Normalized Full Gradient Research Articles

Estimating The Location of a Buried Body from Magnetic Anomaly Through Normalized Full Gradient: A Case Study from The Sapinuwa Ancient City, Turkey

In geophysics, whether the structure is close to the surface or deeper, information about the depth and location of the structure can be obtained by using magnetic data. The importance of this study is an example of the application of the Normalized Full Gradient (NFG) method to an archaeological site to find the depth and location of structures that cause magnetic anomalies collected at the archaeological site. One of the parameters affecting the shape and size of the magnetic anomaly is the depth of the source causing the anomaly. For this reason, it is significant to determine the location of the source correctly. One of the methods used to determine the depth of structure using magnetic field data is NFG technique. In the application of downward analytical continuation, distortions due to the passage of mass depth occur and this method invalidates this. The NFG technique was tested on anomalies caused by prism-shaped synthetic models. Test studies on synthetic models with the NFG technique have yielded satisfactory findings. Based on the findings, the NFG technique was carried out to the real magnetic anomaly collected in the ancient city of Sapinuwa. The findings were compared with the building remains unearthed as a result of the proposed trench excavations. The obtained results have shown satisfactory results.

Crustal structure of the Qiangtang and Songpan-Ganzi terranes (eastern Tibet) from the 2-D normalized full gradient of gravity anomaly

Numerous geophysical studies have revealed the lithospheric structure of the Qiangtang and the Songpan-Ganzi terranes in the eastern Tibetan Plateau. However, crust–mantle evolution and crustal response to the Indian lithospheric subduction are still controversial. Answering these questions requires additional information regarding crustal structure. In this study, the 2-D normalized full gradient (NFG) of the Bouguer gravity anomaly was used to investigate anomalous sources and interpret the crustal structure underneath the Qiangtang and Songpan-Ganzi terranes. The NFG-derived structures with low-order harmonic numbers (N = 33 and N = 43) showed that an anomalous source beneath the southern Qiangtang terrane had a characteristic northeastward-dipping shape, suggesting the northeastward motion of the crustal material induced by underthrusting Indian lithospheric mantle. The NFG images with harmonic number N = 53 showed a large-scale anomalous source in the lower crust of the transformational zone from the Qiangtang terrane to the Songpan-Ganzi terrane, consistent with thickening crust and resistance of lower crustal flow. The anomalous source demonstrated by the NFG results with harmonic number N = 71, located in the upper crust underneath the Ganzi-Yushu fault, suggested a seismogenic body of the 2010 MW6.9 Yushu event.

Imaging the crustal structure beneath the Yinchuan Basin in the western north China Craton using normalized full gradient and 3D gravity inversion

• The crustal structure beneath the Yinchuan Basin is apparently heterogeneous. • The Yellow River fault is divided into two segments, with the boundary at Yongning. • The primary causative structure of the 1739 Pingluo earthquake is the Yinchuan fault. The Yinchuan Basin is located along the transition belt between the Alxa Massif and Ordos Basin, and is characterised by a complex geological structure. However, several important scientific problems remain unresolved, such as, the causative fault of the 1739 Pingluo Ms 8.0 earthquake. In order to provide new insight into the geodynamic processes, the normalized full gradient (NFG) method and 3-D gravity inversion are utilised to image the crustal structure beneath the Yinchuan Basin in the study. The NFG results indicate that the upper crustal structure is complex, particularly at depths shallower than 20 km. The inversion results infer that the locations of large faults are consistent with the high–low gradient zones in horizontal direction. The integrating NFG and density contrasts imaging results reveal that the south-western boundary of the Ordos Basin is the Yellow River Fault which is divided into two segments with the boundary at Yongning; the East Helanshan and Qingtongxia–Guyuan faults are the south-eastern boundary of the Alxa Massif; the Yinchuan fault is the causative fault of the 1739 event and the focal depth of the event is ∼15 km. These findings provide a scientific basis for studying the crustal dynamics and seismogenic mechanisms of strong earthquakes.

Estimating the location of a causative body from a self-potential anomaly using 2D and 3D normalized full gradient and Euler deconvolution

Changes in the size and depth of sources greatly affect self-potential (SP) anomalies. Therefore, it is important to determine the location of the source accurately. In the present study, applications of the normalized full gradient (NFG) method and Euler deconvolution (EUD) were described to determine the location of the sphere-like SP body as complementary approaches to other optimization algorithms. The NFG and EUD methods were tested on synthetic, noise-free, and noisy anomalies caused by sphere-like models in two-dimensional (2D) and three-dimensional (3D) cases. Subsequently, the methods were applied to real field data. The importance of the present study lies in the fact that it is the first 3D application of these methods to the SP anomaly caused by the sphere-like model in the literature. In order to determine the optimum harmonic number in the NFG method, a new criterion was used instead of the usual trial-and-error method, providing more reliable selection possibilities. In a similar way, average values were used to determine the window size accurately in the EUD method. The test results of the synthetic and real field models were satisfactory. They showed that both methods are applicable to determine the location of sphere-like structures, such as ore deposits, in self-potential surveys.

The Geothermal Potential of Büyük Menderes Graben Obtained by Combined 2.5-D Normalized Full Gradient Results

In this study, the normalized full gradient (NFG) method was applied to the Bouguer gravity data for western Anatolia to identify the locations of the structures and the variations within the mediums. The NFG values were calculated for different harmonics using Bouguer gravity profile values, and the locations of possible structures were determined. In the next step, for analyzing the continuity of these structures in detail, 2.5-D NFG maps were created by combining the NFG results of the profiles for the same harmonics. Additionally, the relationship between the structures obtained in this study and the geothermal sources was examined. Based on the study results, the geothermal capacity of the region was estimated using the locations and the depths of the wells at the surroundings of Kizildere-Saraykoy. Thus, the possible fields with higher geothermal potential were identified throughout the region. The structure borders obtained in this study were also evaluated with respect to the earthquakes that have occurred in Aydin and Denizli cities that contain high-temperature geothermal basins, and it was found that the regions, which feed the geothermal sources, are either non-seismic or represent low seismicity.

Structure of giant buried mud volcanoes in the South Caspian Basin: Enhanced seismic image and field gravity data by using normalized full gradient method

Defining the root zone of mud volcanoes (MVs), structural interpretation, and geologic modeling of their body is a problematic task when only seismic data are available. We have developed a strategy for integration of gravity and seismic data for better structural interpretation. Our strategy uses the concept of the normalized full gradient (NFG) for integration of gravity and seismic data to define geometry and the root zone of MVs in the southeast onshore of the Caspian Sea. Our strategy will increase the resolution of the seismic envelope compared with the conventional Hilbert transform. Prior to interpretation, we applied the NFG method on field gravity data. First, we perform a forward-modeling step for accurate NFG parameter definition. Second, we estimate the depth of the target, which is the root zone of the MV here. Interpretation of field gravity data by optimized NFG parameters indicates an accurate depth of the root zone. Subsequently, we apply the NFG method with optimized parameters on a 2D seismic data. Application of our strategy on seismic data will enhance resolution of the seismic image. The depth of the root zone and the geometry of the MV and mud flows was interpreted better on the enhanced image. It also illustrates the complex structure of a giant buried MV, which was not well-interpreted on conventional seismic image. Interpretation of the processed data reveals that the giant MV had lost its connection to its reservoir, whereas the other MV is still connected to the mud reservoir. The giant MV is composed of complex bodies due to pulses in the mud flows. Another MV in the section indicates narrow neck with anticline and listric normal faults on its top. Thus, application of the NFG concept on seismic image could be considered as an alternative to obtain enhanced seismic image for geologic interpretation.

Salt dome boundary detection in seismic image via resolution enhancement by the improved NFG method

Accurate geological modeling of subsurface structures with all available geophysical data is a challenging task in geo-exploration studies. Concern in precise modeling will increase by increasing geological complexity of subsurface structures such as salt dome. Integrating various sources of geophysical data will reduce uncertainty in geological modeling in complex media. In this study, we introduce an integrated strategy for more appropriate detection of salt boundary in seismic image, by applying the normalized full gradient (NFG) method, used in processing of potential field data. In the proposed strategy, we initially, analyzed sensitivity of the NFG parameters by derivation of a synthetic model. Parameter analysis and optimization showed dependency of geometrical properties of the geological target to the harmonic number in the NFG method. Afterwards, seismic traces were processed by the NFG method. Results showed increase in vertical resolution of seismic envelope compared to the result of the well-known Hilbert Transform. The proposed strategy was applied on a synthetic seismic data contains complex salt model. Results have shown that application of the proposed strategy produced higher resolution seismic image compared to the Hilbert Transform method. The method also was applied on a field seismic data with a complex salt dome from southwest of Kazakhstan. Seismic image obtained by the integration procedure could better exhibit body of the salt dome, as well as better interpretation of faults, layer boundary truncation, salt bottom and subsalt layers. Thus, it was concluded that the proposed strategy could be considered as an alternative to resolve some of ambiguities in geological interpretation of seismic data in complex geological settings.

Crustal structure of the southeastern Tibetan Plateau from gravity data: New evidence for clockwise movement of the Chuan–Dian rhombic block

The crustal deformation beneath the Chuan–Dian rhombic block (CDB) and surrounding regions has been studied in geological and geodetic methods, and provide important insights into the kinematics and dynamics about the clockwise movement of this tectonic block. In this work, we present images of the normalized full gradient (NFG) of the Bouguer gravity anomalies from five gravity profiles across the boundary faults of the CDB measured in recent years, and investigate the distribution characteristics of the crustal anomalous bodies along the profiles. Firstly, an anomalous body with eastward dipping exist beneath the Xianshuihe fault, suggesting that crustal mass move to east. Secondly, near the Xiaojiang fault, two anomalous bodies dip westward with depth increasing. The inferred movement direction of the north one is from west to east, and the south one is from east to west. Thirdly, anomalous bodies on the northeast and southwest sides of the Red River fault suggest the directions of crustal movement is from northeast to southwest. These results are also consistent with GPS solutions, and provide gravity evidence for crustal deformation of the CDB with clockwise rotation.

Amplitude inversion of the 2D analytic signal of magnetic anomalies through the differential evolution algorithm

In this work, analytic signal amplitude (ASA) inversion of total field magnetic anomalies (TMA) has been achieved by differential evolution (DE) which is a population-based evolutionary metaheuristic algorithm. Using an elitist strategy, applicability and effectiveness of the proposed inversion algorithm have been evaluated through the anomalies due to both hypothetical model bodies and real isolated geological structures. Some parameter tuning studies relying mainly on choosing the optimum control parameters of the algorithm have also been performed to enhance the performance of the proposed metaheuristic. Since ASAs of magnetic anomalies are independent of both ambient field direction and the direction of magnetization of the causative sources in two-dimensional (2D) case, inversions of synthetic noise-free and noisy single model anomalies have produced satisfactory solutions showing the practical applicability of the algorithm. Moreover, hypothetical studies using multiple model bodies have clearly showed that DE algorithm is able to cope with complicated anomalies and some interferences from neighbouring sources. The proposed algorithm has been then used to invert a small- (120 m) and a large-scale (40 km) magnetic profile anomalies of an iron deposit (Kesikkopru-Bala, Turkey) and a deep-seated magnetized structure (Sea of Marmara, Turkey), respectively to determine depths, geometries and exact origins of the source bodies. Inversion studies have yielded geologically reasonable solutions which are also in good accordance with the results of normalized full gradient (NFG) and Euler deconvolution (EUD) techniques. Thus, we propose the use of DE for not only the amplitude inversion of 2D analytical signal of magnetic profile anomalies having induced or remanent magnetization effects but also the low-dimensional data inversions in geophysics.

Normalized full gradient of full tensor gravity gradient based on adaptive iterative Tikhonov regularization downward continuation

Normalized full gradient (NFG) method depends on the downward continuation of NFG values of gravity data. In this paper, I deduce an improved NFG method of full tensor gravity gradient (FTG) data by using x-, y- and z-directional analytic signals of FTG data. During the calculation, I introduce the adaptive iterative Tikhonov regularization downward continuation method in the calculation process to improve the stability of the NFG method. The new approach is tested on various model data with and without noise, and satisfactory results are obtained. It demonstrates that the new NFG method of FTG can improve the lateral resolution and describe the gravity bodies in more detail. In addition, the method is applied to a real field FTG data acquired over the Vinton Salt Dome, Louisiana, USA. All results demonstrate that the new method can accurately detect the depth of the geologic sources while providing enhanced information of the sources simultaneously.

Improved normalized full-gradient method and its application to the location of source body

The normalized full-gradient (NFG) method is useful for estimating the source position in semi-quantitative gravity interpretations. Several studies using the NFG method to recover source parameters have shown that this method can reliably locate sources but in practice it is difficult to choose the optimal number of harmonics to act as a smooth filter. In this study, a versatile method was developed for determining the optimal number of harmonics for the NFG method. The optimum harmonic number is determined by analyzing two combined curves: the energy ratio curve of the reconstructed anomalies and the depth curve, along with the change in the number of harmonics. This method was tested and compared with the conventional method on synthetic models, with satisfactory results. When applied to real data from a gravity profile normal to the mid-point of an elongated salt wall in the Mississippi Salt Basin, the estimated source position was consistent with seismic information and previous studies.

Collocated cokriging of iron deposit based on a model of magnetic susceptibility: a case study in Morvarid mine, Iran

This paper describes a general framework of incorporating magnetic data as prior information in the modeling of an iron deposit based on sparse drilling boreholes. Since multivariate kriging of a sparse pattern of drilling yields lower uncertainty in mineral deposit modeling, a model of magnetic susceptibility as a second variable which has an acceptable level of correlation with the first variable, iron, is used to make a model of iron grade. Before applying an inversion technique to recover a 3D model of magnetic susceptibility, the normalized full gradient (NFG) approach is used to generate an approximate visualization of probable magnetic anomaly. Based on the NFG result, we have acquired appropriate dimensions of composites to apply the geophysical inversion method. The subsurface of the desired area of the magnetic anomaly is divided into a mesh with a large number of rectangular prisms (composites) with unknown susceptibilities. The recovered magnetic susceptibility model which has a correlation equal to 0.543 with the iron grade is used as a second variable in order to apply a multivariate set of kriging equations. The collocated cokriging method as a modified version of the cokriging system is used to interpolate the iron grade based on a model of magnetic susceptibility. This method has been applied to a real case study in Zanjan Province of Iran, showing its effectiveness when we encounter with such lack of drilled boreholes in the study area.

Structure of the Hellenic Subduction Zone from Gravity Gradient Functions and Seismology

The Normalized Full Gradient (NFG) method has widespread applications in the analysis of potential fields, especially the gravity and magnetic fields. This method is used to identify the lateral and horizontal density variations in the crust and lithosphere. In this study, the NFG method was applied to the gravity data of the Cretan Arc and its surroundings. Because of the tectonic features of the eastern Mediterranean, the Cretan Arc and the neighboring areas are seismically very active. Especially the subduction zone and the complicated crustal features have been defined applying many different geophysical methods. In this study, first the NFG method is tested with synthetic prisms (two cubes). After that, the NFG method was applied to the Bouguer gravity data of the Cretan Arc and its subduction zone (Hellenic subduction zone) and Hellenic subduction zone was defined with the foci depth data (USGS) along the south–north direction. Thus, geometry of the focal depth distribution has been created to determine probable media depths and their localizations. According to the NFG results, vertical structural transitions were observed at a depth ranging between 10 and 180 km. Also, these results were compared with the foci depth model and the other results of the related publications. Finally, some considerations in vertical solution with the NFG method have been presented and locations of the different structures at horizontally have been defined with application of the NFG method.

Detection of High-Potential Oil and Gas Fields Using Normalized Full Gradient of Gravity Anomalies: A Case Study in the Tabas Basin, Eastern Iran

The normalized full gradient (NFG) represents the full gradient of the gravity anomaly at a point divided by the average of the full gradient at the same point. The NFG minimum between two maxima in an NFG section or a closed minimum surrounded by closed maxima on an NFG map may indicate density-deficient anomalies closely related to possible oil–gas reservoirs. On a cross-section, closed minima can be used to estimate the depth to centers of possible hydrocarbon reservoirs. The NFG map can also be used to locate oil–gas exploratory wells for estimation of the depth of possible reservoirs. The objective of this paper is to use two and three-dimensional (2D and 3D) NFG on gravity data of the Tabas basin in Yazd province, eastern Iran. A hypothetical model is first considered to explore the NFG characteristics and their relationship with the geometry of the model. The physical properties of the model are then studied to simplify the interpretation of real data. Finally 2D and 3D NFG models are developed for real gravity data to predict the location of any possible high potential oil–gas reservoirs. The results obtained indicate two zones in the northern and central parts of the Tabas basin suitable for hydrocarbon prospecting. However, the favorable zone located in the middle of the basin in which anticline E is detected at a depth of 5–7 km is more important for the purpose of hydrocarbon exploration.

Isostasy of the Eastern Anatolia (Turkey) and Discontinuities of its Crust

This paper presents a probable isostatic model of the East Anatolian Region, which lies in a belt of significant plate movements. Probable locations of the horizontal and vertical discontinuities in the crust structure were determined using the normalized full gradient (NFG) method. For the purpose of explaining the mechanism that supports topography corresponding to the crust thickness in the region, calculations of effective elastic thickness (T e) were carried out initially by utilizing admittance and misfit functions. According to these results, the effective elastic thickness value obtained was less than the crust thickness, even though the isostatic model does not conform with the Airy model. Consequently, it was assumed that there could be problems beneath the crust. Hence, the NFG method was applied on the Bouguer gravity data of the region in order to investigate probable discontinuities in the crust structure. According to the NFG results, vertical structural transitions were observed at a depth ranging between 10 and 30 km, which begin immediately north of the Bitlis Zagros Suture Zone (BZSZ) and continue in a northerly direction. The relationship between the effective elastic thickness (T e; 13 km in average as determined in the last stage), and the seismogenic zone in the region was investigated. If the T e value happens to be less then the crustal thickness, then one can say that there are problems in the crustal structure of the region similar to Eastern Anatolia. Indeed, when NFG results of the study area are examined, numerous vertical and horizontal discontinuities in the crust can be observed. These discontinuities, which correspond to low Bouguer gravity anomalies and shallow focal depth-earthquakes, are probably the source of the factors which rule the tectonic mechanism of the region.

Application of the Normalized Full Gradient (NFG) Method to Resistivity Data

This paper proposes the application of the normalized full gradient (NFG) method to resistivity studies and illustrates that the method can greatly reduce the time and work load needed in detecting buried bodies using resistivity measurement. The NFG method calculates resistivity values at desired electrode offsets by extrapolation of a function of resistivity measurements (i.e. the gradient) to other depth levels using resistivity measurements done at one electrode offset only. The performance and reliability of the NFG method is tested on laboratory and field resistivity data from two sites by comparing the trend of the resistivity values at six or more electrode offsets, with the trend calculated at the same electrode offsets using the NFG method. The first area is in Rize (NE Turkey) where a resistivity survey was conducted to locate a metal tailings pipeline in unconsolidated gravel deposited by a nearby stream. The second field site is in Trabzon (NE Turkey), where the purpose of the resistivity survey was to map the boundaries of a landslide in clay, marl and geologic units.

Estimation of depth to salt domes from normalized full gradient of gravity anomaly and examples from the USA and Denmark

We present an estimation of depth of anomalous bodies using normalized full gradient (NFG) of gravity anomaly. Maxima in the NFG map can locate the bodies and indicate their depth. Model calculation using a sphere and application of the NFG method to gravity anomalies over salt domes in the USA and Denmark shows effectiveness of the method. However, the accuracy of depth estimation strongly depends on the number of term N in the Fourier series used to calculate the NFG. An optimum N for the calculation can be given from a test.

Application of Normalized Full Gradient Method to Self Potential (SP) Data

Recently, Normalized Full Gradient (NFG) method has widespread applications to natural potential fields, especially in gravity and magnetic. In this study, usage of NFG in Self-Potential (SP) data evaluation is tested. Results are compared to other SP interpretation methods. The NFG method is applied to synthetic and field SP data. As a consequence of application of the method to the anomalies of spherical, cylindrical and vertical sheet models, whose theoretical structures are explicit, the structures were found very close to their actual locations. In order to see the capability of the method in detecting the number of sources, NFG method was applied to different spherical models at different depths and locations. The least-squares inverse solution was applied to the same models and NFG method was found more powerful in detecting model structure. Sensitivity of NFG method for application to noisy data is also tested. An anomaly is generated by adding a random noise to two close sphere SP anomalies. The method seems to work for the two close spheres at high S/N ratio. Then, NFG method was applied to two field examples. The first one is the cross section taken from the SP anomaly map of the Ergani-Suleymankoy (Turkey) copper mine. The depth of the mineral deposit at that site was found about 38 m from the ground level. This result is well matched to previous studies. NFG was also applied to SP data from Seferihisar Izmir (Western Turkey) geothermal field and the location of the point source was determined. The field data of this site have already been modeled by the thermoelectric source (coupling) solution method. When these two methods are compared, they seem to support each other. It is concluded that the NFG method works perfectly when the structure model is simple. It is observed that natural potential sources close to earth’s surface are identified by the method more accurately at greater harmonics, while deep sources are identified at lesser harmonics. It produces reasonable results for noisy multi-source models than the other parameter identification methods (inverse solution, power spectrum, etc.).

Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example

The Normalized Full Gradient (NFG) method which was put forward about 50 years ago has been used for downward continuation of gravity potential data, especially in the former Union of Soviet Socialist Republics. This method nullifies perturbations due to the passage of mass depth during downward continuation. The method depends on the downwards analytical continuation of normalized full gradient values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field. This method has been used in various petroleum and tectonic studies. The Trapeze method was used for the determination of Fourier coefficients during the application of this method. No other techniques for calculating these coefficients have been used. However, the Filon method was used for the determination of Fourier coefficients during the application of the NFG method in this work. This method, rather than the Trapeze method, should be preferred for indicating abnormal mass resources at the lower harmonics. In this study, the NFG method using the Filon method has been applied the first time to theoretical models of gravity profiles as example field at the Hasankale-Horasan petroleum exploration province where successful results were achieved. Hydrocarbon presence was shown on the NFG sections by the application of NFG downward continuation operations on theoretical models. Important signs of hydrocarbon structure on the NFG section for field and model data at low harmonics are obtained more effectively using this method.

Depth Estimates for Slingram Electromagnetic Anomalies from Dipping Sheet-like Bodies by the Normalized Full Gradient Method

The Normalized Full Gradient (NFG) method was proposed in the mid-1960s and was generally used for the downward continuation of the potential field data. The method eliminates the side oscillations which appeared on the continuation curves when passing through anomalous body depth. In this study, the NFG method was applied to Slingram electromagnetic anomalies to obtain the depth of the anomalous body. Some experiments were performed on the theoretical Slingram model anomalies in a free space environment using a perfectly conductive thin tabular conductor with an infinite depth extent. The theoretical Slingram responses were obtained for different depths, dip angles and coil separations, and it was observed from NFG fields of the theoretical anomalies that the NFG sections yield the depth information of top of the conductor at low harmonic numbers. The NFG sections consisted of two main local maxima located at both sides of the central negative Slingram anomalies. It is concluded that these two maxima also locate the maximum anomaly gradient points, which indicates the depth of the anomaly target directly. For both theoretical and field data, the depth of the maximum value on the NFG sections corresponds to the depth of the upper edge of the anomalous conductor. The NFG method was applied to the in-phase component and correct depth estimates were obtained even for the horizontal tabular conductor. Depth values could be estimated with a relatively small error percentage when the conductive model was near-vertical and/or the conductor depth was larger.