Continuous wavelet transform,theoretical aspects and application to aeromagnetic data at the Huanghua Depression,Dagang Oilfield,China

We use the continuous wavelet transform based on complex Morlet wavelets, which has been developed to estimate the source distribution of potential fields. For magnetic anomalies of adjacent sources, they always superimpose upon each other in space and wavenumber, making the identification of magnetic sources problematic. Therefore, a scale normalization factor, a^?n, is introduced on the wavelet coefficients to improve resolution in the scalogram. By theoretical modelling, we set up an approximate linear relationship between the pseudo‐wavenumber and source depth. The influences of background field, random noise and magnetization inclination on the continuous wavelet transform of magnetic anomalies are also discussed and compared with the short‐time Fourier transform results. Synthetic examples indicate that the regional trend has little effect on our method, while the influence of random noise is mainly imposed on shallower sources with higher wavenumbers. The source horizontal position will be affected by the change of magnetization direction, whereas the source depth remains unchanged. After discussing the performance of our method by showing the results of various synthetic tests, we use this method on the aeromagnetic data of the Huanghua depression in central China to define the distribution of volcanic rocks. The spectrum slices in different scales are used to determine horizontal positions of volcanic rocks and their source depths are estimated from the modulus maxima of complex coefficients, which is in good accordance with drilling results.     

Age of the source of the Jarrafa gravity and magnetic anomalies offshore Libya and its geodynamic implications

The interpretation of the Jarrafa magnetic and gravity highs, NW Libyan offshore, suggests that it may be caused by a body of high-density and high magnetization. Analysis of their power spectra indicates two groups of sources at: (1) 2.7 km depth, probably related to the igneous rocks, some of which were penetrated in the JA-1 borehole, (2) 5 km depth, corresponding to the top of the causative body and (3) 10 km depth, probably referring to the local basement depth. The boundary analysis derived from applied horizontal gradient to both gravity and magnetic data reveals lineaments many of which can be related to geological structures (grabens, horsts and faults).The poor correlation between pseudogravity fields for induced magnetization and observed gravity fields strongly suggests that the causative structure has a remanent magnetization (D = −16°, I = 23°) of Early Cretaceous age, fitting with the opening of the Neo Tethys 3 Ocean.Three-dimensional interpretation techniques indicate that the magnetic source of the Jarrafa magnetic anomaly has a magnetization intensity of 0.46 A/m, which is required to simulate the amplitude of the observed magnetic anomaly. The magnetic model shows that it has a base level at 15 km.The history of the area combined with the analysis and interpretation of the gravity and magnetic data suggests that: (1) the source of the Jarrafa anomaly is a mafic igneous rock and it may have formed during an Early Cretaceous extensional phase and (2) the Jarrafa basin was left-laterally sheared along the WNW Hercynian North Graben Fault Zone, during its reactivation in the Early Cretaceous.     

离散小波变换与重力异常多重分解

小波变换多尺度分析是位场分解的有益工具.离散二维小波变换产生的低阶小波细节具有尺度不变的特征,它们不随小波变换的总阶数改变,而总阶数的增加仅增加高阶小波细节的个数和改变最后的高阶逼近.因此,用小波变换分解重力异常时,可根据地质目的来组合小波细节,从而实现有地质意义的异常分解.实验表明,用小波变换分解的重力异常小波细节,同样起到功率谱分解的作用,用分解之后的小波细节功率谱可以精确确定场源的埋深.中国大陆科学钻探场地的重力异常分解给出局部异常分解的典型例子.     

WAVELET TRANSFORM ANALYSES OF FAULTS DETECTION ON ISOSTATIC GRAVITY ANOMALIES: A CASE STUDY FROM THE QAIDAM BASIN AND ITS ADJACENT AREAS

Isostasy is used to describe a condition to which the Earth's crust and mantle tend, in the absence of disturbing forces. Eliminating the gravity effect of crust, isostatic gravity anomalies contain abundant geological structure information, which can be extracted by edge detection methods of gravity or magnetic anomalies. In order to accurately obtain the edge information, a great variety of methods, such as analytical signal amplitude, tilt angle, theta map θ, etc., have been proposed by domestic and international scholars, and many significant advances have been made in recent days. However, each method has its advantages and disadvantages. Wavelet transform is an effective method developed in recent years. It has the enhanced noise resistance and a feature of multi-scale decomposition, and can be used to identify more detailed information of edge. Here with the aim of demonstrating its effectiveness in faults detection, we established a theoretical geological model, which consists of five geological bodies. The geological bodies with different density present a fault zone and the areas on its sides, as well as two geological bodies with different geological properties. We calculated the gravity anomalies caused by this model, in addition, we added 5% Gaussian noise to the gravity anomalies for a comparative analysis to analyze the effects of wavelet transform on edge detection. Finally, we applied wavelet transform method to the decomposition of isostatic gravity anomalies, obtained 1^st to 5^th order wavelet transform details of the gravity anomalies, and compared with the well-studied faults in the Qaidam Basin and its adjacent areas. The results obtained by wavelet transform matched well with the known faults, the anomalies of different order denote the location of different fault zone(e.g. the Tanan Fault is nearly invisible on the original and the first order isostasy gravity anomalies map, but is well expressed on the second order isostasy gravity anomalies map; The apparent details of the 4^th and 5^th indicate that faults in front of the Saishiteng-Xitieshan Shan are deep faults and they are likely to distribute continuously in the deep underground). Besides, we calculated the estimated depth of isostasy gravity anomalies of different order through power spectrum analysis as well, finding that different faults extend to different depth. For example, the Danghe-Nanshan Fault and the Southern Fault in the middle Qilian Shan are 10km in depth approximately, but the faults in front of the Saishiteng-Xitieshan Shan are more than 70km in depth. In addition, we made two comparative studies, the first one is comparing the results mentioned above with the result through wavelet transform of Bouguer gravity anomalies. The second one is comparing with the results through other edge detection methods of isostatic gravity anomalies. In spite of the inconformity between anomalies and the faults to some extent, which is likely caused by the change of lithology or faults distribution in the deep underground, we finally found that:more subtle details induced from faults can be detected from isostatic gravity anomalies by using wavelet transform because of its feature of multi-scale decomposition. The wavelet transform method is proved to be more accurate and reliable(at least in the Qaidam Basin and its adjacent areas)comparing with other methods.     

Crustal Configuration of the Northwest Himalaya Based on Modeling of Gravity Data

The gravity response and crustal shortening in the Himalayan belt are modeled in detail for the first time in the NW Himalaya. The Bouguer gravity anomaly along a ~450-km-long (projected) transect from the Sub-Himalaya in the south to the Karakoram fault in the north across the Indus-Tsangpo Suture Zone is modeled using spectral analysis, wavelet transform and forward modeling. The spectral analysis suggests three-layer interfaces in the lithosphere at 68-, 34- and 11-km depths corresponding to the Moho, the Conrad discontinuity and the Himalayan decollement thrust, respectively. The coherence, admittance and cross spectra suggest crustal shortening because of convergence compensated by lithospheric folding at 536- and 178-km wavelength at the Moho and the upper-crustal level. An average effective elastic thickness of around 31 km is calculated using the coherence method. The gravity data are modeled to demarcate intracrustal to subcrustal regional thrust/fault zones. The geometrical constraints of these faults are obtained in the space scale domain using the wavelet transform, showing good correlation with the major tectonic boundaries. The crustal configuration along the transect shows how the Moho depth increases from 45 to 80 km towards the north with the locus of flexure of the Indian crust beneath the Higher Himalayan zone. The combination of forward modeling and wavelet analysis gives insight into the subsurface extent and geometry of regional structures across the NW Himalaya.     

Shallow and Deep Structure of a Supradetachment Basin Based on Geological,Conventional Deep Seismic Reflection Sections and Gravity Data in the Buyuk Menderes Graben,Western Anatolia

The Buyuk Menderes Graben is a depression in the Menderes core complex of western Turkey. The region is one of the most rapidly deforming regions of continental crust in the world and has exceptionally high seismic activity. In this study, shallow and deep seismic studies were conducted at the Buyuk Menderes graben. These studies included surface geological mapping and two seismic reflection sections. Detailed modelling was performed with the seismic study. In addition to these, a moving windows power spectrum was applied to the Bouguer gravity profile data of the study area. Since no deep well is available in this area, the geological interpretation of the seismic stratigraphy is based on the correlation with the surface geology, this was combined with the major reflections and the seismic facies observed along the profiles, and, thus, four main seismic units can be distinguished in the basin fill. Structural features of the basin is driven by a complex extensional faults system, consisting of a low-angle, S-dipping Buyuk Menderes detachment and by its synthetic and antithetic splays, bordering the opposite flanks of the basin. As a result of conventional deep seismic reflection sections and gravity data, three layers were defined in the study area. The first layer occurs at a thickness of 6 km, and the second layer is between 13 and 18 km. The third layer is at ~33 km and may also emphasize Moho depth. The Buyuk Menderes graben has three clear reflectors which are base sediments, brittle-ductile transition, Moho and faults that show a half-graben floored by a detachment. The Moho depth is comparable with previous estimates. According to the results obtained, Bouguer gravity and seismic results are very much consistent with each other. It was observed that at the depths determined from seismic and gravity data, the distribution percentage of earthquake focal depths also rises.     

Interpretation of regional aeromagnetic data by the scaling function method: the case of Southern Apennines (Italy)

A complex aeromagnetic anomaly in Southern Apennines (Italy) is analysed and interpreted by a multiscale method based on the scaling function. We use multiscale methods allowing analysis of a potential field along ridges, which are lines defined by the position of the extrema of the field at the considered scales. The method developed and applied in this paper is based on the study of the scaling function of the total magnetic field. It allows recovering of source parameters such as depth and structural index. The studied area includes a Pleistocene volcanic structure (Mt. Vulture) whose intense dipolar anomaly is superimposed on a longer wavelength regional anomaly. The interpretation of ridges of the modulus of the analytic signal at different altitude ranges allows recognition of at least three distinct sources between about 5 km and 20 km depth. Their interpretation is discussed in light of borehole data and other geophysical constraints. A reasonable geological model for these sources indicates the presence of intrusions, probably linked to the past activity of Mt. Vulture.     

Euler homogeneity equation along ridges for a rapid estimation of potential field source properties

The Euler deconvolution is the most popular technique used to interpret potential field data in terms of simple sources characterized by the value of the degree of homogeneity. A more recent technique, the continuous wavelet transform, allows the same kind of interpretation. The Euler deconvolution is usually applied to data at a constant level while the continuous wavelet transform is usually applied to the points belonging to lines (ridges) connecting the m -order partial derivative modulus maxima of the upward-continued field at different altitudes in the harmonic region. In this paper a new method is proposed that unifies the two techniques. The method consists of the application of Euler's equation to the ridges so that the equation assumes a reduced form. Along each ridge the ratio among the m -order partial derivative of the field and its vertical partial derivative, for isolated source model, is a straight line whose slope and intercept allows the estimation of the source depth and degree of homogeneity. The method, strictly valid for single source model, has also been applied to the multisource case, where the presence of the interference among the field generated by each single source causes the path of the ratio to be no longer straight. The method in this case gives approximate solutions that are good estimations of the source depth and its degree of homogeneity only for a restricted range of altitudes, where the ratio is approximately linear and the source behaves as if it were isolated.     

分析研究基于小波分析与谱分析提高重力异常的分辨能力

重力数据是所有地下场源产生的重力场的叠加,探测对象经常被淹没在区域背景场之中,因此剩余异常的分离对于重力资料研究至关重要,而近来被引入位场领域的小波算子作为了滤波器和场源分析工具,在这里我们分析研究基于小波分析与谱分析的二维离散小波变换用于提高重力异常的分辨能力,再现出由简单形状场源描述密度不均匀的几何特征.本文先介绍二维多分辨率分析小波的基本理论及其提升算法,利用对数功率谱估计平均深度方法理论,接着对理论模型数据进行多尺度异常分解,估计地质体的形状、大小和深度,最后又对实测重力数据进行分析,并与传统常规方法进行比较分析,结果表明对于实际数据分析其方法也是具有可行性的.     

The theory of the continuous wavelet transform in the interpretation of potential fields: a review

We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreau et al . in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal-to-noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.     

贺兰山—银川地堑及邻区重力异常特征及构造意义

贺兰山—银川地堑及邻区地质结构复杂,对该区域深浅结构特征的研究具有重要意义.本文采用重力归一化总梯度成像和二维小波多尺度分解方法对研究区内重力异常进行了垂向和横向构造分析.重力归一化总梯度成像结果显示高低转换带的倾角、倾向与地质上的贺兰山东麓断裂、银川断裂和黄河断裂分布吻合较好,贺兰山西麓断裂与贺兰山东麓断裂汇交深度约18 km,银川断裂与黄河断裂汇交深度约25 km;二维小波多尺度分解成像结果表明正谊关断裂、贺兰山西麓断裂、芦花台断裂和银川断裂为上地壳断裂,贺兰山东麓断裂、青铜峡—固原断裂以及黄河断裂为下地壳断裂,且这三大断裂可能分别是阿拉善地块东南边界和鄂尔多斯地块西南边界;1739年平罗M 8.0古地震震中与银川断裂在重力剖面深度约15 km汇交,其垂向高低梯度为强变形带,同时古地震震中位于重力正负异常转换部位的低值区,据此可推断此次古地震的发震构造是银川断裂.这些结论可提高对贺兰山—银川地堑及邻区地质结构的认识,为该区地壳动力学过程及强震的孕震机理研究提供一定的科学依据.     

渭河盆地及邻区重力异常小波多尺度分解与解释

基于EGM2008重力场模型计算获得了渭河盆地及邻区布格重力异常。采用小波多尺度分解方法对布格重力异常进行了4阶小波逼近和小波细节分解,同时基于平均径向对数功率谱方法定量化地计算出1~4阶小波细节和小波逼近所对应的场源平均埋深。结合区域地质和地震资料,对获得的重力场结果进行分析,得到如下结论:①鄂尔多斯地块、渭河盆地、秦岭造山带3个一级构造单元的布格重力异常之间存在明显差异;构造区内部重力异常也存在横向的显著差异。布格重力异常的走向、规模、分布特征与二级构造区及主要的断裂具有一定的对应关系。②渭河盆地及邻区布格重力异常1~4阶细节对应4~23 km不同深度的场源信息,鄂尔多斯地块南缘东、西部的地壳结构存在明显的差异;渭河盆地凹陷、凸起构造区边界清晰,断裂边界与重力异常边界具有较好的一致性;秦岭造山带重力异常连贯性不好,东、西部重力异常变化特征表现出明显的差异。③渭河盆地及邻区布格重力异常分布与莫霍面埋深具有非常明显的镜像关系。渭河盆地及邻区地震主要分布在六盘山—陇县—宝鸡断裂带、渭河断裂与渭南塬前断裂交汇处、韩城断裂与双泉—临猗断裂交汇处。渭河盆地及邻区重力异常主要由中上地壳剩余密度体所影响,这可能是该区地震以浅源地震为主的主要原因。     

A view of tectonic structure and gravity anomalies of Hatay Region Southern Turkey using wavelet analysis

In this study, we demonstrate wavelet analysis as a method of delineating the boundaries of subsurface geological structures. We applied wavelet transform to Bouguer anomaly data of the Cilicia Region and adjacent areas. The residual anomalies are the results of various depth and other properties of buried structures on the gravity anomaly map. The superposition of anomaly of the underground structures with different properties such as depth, density and size, increases the complexity of the overall system. Thus the extraction of the desired properties from the anomaly map becomes difficult. Different separation techniques are used to solve this problem. Wavelet transform is one of these modern approaches. Here, we tested various types of wavelet transform modeling on synthetic examples and then applied them to the gravity anomaly map of the Cilicia Region in Turkey. We have detected the borders of the Hatay Region in southern Turkey and proposed the tectonic model of this real complex structure using the wavelet transformation. The most important result we have found is the presence of a triple junction near the Hatay region.     

羌塘地块中部南北向断裂的构造特征及其动力学意义

青藏高原内部除大规模的东西向走滑断裂以外,另一个显著的地质特征就是在藏南及高原腹地广泛发育东西向的伸展构造,形成走向近南北的断裂构造,如亚东一谷露裂谷带及双湖断裂.伸展构造已经成为青藏高原地质研究的一个焦点问题.在羌塘地块89°E附近存在明显的低重力、负磁、深度达300 km的低速异常及连通壳幔的高导异常,且地表伴生大规模的新生代火山岩,这些特殊的地质及地球物理场特征的发生位置与地表双湖断裂的位置基本对应.本文通过卫星重力数据的多尺度小波分析结果发现,双湖断裂之下,存在一明显由上地壳一直向下延伸至地幔深部的低重力异常,说明双湖断裂向下延伸深度大,且上下连通性好.结合已有的地质和地球物理资料,认为由于双湖断裂的存在,使得深部幔源岩浆沿断裂构造薄弱带上涌,从而导致羌塘地块之下壳幔温度的升高及大规模部分熔融的发生.     

Interpretation of magnetic and gravity gradient tensor data using normalized source strength – A case study from McFaulds Lake,Northern Ontario,Canada

In this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies. In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices. This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface. Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden.     

用于区域重力场定量解释的多尺度刻痕分析方法

本文介绍一个把小波多尺度分析、表面刻痕分析以及位场频率域解释理论和反演方法结合起来的数据处理、反演解释和信息提取的方法系统.这一方法系统简称为区域重力场多尺度刻痕分析方法,应用于刻画地壳分层的三维密度结构、地壳变形带分布和构造单元分区.多尺度刻痕分析包含频率域重力场场源分层、重力场小波变换多尺度分解、场源分层深度及密度扰动反演、分层刻痕分析和构造边界定位四个子系统.文中扼要地介绍这四个子系统基本原理、方法技术及应用效果.从地球物理探测到大地构造学发现,是一个多学科综合研究的探索过程.要取得重大研究成果,必须研发和组合来自不同学科的多个新方法技术,使多学科综合研究有宽厚的理论支撑.本文介绍的四个子系统组合的理论支撑分别来自应用数学、地球物理学和信息科学.     

北天山中段时变重力场离散小波多尺度分解

利用北天山地区2016～2019年观测的4期流动重力观测资料,分析研究一年尺度的重力场动态变化特征,并利用小波分析方法,将不同场源深度的重力异常进行分离。通过功率谱分析,获取各阶小波重力细节对应的场源深度。研究结果表明,2017年8月9日精河M_S6.6地震前,震中位于负值集中区,四阶小波重力细节显示震中附近出现明显的四象限分布;2020年1月16日库车M_S5.6地震前,震中位于负值区,小波重力细节整体量值较小;功率谱估算的场源近似深度与2次地震的震源深度相近。     

Toward a full multiscale approach to interpret potential fields

The way potential fields convey source information depends on the scale at which the field is analysed. In this sense a multiscale analysis is a useful method to study potential fields particularly when the main field contributions are caused by sources with different depths and extents. Our multiscale approach is built with a stable transformation, such as depth from extreme points. Its stability results from mixing, in a single operator, the wavenumber low‐pass behaviour of the upward continuation transformation of the field with the enhancement high‐pass properties of n‐order derivative transformations. So, the complex reciprocal interference of several field components may be efficiently faced at several scales of the analysis and the depth to the sources may be estimated together with the homogeneity degrees of the field. In order to estimate the source boundaries we use another multiscale method, the multiscale derivative analysis, which utilizes a generalized concept of horizontal derivative and produces a set of boundary maps at different scales. We show through synthetic examples and application to the gravity field of Southern Italy that this multiscale behaviour makes this technique quite different from other source boundary estimators. The main result obtained by integrating multiscale derivative analysis with depth from extreme points is the retrieval of rather effective information of the field sources (horizontal boundaries, depth, structural index). This interpretative approach has been used along a specific transect for the analysis of the Bouguer anomaly field of Southern Apennines. It was set at such scales, so to emphasize either regional or local features along the transect. Two different classes of sources were individuated. The first one includes a broad, deep source with lateral size of 45∼50 km, at a depth of 13 km and having a 0.5 structural index. The second class includes several narrower sources located at shallowest depths, ranging from 3–6 km, with lateral size not larger than 5 km and structural indexes ranging from 1–1.5. Within a large‐scale geological framework, these results could help to outline the mean structural features at crustal depths.     

3D upper crustal density structure of the Deccan Syneclise,Central India

A constrained 3D density model of the upper crust along a part of the Deccan Syneclise is carried out based on the complete Bouguer anomaly data. Spectral analysis of the complete Bouguer gravity anomaly map of the study region suggests two major sources: short wavelength anomalies (<100 km) caused primarily due to the density inhomogeneities at shallow crustal level and long wavelength anomalies (>100 km) produced due to the sources deeper than the upper crust. A residual map of the short wavelength anomalies is prepared from the complete Bouguer anomaly using Butterworth high‐pass filter (100 km cut‐off wavelength). Utilizing the constraints from deep resistivity sounding, magnetotellurics and deep seismic sounding studies, 2.5D density models have been generated along 39 profiles of this region. The mismatch between the calculated response of the a priori 2.5D model with the residual (short wavelength) gravity anomalies is minimized by introducing high‐density intrusive bodies (≥2.81 g/cm³) in the basement. With these 2.5D density models, the initial geometry of our 3D density model, which includes alluvium, Deccan trap, Mesozoic sediment and high‐density intrusive bodies in the basement up to a depth of 7 km (upper crust), is generated. In the final 3D model, Deccan trap extends from 200 m to nearly 1700 m below the 90–150 m thick Quaternary sediment. Further down, the sub‐trappean Mesozoic sediment is present at a depth range of 600–3000 m followed by the basement. The derived 3D density model also indicates six intrusive bodies of density 2.83 g/cm³ in the basement at an average depth of about 4–7 km that best fits the residual gravity anomaly of the study area.