Inversion of gravity data in wavelet domain using normalized forward models



Due to the remarkable advantages of wavelet transformation, this technique is now very common in gravity analysis. In this research the Green’s function occurring in the Poisson potential field theory is used to construct non-orthogonal, non-compact, continuous wavelets. This kind of wavelet is directly corresponded to upward continuation procedure. Simple geometrical forward models such as Sphere, Vertical and Horizontal Cylinder, Thin sheet and Vertical sheet are applied as forward models. First, analytical wavelet transform of the models is calculated, and then the amplitude and the location of the maximum of the product is applied as a new mathematical model (forward model).
The new models have a mathematical relation with the source parameters such as depth and shape of anomaly. However, because of being normal the forward models do not have any relation with the physical parameter of density contrast.
In order to examine the accuracy, precision, behavior and application of the offered method, the synthetic data for both noisy and noise-free data, has been applied. Subsequently, considering the applicability and expansion of the method for applied goals, some suitable real datasets have been used. For the purpose of gathering data and testing the algorithm, two sources of data were accessible: Institute of Geophysics University of Tehran and the National Iranian Oil Company. Formal permission was granted by both institutions. The outcome of this process was compared with the result of other established classical methods. The parameter of depth estimated by both methods is very close (about 400m difference for the depth of about 3.5km).
After careful assessment, it became evident that results obtained from these comparisons are beneficial and useful. Real data are separated into regional and local signals using discrete wavelet analysis. The maximum points of wavelet transforms (worn diagrams) are also applied to interpret the depth of the anomaly compared to adjacent anomalies.
The result obtained by inverting the data using the parameter of amplitude has less standard deviation compared to the location of the MSE, and is believed to be more accurate. It is observed that adding noise causes higher standard deviation; however after adding 20 percent noise in synthetic data, less than 6% error occurred in the parameter of depth (still yields good results) which shows remarkable stability against noise.