏变化在该计算点所引起的重力异常,在提高计算效率的同时避免了由于垂直线元公式在观测点附近精度低而带来的误差。通过棱柱体模型试验,给出了选定区域R大小的一般原则,并利用洛杉矶盆地的重力异常试验验证了该原则的正确性。本文在沉积盆地基底反演的迭代公式中增加了加速收敛因子以加快反演过程,并假设盆地沉积层与基底的密度差沿横向变化以更符合实际情况。通过模型试验和渭河盆地实际资料处理,证明该方法能够准确、有效地用于沉积盆地基底深度反演。

The forward calculation of gravity anomalies is a non-negligible aspect contributing to the time consumption of the entire process of basement relief estimation.In this study,we develop a fast hybrid computing scheme to compute the gravity anomaly of a basement.We use the vertical prism source equation in a given region R centered at a certain gravity observation point and the vertical line source equation outside R to derive the gravity anomaly.We observe that the computation with the vertical line source equation is much faster than that of the vertical prism source equation,but the former is slightly inaccurate.Therefore,our method is highly effi cient and able to avoid the errors caused by the low accuracy of the vertical line source equation near the observation point.We then derive the general principle of choosing the size of R via a series of prism model tests.Our tests on the gravity anomaly over the Los Angeles Basin confirm the correctness of our proposed forward strategy.We modify Bott’s method with an accelerating factor to expedite the inversion procedure and presume that the density contrast between the sediments and the basement in a sedimentary basin varies laterally and can be obtained using the equivalent equation.Synthetic data and real data applications in the Weihe Basin illustrate that our proposed method can accurately and effi ciently estimate the basement relief of sedimentary basins.