Fourier-Domain Modeling Of Gravity Effects Caused By A Vertical Polyhedral Prism, With Application To A Water Reservoir Storage Process

We have developed a new Fourier-domain algorithm for the modeling of gravity effects caused by a vertical polyhedral prism. Simplified and more compact Fourier-domain expressions are derived for the vertical gravity anomaly on a 2D plane either above, in the middle of, or below the vertical polyhedral prism. A new Fourier-domain algorithm, which combines a low order Gauss fast Fourier transform (FFT) algorithm and a low order nonuniform FFT algorithm, to permit polar sampling near the zero wave vector, is introduced. To validate the numerical efficiency of the new algorithm, we carry out a series of synthetic tests. Numerical results show that the new algorithm is superior in numerical accuracy and efficiency compared to a pure Gauss-FFT algorithm, and both Fourier methods run much faster than traditional space-domain analytical solutions. We then apply the Fourier forward algorithms to the prediction of vertical component of gravity at many survey points, as a function of the water level of a reservoir located in Xianlin, Hangzhou, China. The reservoir geometry is approximated by a single vertical polyhedral prism. Water storage corresponds to increased heights of the polyhedral prism. Detailed maps of vertical gravity value changes corresponding to a water level rise of 5 and 10 m, with spatial resolution 1 x 1 m, on the local topography covering a study area of approximately 2.6 x 2.2 km around the water reservoir, are calculated using the new algorithm. Then, the gravity values are classified according to the accuracy of the gravimeter, providing a reference of optimal site selection for a proposed cold-atom gravimetry survey to be carried out in the near future.