The use of two-dimensional discrete wavelet transform in theboundary estimation of gravity sources

Wavelet transform is one of the new methods in potential data interpretation. This transform can be applied in both continuous and discrete forms. As the gravity data are discrete, the wavelet discrete transform is used to interpret the data. Moreover, this transform can be used in two- and three3-dimensional forms depending on the nature of the anomalies. The two-dimensional transform is applicable when the length of the anomaly is approximately more than 10 times its width.
For this kind of anomaly, the discrete transform can be used along the profile perpendicular to the strike of the linear anomalies. These perpendicular profiles can also be used for three-dimensional interpretation of the anomalies. The variety of the methods in wavelet transform provide widespread potential for estimating the unknown parameters in gravity interpretation, such as depth and shape. The results can also be tested with several routine algorithms. On the other hand, the toolboxes prepared in Matlab can facilitate the process. The two-dimensional discrete wavelet transform has different uses in analyzing and processing potential fields. This paper describes attempts to use this method in estimating boundaries of gravity potential fields and the attenuating effect of noise in gravity data. According to the theory of the method, the detail coefficient values of the wavelet transform correspond to the maximum or minimum boundaries of the source; consequently, horizontal boundaries (long direction), vertical boundaries (width direction), and corners of the sources are estimated by calculating and reconstructing the horizontal, vertical, and diagonal detail coefficients. To study the resolution of the method, it was applied on both synthetic and real data and the results were compared with those of the Enhanced Horizontal Derivative (EHD) method. Calculations show that the resolution of the method is more accurate than that of the EHD method. Moreover, data analysis at special levels makes it possible to mute high frequency properties of the signal (caused by the effects of existing noise in the data). Hence, corresponding to the amplitude of noise, the noisy synthetic data (%1 ratio of random noise) and real data were analyzed in the second and third levels, respectively. The following observations can be considered as the advantages of this method in preference to the EHD method:
1. The boundary estimation of sources is more accurate than that of EHD method.
2. The corners of sources are estimated.
3. The stability of this method against noise is higher than the stability of the EHD method because the magnitude of maximum amplitude of noise is %4 in the wavelet transform method whereas it is only %1 in the EHD method.