euler deconvolution

Airborne magnetic and electromagnetic methods are among the most efficient geophysical techniques for the detection of buried anomalies. There are several methods that can be used to estimate the depths of the buried anomalies. In general, modeling methods can be used not only to estimate the depths of the buried anomalies, but also, to determine physical and other geometric factors of the anomalies such as lateral extension, thickness, dip and so on. In this research, magnetic lineaments have been determined using the airborne magnetic data, acquired in a part of Bazman area with an area of 24 square kilometers located in about 125 kilometers northwest of the city of Iranshahr. By applying filters such as reduction to the pole, first horizontal derivatives, analytical signal, tilt angle and upward continuation filters. For processing and interpretation of the airborne magnetic data, the Oasis Montaj module of Geosoft software package has been used. The processing, display and interpretation of the airborne electromagnetic data have been made Conductivity Depth Imaging (CDI) using EM Flow and Profile Analyst software packages of Encom Company. Furthermore, the depths of the lineaments in this area have been estimated using Euler deconvolution method. Then, the obtained results have been compared with the results of airborne electromagnetic investigations for the frequencies of 900, 7200 and 56000 Hz using horizontal and vertical coplanar coils. Also, the obtained findings from the airborne magnetic and electromagnetic methods have been validated by the geological information of the area. The airborne magnetic and electromagnetic data of the area have been acquired using airborne magnetometer and DIGHEM5 electromagnetic instruments, respectively. The airborne magnetic and electromagnetic surveys over the study area have been made by Geological Survey of Iran (GSI) in 2005. As a result of this study, 22 magnetic lineaments in the area have been identified in which 4 lineaments coincide on the main faults of the area as the validation results indicate. In this regard, the main faults can be observed on the obtained magnetic maps in which different filters have been applied, however, the tilt angle magnetic map indicates the main faults of the area more clearly. This implies the better performance of the tilt angle filter over the other filters in displaying magnetic lineaments. Totally, 22 magnetic lineaments have been determined on the magnetic maps. By the results of this study, we can conclude that the main faults of the area have an approximate trend of northeast-southwest. Some of these faults, which have been determined from the airborne magnetic investigations of the area, cannot be determined from geological studies of the area as they have been overlain by the Quaternary sediments. The different performances of these main faults on the lithological variations and tectonic activities of the area have been clearly evident by the result of this study. The main faults of the area have also played a vital role on the formation of folds and fractures, and occurrence of weak earthquakes. The approximate depths of the lineaments, which have been estimated by applying the Euler deconvolution method on the acquired magnetic data are around 100-200 meters.

Depth estimation of geological structures is one of the most important objectives in geophysical studies. Euler deconvolution (standard Euler) is a well-known method in the depth estimation. Based on standard Euler, various methods are introduced to reduce error of the depth estimation. In this study we have used a new method called Euler RDAS. This method is based on the standard Euler. In this method derivatives of analytic signal and first vertical are used in Euler equation. Applying derivatives of analytic signal for depth estimation is better than the analytic signal. There is no problem of choosing structural index in this method which increases accuracy in the depth estimation. To examine the performance of this method, depths of several synthetic models are estimated and their results are compared to that of the standard Euler. In all models, results of the RDAS Euler shows fewer errors in high depth model in comparison to that of the standard Euler. This method was tested on synthetic data with noise. RDAS Euler sensitive to noise due to usage of high-degree derivatives is less than the standard Euler. Study shows that if the noise in the data is reduced by methods such as filter upward, it can provide an appropriate estimate of the depth. In this study, the depth of gravity anomalies caused by the masses of hematite located in Kerman, has estimated using standard Euler and RDAS Euler. Upward continued by 3 m has been used for reducing noise in this data. There are 3 possible hematite masses in residual map of the study area. The minimum of high depth anomalies indicates masses of hematite, which is calculated using RDAS Euler and was about 5 meters and a maximum of high depth is about 20 meters. The minimum depth obtained using standard Euler for this anomaly is about 5 meters and the maximum depth is about 40 meters. Responses of RDAS Euler is more compatible that of standard Euler with the boundary anomalies and has smaller vertical interval which can be a criterion for more precise solutions of the RDAS Euler. For further examination, the gravity data of hematite mine is used with inverse modeling of Camacho method. Minimum and maximum upper depths obtained for these anomalies are 5 to 35 meters, respectively. In addition, the modeling results is compared with the results of depth estimation of Euler. To this, 10 points in the anomalies area are pointed and the calculated depth of these points using standard Euler, RDAS Euler and modeling are shown. Root mean square error (RMS) between Euler’s and modeling results is calculated. In comparison of the results in different methods, which are not standard, results of two methods that have the lowest RMS error is considered as the selection criteria. RMS for standard Euler with MATLAB code, Geosoft, and RDAS Euler are equal to 11.43, 8.5, and 2.66 respectively. The results of two methods among these three methods which are used to estimate the depth of hematite masses are close hence they can be more reliable results. Therefore, due to fewer errors of RMS of RDAS Euler and modelling results are more accurate than that of the standard Euler.

The analytic signal method is a semiautomatic method for estimating the location of causative bodies in magnetic and gravity methods. The application of analytic signal for interpretation of two dimensional (2D) structures was introduced by Nabighian (1972). The analytic signal is defined as a complex function in which the real and imaginary parts are a pair of Hilbert transforms. In other words, the analytic signal is a combination of horizontal and vertical gradients of potential field. Analytic signal is a symmetric function with amplitude sensitive to parameters of the source. In case of 2D structures, the amplitude of the analytic signal is independent of the directional parameters such as inclination, declination and strike angle (Nabighian, 1972; Atchuta et al., 1981; Roest et al., 1992). The depth of 2D structures can be estimated using the width of the analytic signal or the ratio of the analytic signal to its higher derivatives (Hsu et al., 1996; Roest et al., 1992). Source’s parameters of a dyke such as width, dip, strike, magnetization and depth can be estimated by analytic signal method (Bastani & Pedersen, 2001). The nth-order enhanced analytic signal is defined as the analytic signal of the nth-order vertical derivative of the potential field. An automated method for estimating the depth, horizontal location and shape of 2D magnetic structures is the horizontal gradient of analytic signal method. This method is capable of interpreting low quality data because of using the first and second order derivatives of potential field in the main equations. The method of analytic signal estimates the horizontal location of the source by approximating the maximum amplitude of the signal; hence noise can affect the estimations. On the other hand, by using the horizontal gradient of analytic signal expressions, all of the source’s parameters could be approximated simultaneously. In this method, equations of the analytic signal, Euler enhanced analytic signal and horizontal gradient of analytic signal are combined to derive a linear equation. Using the first order analytic signal, horizontal gradient of analytic signal and linear inversion method, the depth and horizontal location of 2D magnetic bodies are obtained. The location estimation is independent of the shape of the causative bodies. The causative body’s geometry is estimated as a structural index by applying the least squares method. Data selection for solving the equations or width of windows is based on data quality. The optimum size is defined somehow to detect a signal specific anomaly and also variations of the anomaly in one window. In this study, in order to solve the equations of the horizontal gradient of analytic signal method, the data greater than twenty percent of maximum amplitude of the analytic signal were used. The analytic signal-Euler deconvolution combined method is an automated method to estimate depth and shape of the sources. This method is used to interpret 2D & 3D magnetic and gravity data. After substituting the appropriate derivatives of the Euler’s homogeneous equation in the equation of the analytic signal, major independent equations which are used to estimate the depth and shape of causative bodies, are derived. The horizontal location of causative bodies is estimated by Euler method or locating the maximum amplitude of the analytic signal. In this study, the accuracy and efficiency of each of the mentioned methods in interpretation of magnetic anomalies are evaluated. Methods were tested for different synthetic datasets provided by forward modeling. 2D magnetic models placed at different depths and random noise added for some models. Derivatives were calculated in frequency domain by using Fourier transform techniques. In this technique, bell-shapedness effect appears at the edges of the profiles. This effect could be corrected by linearly expanding the profiles. Upward continuation filter was applied on some synthetic data to decrease the noise level. In this paper, the applicability of the horizontal gradient of analytic signal method and the analytic signal-Euler combined method were tested. Both methods estimate the parameters of the causative bodies without any prior information. In both methods, there is not any explicit dependence on directional parameters (e.g. magnetization) in the main equations; hence, as the results show, estimations were not affected by remanent magnetization. The results also show accurate estimations of the horizontal gradient of analytic signal method for shape and horizontal location and efficient estimations of the analytic signal-Euler deconvolution combined method for depth.