Different methods are used for seismic velocity analysis, including spectral analysis based on semblance, which is a reliable way to estimate the stacking velocity. The proposed method in this research is superior over other seismic velocity analysis methods because in the proposed method, the wave due to the absorption of the earth makes a reduction of the frequency content of the source in time, and results in poor temporal resolution. In this paper, the velocity analysis performed in the wavelet domain using undecimated discrete wavelet transform (UDWT). Random noise is often placed in high-frequency sub-bands and their effect leads to a reduction in coherency than other sub-bands. In this way, data analyses to high-pass and low-pass sub-bands and velocity analysis at any scale are performed using discrete wavelet transform and scaling filters. A Comparison of the obtained results showed that the spectral analysis of the velocity in the wavelet domain increases the accuracy of the velocity analysis in each band of frequencies.

This paper deals with the one-dimensional discrete wavelet transform (1D DWT) of four scaling coefficients are computed numerically by designing a convolutive operator. The near-zone contribution of the integral is calculated through wavelet transform and for the far-zone contribution the classic expansion of the spherical harmonics applied. Finally the geoidal heights are determined over a territory in Canada.

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.

Reflection seismic data is often contaminated by a variety of coherent and incoherent noises that influence the reliability of the seismic data to provide a better understanding of the hydrocarbon reservoir characteristics. The groundroll noise is characterized by dispersive wave, low frequency, high amplitude that propagates along and near the surface of the earth and will often obscures the seismic reflection data. Removal of this type of noise is an essential part of land seismic data processing. Most of ground-roll noise removal or attenuation methods are based on transforms. Radial trace transform and wavelet transform are two of the most important and common transforms, which are used to attenuate ground-roll noise. Various methods have been introduced by different authors to attenuate the ground-roll noise. In this paper, we have used the wavelet transform on radial basis to attenuate the ground-roll noise. The method is based on the joint application of the two-dimensional discrete wavelet and radial transforms in order to eliminate the coherent noise, especially ground-roll noise. Since the radial trace transform reassign the linear events in the x-t domain into vertical events in the r-t domain, it provides a pleasant framework for two-dimensional (2D) discrete wavelet transform. The de-noised signal can be obtained by suppressing the vertical band of one-level, 2D discrete wavelet transform of the radial transformed seismic gather followed by transforming back the filtered radial-wavelet transform into the x-t domain. To evaluate the efficiency of the proposed method to eliminate the ground-roll noise, we have tested the method on a real reflection seismic gather from an oilfield in southwest of Iran. We have also compared the obtained results with those from the f – k filtering for ground-roll noise suppression from seismic data. The results obtained from applying the proposed method on the real data test prove that the proposed method for ground-roll noise attenuation is as good as, or better than, those produced using f – k filtering.