JOURNAL OF RESEARCH ON APPLIED GEOPHYSICS
Year:2019 | Volume:4 | Issue:2 |Papers Count:20

The exploration of geothermal resources in the Bushli area of Ardebil Province utilizing magnetotelluric (MT) data is presented in this paper. This study is performed on 60 MT stations in an area surface of 90 square kilometers of Bushli area, located in southeast of Nir district. The data has been processed using algorithms based on robust methods, which are resistant to noise. After that, dimensionality analysis has been applied to the MT data having appropriate limits of frequencies related to all stations. Considering dimensionality analysis results, the regional structures are mostly identified as two-dimensional structures with north-south strike direction. Regional structures have been interpreted following one dimensional (1D) and two dimensional (2D) inverse modeling applied on the data. The results of 1D and 2D inverse modeling integrated with geological data indicate that the upper part of the geothermal reservoir is composed of a low resistivity area at the depth of 500 to 2000 meters. Final results have shown that the location of the geothermal reservoir extends to the southern parts of the study area. ...

Summary In this study, a novel approach for linearized amplitude versus offset (AVO) inversion in a Bayesian framework is presented. Objective is to estimate the posterior distribution of three elastic parameters, P wave velocity, S wave velocity and rock density. The methodology is based on the convolutional model and a weak contrast linearized approximation of Zoeppritz equation for PP waves. In this study, assuming a priori Gaussian distribution for input parameters, and also, a Gaussian distribution for seismic misfit function, Bayesian equation also yields a Gaussian distribution for posterior parameters, which can be analytically computed. This analytic solution is a rather fast approach for inversion of elastic parameters along with their uncertainty distribution. This methodology is tested on both synthetic and field data sets and in both cases yields reasonable solutions. In the current study, assuming a weak contrast model for rock properties, a linearized AVO approximation of Zoeppritz equation is used in a Bayesian framework to invert prestack seismic data for the above-mentioned three elastic parameters. The methodology is tested on both synthetic and field data sets. The results show preferably good matches with the true data. Introduction Inversion of seismic AVO is a way to estimate elastic parameters from prestack seismic data. This technique can be solved in both nonlinear (Dahl and Ursin, 1991) and linear (Smith and Gildow, 1987) approaches. Lortzer and Berkhout (1993) also used the same methodology as presented here, but they used the relative contrast of elastic parameters instead of their absolute values. Methodology and Approaches Assuming a Gaussian distribution for elastic parameters and seismic noise, and also, a linearized formulation for forward modeling, distribution for posterior parameters will also be Gaussian. Based on this methodology, the mean and covariance matrices of prior distribution are estimated from well data. Then using the linearized formulation of AVO, the mean and covariance matrices of observed seismic data are estimated. Having the statistical parameters of prior and likelihood functions, the statistical parameters of posterior distribution is analytically yielded based on Bayesian formulation. The covariance matrix of posterior distribution gives an estimate of the uncertainty in the elastic parameters. Results and Conclusions A Bayesian AVO inversion method was proposed and tested on both synthetic and field data sets. In case of synthetic data, the estimated parameters fitted the true values almost exactly. The result for the field dataset was also reasonable and matched the well log data relatively well except in some locations where prestack seismic data were not preconditioned very well. The initial models used for this methodology does not need to be detailed at all and very simple initial models such as constant or linear values lead to good estimation of the posterior distribution. Therefore, this approach can be a good choice for generation of pseudowells where not a rich dataset is available.

Water saturation (Sw) of a hydrocarbon reservoir is an important petrophysical parameter having a great impact on the accuracy of primitive estimation of the reservoir. Due to highly importance of this parameter dealing with the economic calculations of the reservoir, it must be estimated precisely. Although experimental analysis of core samples taken from a reservoir leads to very useful information about Sw of the reservoir, this experimental method is highly expensive and time consuming; and therefore, this method is applicable only for a small number of wells in a field. To overcome this problem, an intelligent pattern recognition method, known as support vector regression (SVR), has been employed in the current research to estimate Sw from well logs data of 3 wells in one of the largest oil fields of Iran. The performance of the algorithm has also been validated through different criteria. The results of this research indicate that the SVR model can estimate Sw from well logs data accurately, in which the determination coefficients of 87 and 76 percent have been obtained from the training and test steps, respectively.

The resolution of seismic data decreases due to tuning effect, attenuation, and absorption and has always been one of the challenges for the interpreters. We can perform resolution enhancement in many ways, and in this regard, spiking deconvolution is the most critical approach. The ideal method to increase the resolution is to magnify or retrieve weak high frequency signals to provide a broad frequency spectrum, and therefore, substantially compressed signals. In this paper, a Hilbert-wavelet derived method has been investigated for this purpose. First, the input data using the wavelet transform (WT) are decomposed and enhanced by the Hilbert transform (HT) in the wavelet domain. The inverse WT yields compressed data based on current frequencies without any estimate and approximations. The Lack of significant distortions of recovered frequencies makes this process more distinctive than introduced methods. In this study, complex wavelet transform (CWT) and undecimated discrete wavelet transform (UDWT) are used. In fact, UDWT provides increased resolution, but on the opposite side, CWT presents impressive results. It deliveres fewer artifacts because of its time-frequency representations due to its unique combination of shift-invariant. This approach has been proposed and implemented to shot gathers after preliminary processing.

In this research, the efficiency of electrical sounding method in recognizing the mineral layer in karstic bauxite deposits having coarse topography is investigated. For this purpose, 21 electrical sounding locations beside drilled points along a survey line in one of Jajarm bauxite deposit have been designed and surveyed. First, the acquired data have been interpreted using standard curves, and then, the obtained results have been modelled by IXID software. Because of enough resistivity contrast between the bauxite and dolomite bed rock, the recognition of basement is possible. Despite this, due to low resistivity contrast between the bauxite and upper layers, the recognition of upper layers, and thus, determination of the bauxite layer thickness is difficult. ...

The resistivity method is frequently used in fields of engineering geology and exploration of mineral resources. The simplicity of the equipment, the low cost of the survey in comparison with other methods, and the abundance of interpretation methods makes it as a popular geophysical method. There are many methods for inversion of resistivity data. Validation of inverted models is an important step in modeling. In general, validation of the resistivity results is performed by calculating the difference between observed and estimated values, but in this study, a validation technique based on data resolution matrix and model resolution matrix is proposed. The applied method for validation of the results has not been used so far, in this research work, resistivity and induced polarization data have been collected using dipole-dipole electrode array in Hamyj copper deposit located near the city of Birjand. The results of data resolution matrix and model resolution matrix have shown that generalized inversion is a suitable method for processing of resistivity data, because both data and model resolution matrix have been close to an identity matrix. ...

Crustal velocity structure beneath four broadband seismic stations located in northeast of Iran, including Shahrood (SHRO) and Maraveh Tappeh (MRVT) stations set up by Iran National Seismic Network (INSN) and Sabzevar (SZBV) and Jarkhoshk (JRKH) stations set up by Iranian Seismology Center (IRSC), have been investigated by joint inversion of P receiver function and Rayleigh wave phase and group velocity dispersion curves. A three-year teleseismic data (2012-2014) with epicentral distance of 25o-90o and magnitude more than 5. 5 have been used to determine the receiver functions by iterative deconvolution in time domain proposed by Ligorria and Ammon (1999). Iterative deconvolution in time domain to determine the receiver functions are more stable with noisy data in comparison to frequency domain. The fundamental mode of Rayleigh wave group and phase velocity dispersion curves have been provided by the study on the structure of crust and upper mantle of the Iranian Plateau for the period interval of 10-100 seconds made by Rahimi (2010). ...

Pore pressure is defined as the pressure of the fluid inside the pore space of the formation that is also known as the formation pressure. When the pore pressure is higher than hydrostatic pressure, it is referred to as overpressure. Knowledge of this pressure is essential for cost-effective drilling, safe well planning, and efficient reservoir modeling. To optimize drilling decisions and well planning in overpressure areas, it is essential to predict pore pressure in the first step. Before drilling, reliable prediction of pore pressure is critically important at different stages of petroleum engineering investigations. Pore pressure prediction has an important application in proper selection of casing and reliable mud weight. Currently pore pressure prediction in carbonate reservoir is still far from satisfaction, and there is no specific method widely accepted. The existing methods and theories in the pore pressure prediction community are almost all based on the shale properties. Although these methods are not the proper way to predict pore pressure in carbonates and may probably lead to dangerous errors, they are still used in the field practice of carbonate reservoirs. Introduction The generation of abnormal pore pressure in carbonate formation is different from a reservoir to another reservoir because of different depositional and geological conditions. Although most studies currently point out that under-compaction mechanism is the dominant mechanism of abnormal pore pressure generation, the role of this mechanism in carbonate formations needs further study and discussion. Over-pressure can be identified by direct and indirect methods. Direct methods such as measured pressure data obtained from drill stem test (DST), repeat formation tester (RFT), modular dynamic test (MDT) and mud weight, and they are reliable evidences that reflect the over-pressure phenomenon in permeable reservoirs. Methodology and Approaches Pressure coefficient, which is the ratio of the actual fluid pressure versus corresponding normal hydrostatic pressure at the same depth, has also been proposed and applied to investigate over-pressure. On the contrary, indirect methods, such as well logging, seismic and rock mechanic data, can identify abnormal pressure zones based on various response anomalies compared with the normal pressure system. The main objective of this study is to determine pore pressure using Eaton’ s and Bowers’ methods and to compare their accuracy and usage. To obtain this goal in Bowers’ method, researchers try to directly link the formation velocity to the effective stress. One of these models was developed by Bowers (1995). Results and Conclusions Sonic and density data in the distance between wells have been predicted using a combination of sequential Gaussian simulation and collocated cokriging techniques. Then, effective stress cube and overburden pressure cube have been predicted using velocity to effective stress transform and density to overburden pressure relation. Eventually, formation pore pressure has been predicted using Terzaghi’ s method. Another way to estimate pore pressure is used from well logging data by applying Eaton's method (1975) with some modifications. In this way, sonic transient time trend line is separated by lithology changes determined from Zhang’ s method. Our results show that the best correlation with the measured pressure data is obtained by the modified Eaton’ s method with the Eaton’ s exponent of about 0. 4.

Complex structures in seismic images introduce ambiguities in structural and stratigraphic interpretation of seismic data. On the one hand, using high quality seismic image could resolve some of structural ambiguities of seismic image. On the other hand, some seismic attributes, which extract additional information from seismic data, could be used in interpretation step. However, vast number of introduced attributes brings another ambiguity that is which attributes would be appropriate for the specified purpose. Thus, several methods have been introduced to select appropriate attributes for a special case and furthermore, integrate attributes to extract as much as possible information and make their contribution in one single image. In this study, we have introduced a novel strategy for integration of seismic texture attributes in GIS environment. In the proposed strategy, each attribute is considered as a separate information layer, and then, these attributes undergo fuzzification process, and subsequently, are weighted by conventional functions and are integrated in GIS environment. ...

Velocity analysis is one of the most important stages of seismic processing. The most conventional method for velocity analysis is to calculate the semblance coefficients. Traditional semblance has some shortcomings, for instance, low resolution in time and velocity direction, high computational cost, and having trouble in presence of amplitude variation-with-offset (AVO) phenomenon. In order to compensate for the latest shortcoming, AB semblance has been proposed. However, this method has approximately twice the lower resolution than traditional semblance. On the other hand, due to effects of the source wavelet, seismic events have band-limited nature, which leads to a decrease in temporal resolution. Recently, the deconvolutive Radon transform has been introduced to overcome the latest problem. In this paper, we have developed the deconvolutive hyperbolic Radon transform for AVO preserved velocity analysis. We have also used the log-polar domain in order to reduce computational cost. We tested this method on both synthetic and real field data sets to show resolution improvement in the proposed method. ...

Recently, geophysical methods have been used successfully to determine geotechnical characteristics or parameters of subsurface layers. In this research, the integrity of vertical piles, the dynamic elastic parameters of soil and the thickness of the piles in a residential construction site in Kelarabad, located in west of Mazandaran, Iran, were delineated using pile integrity testing (PIT), downhole and crosshole methods. ...

Polour basalts are located 75 km away from Tehran. It is situated in northeast of Tehran and south of Damavand volcano. The basalt emission point has not been distinguished yet, whereas its occurrence is a debatable topic among geologists. The procedure of formation, geological setting and the way of ascending have been always as controversial issues. Petrologically, Polour basalts are basalt– basalt trachyte rocks. Similar units are found at the east of Damavand volcano and as expected, the composition, age and feeder source are different from Damavand volcano. Polour basalts occurred as arc-shaped bodies at shallow depth in central part of study region, where they mostly consist of old terraces and alluvial fans. Because of having considerable amount of magnetic susceptibility, magnetometric survey might delineate the location of such geological units. Various depth estimation techniques have been employed to determine the depth of causative sources associated with the basaltic units in the region of interest.

The attenuation of seismic waves with respect to distance is one of the most important parameters in seismological and earthquake engineering studies. The purpose of this study is to estimate quality factor of shear waves (QS) of seismic data of the earthquake occurred in the Central Alborz at 34º to 37º north latitude and 50º to 56º east longitude, using the spectral drop. For this purpose, the data from earthquake of May 28, 2004 Firouzabad-Kojur and its aftershocks, recorded by seismic networks of Sari and Semnan, affiliated with the Institute of Geophysics of Tehran University have been used; and the quality factor of direct S wave (QS) at the seven central frequencies of 1. 5, 3. 0, 4. 5, 6. 0, 9. 0, 12. 0 and 18. 0 Hz has been estimated. The estimated frequency-dependent relationship of QS on N-S and E-W components are QS=76. 61f 0. 8 and QS=70. 35f 0. 85, respectively. The mean values of QS for the two components indicate a relation with frequency that is QS=73. 54f 0. 83. The results show an increase in QS with increasing frequency, and Q0 value for this area corresponds with the seismotectonic study of the region. ...

This paper presents a new method for interpretation of two dimensional (2D) magnetic anomaly data. The new method uses a combination of analytic signal and its total gradient to estimate the depth and nature-i. e. structural index-of an isolated magnetic source. However, the proposed method is sensitive to noise. In order to lower the effect of noise, upward continuation technique is applied to smooth the anomaly. Tests on synthetic noise-free and noise-corrupted magnetic data show that the new method can successfully estimate the depth and nature of the causative source. For practical application of the method, it was applied to measured magnetic anomaly data from Khalilabad area. For validity of the method, it was tested on a synthetic example with and without random noise. After adding 5%, 10% and 15% random noise to the synthetic data, the maximum error for the model parameters was seen to be less than ± 3%. Moreover, it was found that the inversion results of magnetic data from an area in northeast Sirjan was in good agreement with the results from Euler deconvolution of the analytic signal of the magnetic data. Introduction An important goal in the interpretation of magnetic anomaly data is to obtain the depth and the geometry or structural index of the causative source. To this end, a large number of methods exist to accomplish this goal. The analytic signal method is a popularly used method for this purpose. Using the analytic signal method, we can calculate both the depth and structural index of causative sources. However, the improved analytic signal method, presented in his paper, needs the computation of third-order derivatives of the magnetic anomaly and requires data of high precision or strict filtering. Methodology and Approaches In this paper, we present an improved analytic signal method to interpret 2D magnetic anomaly data. The proposed method uses a combination of the analytic signal and its total gradient to estimate the depth and the structural index of the causative source. The feasibility of the proposed method to compute the source parameters is displayed on synthetic and measured magnetic anomalies. Results and Conclusions We have proposed a new method to estimate the depth and the structural index of the causative source using the ratio of analytic signal to its total gradient. Our method provides two linear equations to estimate individually the depth and nature of a magnetic source. The feasibility of the new method is demonstrated on synthetic magnetic anomaly with and without random noise. For noise-free data, the structural index and the depth, estimated by the new method, are consistent with the theoretical values. For noise-corrupted data, our approach can provide reasonable results by applying upward continuation technique to lower the effect of noise. Application of the method on measured data indicates that the results of the method are in god agreement with the results computed by the Euler deconvolution of analytic signal method.

Resistivity logs are among the most important logs since their measurements are directly related to hydrocarbon saturation. Conventionally, Chartbooks as theoretical response of logs are used for interpretation of electrical logs. One dimensional (1D) computer codes are the cornerstones of chartbooks. These codes solve Maxwell’ s equations by ignoring layer inclination, non-uniform mud invasion, shoulder bed effect and well deviation. Simplifying the geometry of the model introduces significant amount of error in the interpretation of resistivity logs. Consequently, it is necessary to utilize complex numerical models for interpretation of the logs. ...

Edge detection of subsurface structures is an important objective in interpretation of magnetic data. In this paper, curvature gradient tensor (CGT) of magnetic data has been used along with tilt angle method to detect edges of subsurface structures. Application of these methods on synthetic and real gravity data has shown that the CGT of magnetic data, compared to the tilt angle method, can determine the edges of subsurface structures better. Introduction The main objective of the interpretation of magnetic data is to extract information about subsurface structures. Edge detection is an important means to image the edges of subsurface structures. Therefore, edge detection has traditionally been an important objective in the interpretation of magnetic data. There are various methods for edge detection. Tilt angle method is a traditional method that can detect edges of subsurface structures quantitatively. The value of Tilt angle is zero above the edges of subsurface bodies. The curvature gravity gradient tensor (CGGT) has also been used to interpret subsurface geological structures quantitatively. The eigenvalues of CGGT are zero above edges of subsurface bodies. In this paper, the CGT of magnetic data has been used for edge detection of subsurface magnetic bodies. The results of using the CGT of magnetic data have been compared with the results obtained from applying Tilt angle method on the data. Methodology and Approaches In order to obtain the CGT of magnetic data, at first, the magnetic data are reduced to pole (RTP). Then, horizontal vector gradients of the gradient tensors are computed from the RTP data using a Fourier transform technique. Then, the eigenvalues of the CGT of magnetic data are obtained. The small eigenvalue can only be used to detect the edges of bodies with positive susceptibility contrast, and the large eigenvalue can only be used to determine the edges of bodies with negative susceptibility contrast. As an example, chromite ore has positive density contrast with the host rock and produce positive gravity anomaly. Finally, the tilt angle method is also applied to compare its results with those of the CGT of magnetic data. Results and Conclusions The robustness of the method used for the enhancement of edge detection is tested with a magnetic anomaly map caused by two prisms of synthetic bodies with positive and negative susceptibility contrast. The results have shown that the zero contour of the small eigenvalue of the CGT of magnetic data compared to the zero contour of the tilt angle method can better detect the edges of synthetic bodies with positive susceptibility contrast. Moreover, the zero contour of the large eigenvalue of the CGT of magnetic data compared to the zero contour of the tilt angle method can better detect the edges of synthetic bodies with negative susceptibility contrast. The Tilt angle method is also more sensitive to noise than the CGT of magnetic data. The CGT method has been applied to real magnetic data from Qahan porphyry copper deposit in Markazi Province, Iran. The results have indicated that the large eigenvalue of the CGT can determine the edges of porphyry deposit and the small eigenvalue can outline positive magnetic anomalies caused by propylitic alteration. However, the tilt angle method has not been capable of finding the edges of the porphyry deposit.

Summary In this study, the influence of pore fluid salinity on the complex electrical conductivity responses of sandstone and sand samples is analyzed. The investigated samples in this study include clean sandstone and sand samples provided by an Iranian offshore oil company and sandstone samples containing clay minerals that have taken from a sandstone aquifer located in northwest of England. All samples have been saturated with sodium chloride solution. The fluid electrical conductivity ( ) of sodium chloride solution has gradually been increased from 57 mS/m to 6000 mS/m. The expected linear relation between and the real component of electrical conductivity ( ) of the saturated samples has been observed. It is also observed that the imaginary component ( ) increases with the increase of salinity, and consequently, the increase of fluid conductivity. To determine the relaxation time ( ) of spectral induced polarization (SIP) data, Cole-Cole model has been fitted on the measurements carried out at four different salinities of sandstone aquifer samples. The Cole-Cole relaxation time increases with the increase of fluid conductivity for all samples except two samples. The behavior of is also comparable to as both parameters measure the polarizability. In other words, normalized chargeability also increases with the increase of fluid salinity. In this study, the dependence of polarizability on fluid salinity is also demonstrated. Maximum values of polarizability are observed at high salinity for quartz dominated siliceous material. Introduction The induced polarization (IP) geophysical method measures the low-frequency electrical properties of rocks and soil materials. This method has appeared as a potentially powerful tool for subsurface imaging due to the dependence of the measurements on rock or soil internal surface area. Given the increasing interest in using IP measurements to deduce rock textural properties such as permeability, further studies of the dependence of IP measurements on pore fluid composition are needed. In SIP, a phase lag between the current and the electrical field provides complementary information to electrical conductivity measurements. The conductivity and the phase can be rewritten into a complex conductivity (or a complex resistivity) that can be measured over a broad range of frequencies, typically from 1 mHz to few tens of kHz in the laboratory and from 10 mHz to 10– 100 Hz in the field. Methodology and Approaches SIP measurements were collected in a fully saturated state for each sample at four different salinities. All samples were saturated with a NaCl solution starting with the lowest salinity and then fluid electrical conductivity ( ) of sodium chloride solution was gradually increased from 57 mS/m to 6000 mS/m. The electrical impedance was measured using a four-electrode array. Two silver coils were used as current electrodes to inject an alternating sinusoidal current. The voltage and the phase shift between the applied current and measured voltage was determined using Ag-AgCl nonpolarized potential electrodes. Electrical measurements were taken using the ZEL-SIP04-V02 impedance meter in a frequency range of 2 mHz to 45 kHz (Forschungszentrum Julich GmbH). Results and Conclusions Our investigation has shown that the fluid chemistry is an important parameter that controls the polarizability of the mineral-fluid interface. Real and imaginary components of conductivity increase with the increase of saturating fluid conductivity. It has also been demonstrated that normalized chargeability show a positive power law relationship with fluid conductivity. The results of Cole-Cole model fitted on data have indicated that relaxation time increases with salinity for all samples except two samples. We have also shown that polarizability parameters are controlled by fluid conductivity.

Geothermal energy can be a good replacement for any kind of energy we use today. Estimation of curie point depth (CPD) is one of the first steps in geothermal exploration. Spectral analysis of aeromagnetic data can provide important information about temperature distribution in depth. In this study, we attempt to estimate the CPD using centroid method and forward modeling in northwest of Iran. The reduced-to-pole (RTP) aeromagnetic data were divided into 11 overlapping windows of the size of 100 100 km. In the centroid method, the average depth to the top of the deepest crustal block, t Z was first computed by linear fitting to the second longest wavelength segment of the power spectrum of aeromagnetic data. Then, depth to the centroid of the deepest crustal block, o Z was computed by linear fitting to the longest wavelength segment of power spectrum of aeromagnetic data. In forward modeling, the modelled spectra were fitted to the observed spectrum iteratively and the depth to the top and bottom of the block was finally estimated. According to the obtained results, the CPD is shallow in the west part of the area and as a comparison of the results with the locations of hot springs in the area, we conclude that the west part of the area has a good potential for geothermal exploration. ...

First and second vertical gradients are widely used in the interpretation of gravity data. Vertical gradients are sensitive to noise. Accuracy of vertical gradient calculation directly effects the accuracy of interoperations. Therefore, accurate and without noise calculation of vertical gradient is vital. The most common method to calculate vertical gradients is to use Fourier transform. Low noise in the gravity data causes that the vertical gradients, calculated by Fourier transform, have severe noise. In this research, we have used discrete cosine transform (DCT) to calculate vertical gradients. Results of DCT and Fourier transform are completely equal when the gravity data are noise free, but in the case of noisy data, DCT has better performance than FFT. This improvement is investigated by using signal to noise ratio (SNR). The SNR of the results of DCT compared to Fourier transform is larger, therefore less noise enters in the calculation of vertical gradients by using DCT. We have tested these two transforms on the synthetic data containing Gaussian noise. First and second vertical gradients are calculated by DCT and Fourier transform. The results have shown that DCT in comparison with Fourier transform is less sensitive to noise. Moreover, these two transforms are used for calculating first and second vertical gradients of gravity data obtained from Safo manganese mine. The results have shown that less noise enters in vertical gradient map obtained using DCT. Edge detection of anomalies is one of the usage of gradients in the interpretation of gravity data. Analytic Signal has been used for edge detection of anomalies in the cases of real and synthetic gravity data. Vertical gradient of analytic signal calculated by DCT, compared to Fourier transform, has less noise and better quality. Introduction The first and second vertical gradients are used to distinguish the difference between two adjacent anomalous bodies, reduce the effects of interference of the amplitudes of anomalies, separate the local field superimposed on the background determine, and to determine the location and dimensions of the anomalies. The gradient data are used in direct interpretation and inversion and inputs of many interpretations. Vertical gradients are more sensitive to noise than bouguer map, and second vertical gradients is more sensitive to noise than first vertical gradients. Methodology and Approaches Generally, the relation between cosine and sine transforms with Fourier transform is equal to ‘ F=C + iS’ . Where F, denotes Fourier transform and C and S denote cosine and sine transforms, respectively. If the function is positive or constant, imaginary part of the Fourier transform is equal zero. In other words, Fourier transform and DCT will be equal. It can be assumed that noise is a function that is added to gravity signal. Because of the nature of noise, Fourier transform and DCT of noise will not be equal. Then, the signal to noise ratios for DCT and Fourier transform of noisy gravity signals are not the same. Hence, less noise enters the gradient map when calculating vertical gradients using DCT. Results and Conclusions In this research, we have used DCT to calculate vertical gradients. We analytically have proven that DCT in noise-free data has equal results with Fourier transform results. However, the DCT of noisy data have shown less noise enters the data compared to Fourier transform. We have examined this issue by using synthetic data containing Gaussian noise. A comparison between vertical gradients obtained by DCT and Fourier transform indicates that DCT is less sensitive to noise. We have obtained similar results by using real data. The results of analytic signal calculated by DCT and Fourier transform in both cases of real and synthetic data have been compared. Edge detection calculated by using DCT has shown less noise due to less noise in the DCT and also has better quality compared to using Fourier transform.

Anisotropic diffusion filtering (ADF) is widely used as an efficient method in random noise attenuation problems, and various modifications to its original version have been proposed. The main reason could be the thought that ADF preserves edge features with acceptable performance beside noise attenuation procedure. In seismic data processing, however, it should be noticed that using ADF could cause severe changes (artifacts) in the zones that are highly contaminated with random noise. In this paper, the optimum value is derived, by introducing an automatic framework based on two artificial intelligence (AI) algorithms, adaptive neuro-fuzzy inferences (ANFIS) and fuzzy c-mean clustering (FCM). The neuro-fuzzy network is trained using original data, successive ADF values are calculated for each data point, and FCM output is obtained in a weighted averaging manner adapted with estimated noise level. The trained network is, then, generalized to all data, and thus, the ANFIS optimized version of ADF, called here AOADF, is achieved. Comparison of the results of the ADF and AOADF experiments reveals that in synthetic common mid-point (CMP) gathers, the proposed method improves peak signal to noise ratio (PSNR) value, 40% higher than ADF (in the best case) and in real CMP and common offset sorted gathers, the performance of AOADF is considerably higher than ADF, in terms of random noise attenuation without adding unwanted artifacts and preserving continuity of coherence components.