重力全梯度张量的延拓

摘要

We proved that gravity gradient tensor is satisfied with Laplace equation and implement the continuation calculation of gravity gradient tensor based on Fourier transform. The results of three-dimensional fault model show that the calculation of upward continuation is theoretically rigorous and can be implemented. The calculation error is mainly due to the limited integration range, the higher the height of upward continuation the higher the error. The downward continuation of gravity gradient tensor is an ill-posed problem. Usually, there will be a serious oscillation phenomena, leading to helpful gradient tensor information drowned while the height of downward continuation is greater than three times dot spacing. We verified the practicality of the continuation of gravity gradient tensor by the real data of Heilongjiang province Hulin basin.%以傅里叶变换为基础,证明了重力全梯度张量满足拉普拉斯方程,进而实现了梯度张量的延拓计算.三维断层模型试验结果表明,基于傅里叶变换的梯度张量向上延拓计算在理论上是严密且可以实现的,计算误差主要是由有限的积分范围所致,延拓高度越高则误差越大.而梯度张量的向下延拓则属于不适定问题.一般情况下,当延拓高度大于三倍点距时即出现严重的振荡现象,导致有用梯度张量信息的淹没.结合黑龙江省虎林盆地的梯度张量,验证了梯度张量延拓的实用性.