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.     

鄂尔多斯南缘地区重力变化场源特征

以鄂尔多斯南缘地区布格重力异常数据及2014—2017年相对重力观测数据为基础,采用欧拉反褶积方法,对引起重力变化的场源深度进行反演,并对空间分布规律予以解释。通过构建理论模型,反演得到最优模型参数,并对实际数据进行计算和分析。为了减弱和消除欧拉解的发散性,利用水平梯度滤波法优化反演结果。结果表明:①构造指数为1时,适合对相对重力数据进行反演,当滑动窗口选择4—8倍测点间距时,可以获得较为可靠的场源参数;②在主要断裂附近,不同时间尺度的场源呈较好的一致性特征;③引起重力变化的场源深度集中在10—30 km,与鄂尔多斯南缘地区的震源深度基本一致;④不同时间尺度的场源位置相对分散,表明引起重力变化的物质流动具有随机性和波动性。     

Multiridge Euler deconvolution

Potential field interpretation can be carried out using multiscale methods. This class of methods analyses a multiscale data set, which is built by upward continuation of the original data to a number of altitudes conveniently chosen. Euler deconvolution can be cast into this multiscale environment by analysing data along ridges of potential fields, e.g., at those points along lines across scales where the field or its horizontal or vertical derivative respectively is zero. Previous work has shown that Euler equations are notably simplified along any of these ridges. Since a given anomaly may generate one or more ridges we describe in this paper how Euler deconvolution may be used to jointly invert data along all of them, so performing a multiridge Euler deconvolution. The method enjoys the stable and high‐resolution properties of multiscale methods, due to the composite upward continuation/vertical differentiation filter used. Such a physically‐based field transformation can have a positive effect on reducing both high‐wavenumber noise and interference or regional field effects. Multiridge Euler deconvolution can also be applied to the modulus of an analytic signal, gravity/magnetic gradient tensor components or Hilbert transform components. The advantages of using multiridge Euler deconvolution compared to single ridge Euler deconvolution include improved solution clustering, increased number of solutions, improvement of accuracy of the results obtainable from some types of ridges and greater ease in the selection of ridges to invert. The multiscale approach is particularly well suited to deal with non‐ideal sources. In these cases, our strategy is to find the optimal combination of upward continuation altitude range and data differentiation order, such that the field could be sensed as approximately homogeneous and then characterized by a structural index close to an integer value. This allows us to estimate depths related to the top or the centre of the structure.     

塔里木盆地航磁场分析与磁源体结构

本文研究塔里木盆地区域磁异常图的反演及磁源体结构.由于众多异常的叠加和反演固有的多解性,区域磁异常图的准确解释是非常困难的.三维欧拉反褶积是一种确定地质体位置和埋藏深度的自动定量反演方法,比较适用于计算区域磁异常源的埋藏深度.由于大型克拉通沉积盆地地层具有上新下老的规律性,将磁异常源分解为三个深度层次,圈定它们各自的分布区域,便可将它们与形成的地质作用及时代联系起来,为准确解释区域磁异常图提供可靠的依据.本文应用三维欧拉反褶积反演方法,计算出的塔里木盆地深度为2~5 km、5~10 km、10~20 km三个等级的磁异常源,它们与形成的地质作用及时代分别为: 中生代构造运动,海西期玄武岩侵位和太古代结晶基底的变质作用;圈定了它们各自的分布区域.     

Length of phytoplankton species patches on the Southern California Shelf

Study of a longshore transect off Southern California suggests that the length scales (22 to 27 km) of phytoplankton species patches may be related to those of low-frequency currents. The patch boundaries were independent of shelf width but they were probably not independent of changes in chlorophyll fluorescence, temperature, and bottom topography.     

Inversion of potential field data using the structural index as weighting function rate decay

Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.     

Mapping basement structures in the northwestern offshore of Abu Dhabi from high‐resolution aeromagnetic data

This paper presents a case study of mapping basement structures in the northwestern offshore of Abu Dhabi using high‐resolution aeromagnetic data. Lineament analysis was carried out on the derivatives of the reduced‐to‐the‐pole magnetic data, along with supporting information from published geologic data. The lineament analysis suggests three well‐defined basement trends in the north–south, northeast–southwest, and northwest–southeast directions. The reduced‐to‐the‐pole magnetic data reveal high positive magnetic anomalies hypothesized to be related to intra‐basement bodies in the deep seated Arabian Shield. Depth to basement was estimated using spectral analysis and Source Parameter Imaging techniques. The spectral analysis suggests that the intruded basement blocks are at the same average depth level (around 8.5 km). The estimated Source Parameter Imaging depths from gridded reduced‐to‐the‐pole data are ranged between 4 km and 12 km with a large depth variation within small distances. These estimated depths prevent a reliable interpretation of the nature of the basement relief. However, low‐pass filtering of the horizontal local wavenumber data across two profiles shows that the basement terrain is characterized by a basin‐like structure trending in the northeast–southwest direction with a maximum depth of 10 km. Two‐dimensional forward magnetic modelling across the two profiles suggests that the high positive magnetic anomalies over the basin could be produced by intrusion of mafic igneous rocks with high susceptibility values (0.008 to 0.016 SI.     

Detection of potential fields source boundaries by enhanced horizontal derivative method

A high‐resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced‐to‐the‐pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal‐to‐noise ratios and depths‐to‐source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high‐order vertical derivatives is also suggested. This involves both frequency‐ and space‐domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep‐seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high‐resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method.     

Interpretation of gravity data by the continuous wavelet transform: The case of the Chad lineament (North-Central Africa)

A slightly bended gravity high along the Chad lineament in Central North Africa is analyzed and interpreted by the continuous wavelet transform (CWT) method. We use scale normalization on the continuous wavelet transform, allowing analysis of the gravity field in order to determine the sources at different depths. By focusing on homogenous standard sources, such as sphere or cube, horizontal cylinder or prism, sheet and infinite step, we derive the relationships between the source depth and pseudo-wavenumber. Then the source depth can be recovered from tracing the maximal values of the modulus of the complex wavelet coefficients in the CWT-based scalograms that are function of the pseudo-wavenumber. The studied area includes a central gravity high up to 75 km wide, and a secondary high that occurs at the southern part of the anomaly. The interpretation of the depth slices and vertical sections of the modulus maxima of the complex wavelet coefficients allows recognition of a relatively dense terrane located at middle crustal levels (10–25 km depth). A reasonable geological model derived from the 2.5D gravity forward modelling indicates the presence of high density bodies, probably linked to a buried suture, which were thrusted up into the mid-crust during the Neo-Proterozoic terrane collisions between the Saharan metacraton and the Arabian-Nubian shield. We conclude that the Chad line delineates a first order geological boundary, missing on the geologic maps.     

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.     

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。     

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.     

2010年以来四川地区中强地震震源机制反演及深度确定

2008年5月12日四川龙门山断裂带发生了汶川8.0级地震,之后四川境内发生了两次7.0级地震(其中一个是芦山地震),为了研究汶川地震之后龙门山断裂带及周边区域的地震活动性,本研究收集了国家地震台网和四川区域地震台网2010年1月1日—2017年12月31日四川地区发生的17次M≥5.0地震以及120多次5.0>M≥4.0地震的波形资料,利用波形拟合法反演了震源机制解及区域应力场.反演结果显示,位于龙门山断裂带上的地震,震源机制以逆冲型为主,鲜水河断裂带地震震源机制以走滑型为主,而川滇块体西南部的理塘断裂、金沙江断裂附近,震源机制解以正断层为主.根据震源机制解反演得到的龙门山地区、鲜水河地区的主压应力场方向为WNW、近EW向.川滇块体的巴塘、理塘等地区,其主压应力轴方向为12°左右,接近SN向,且仰角接近40°左右.本研究利用面波振幅谱特征对震源深度进行了精确定位,定位结果与中国地震台网中心(CENC),美国地震调查局(USGS),国际地震中心(ISC)等机构地震目录进行了对比.结果显示,四川地区强震震源深度主要分布在20km以上的中上地壳.龙门山地区震源优势分布在10～20km,鲜水河断裂地震震源深度在10km左右,川滇块体西南部的理塘断裂,巴塘断裂,金沙江断裂等地区,震源深度一般在5～10km范围.     

Inversion of elongated magnetic anomalies using magnitude transforms

The calculable magnitudes of the anomalous magnetic field from simple 2D sources and their gradients and Laplacians appear as ratios that can be synthesized in functional forms, corresponding to the different source shapes. Field components and first‐order derivatives are involved in the inversion procedures presented. The structural index and source depth are estimated independently of each other. The applied functions allow magnetic profiles and magnetic maps to be shape‐ and depth‐converted with immediate imaging of the inversion results. The contours of these functions outline elongated loops around the 2.5D anomaly axis on magnetic maps. The width of the loops reflects the depth and structural index N of the source in the scale units of the inverted map. Model and field tests illustrate the effectiveness of this approach for fast automatic inversion of large sets of magnetic data for depth, shape, length and location of simple sources.     

Mapping of magnetic basement in Central India from aeromagnetic data for scaling geology

The Central Indian region has a complex geology covering the Godavari Graben, the Bastar Craton (including the Chhattisgarh Basin), the Eastern Ghat Mobile Belt, the Mahanadi Graben and some part of the Deccan Trap, the northern Singhbhum Orogen and the eastern Dharwar Craton. The region is well covered by reconnaissance‐scale aeromagnetic data, analysed for the estimation of basement and shallow anomalous magnetic sources depth using scaling spectral method. The shallow magnetic anomalies are found to vary from 1 to 3 km, whereas magnetic basement depth values are found to vary from 2 to 7 km. The shallowest basement depth of 2 km corresponds to the Kanker granites, a part of the Bastar Craton, whereas the deepest basement depth of 7 km is for the Godavari Basin and the southeastern part of the Eastern Ghat Mobile Belt near the Parvatipuram Bobbili fault. The estimated basement depth values correlate well with the values found from earlier geophysical studies. The earlier geophysical studies are limited to few tectonic units, whereas our estimation provides detailed magnetic basement mapping in the region. The magnetic basement and shallow depth values in the region indicate complex tectonic, heterogeneity, and intrusive bodies at different depths, which can be attributed to different thermo‐tectonic processes since Precambrian.     

Comparison of surface seismic sources at the CO2SINK site, Ketzin, Germany

In 2004 three seismic surface sources (VIBSIST, accelerated weight drop and MiniVib) were tested in a pilot study at the Ketzin test site, Germany, a study site for geological storage of CO₂ (EU project CO₂SINK). The main objectives of this pilot study were to 1) evaluate the response of the Ketzin site to reflection seismics, especially at the planned injection depth, 2) test different acquisition parameters and 3) use the results to guide the planning of the 3D survey. As part of these objectives, we emphasize the source performance comparison in this study. The sources were tested along two perpendicular lines of 2.4 km length each. Data were acquired by shooting at all stations (source and receiver spacing of 20 m) on both lines, allowing common‐midpoint stacked sections to be produced. The sources' signal characteristics based on signal‐to‐noise ratio, signal penetration and frequency content of raw shot records were analysed and stacked sections were compared. The results show that all three surface sources are suitable for reflection seismic studies down to a depth of about 1 km and provide enough bandwidth for resolving the geological targets at the site, i.e., the Weser and Stuttgart Formations. Near surface conditions, especially a thick weathering layer present in this particular area, strongly influence the data quality, as indicated by the difference in reflectivity and signal‐to‐noise ratio of the two common‐midpoint lines. The stacked sections of the MiniVib source show the highest frequency signals down to about 500 ms traveltime (approximately 500 m depth) but also the shallowest signal penetration depth. The VIBSIST source generates signals with the highest signal‐to‐noise ratio and greatest signal penetration depth of the tested sources. In particular, reflections below 900 ms (approximately 1 km depth) are best imaged by the VIBSIST source. The weight drop performance lies in between these two sources and might be recommended as an appropriate source for a 3D survey at this site because of the shorter production time compared to the VIBSIST and MiniVib sources.     

Focal depths of earthquakes in the Baikal region: A review

Conditions and specific features in the determination of the focal depths of the earthquakes in the Baikal region are considered. Particular attention is given to the procedure of relocation of the hypocenters in accordance with the programs based on the method of minimization of rms residuals in the seismic wave traveltimes, which is widely used at present. The advantages and shortcomings of this approach are demonstrated. The available determinations of the source depths are reviewed, and examples for the interpretation of the results are presented. The averaged depth distribution of the hypocenters shows that the strongest seismic activity is observed in the depth range 10–20 km. The bottom of the seismically active layer corresponding to the level, above which 90% of sources are located, lies at a depth of 25 km. The trend of the deepening of seismic sources is observed at the northeast flank of the rift zone, where seismic activity involves the lower part of the crust.     

Imaging magnetic sources using Euler's equation

The conventional Euler deconvolution method has the advantage of being independent of magnetization parameters in locating magnetic sources and estimating their corresponding depths. However, this method has the disadvantage that a suitable structural index must be chosen, which may cause spatial diffusion of the Euler solutions and bias in the estimation of depths to the magnetic sources. This problem becomes more serious when interfering anomalies exist. The interpretation of the Euler depth solutions is effectively related to the model adopted, and different models may have different structural indices. Therefore, I suggest a combined inversion for the structural index and the source location from the Euler deconvolution, by using only the derivatives of the magnetic anomalies. This approach considerably reduces the diffusion problem of the location and depth solutions. Consequently, by averaging the clustered solutions satisfying a given criterion for the solutions, we can image the depths and attributes (or types) of the causative magnetic sources. Magnetic anomalies acquired offshore northern Taiwan are used to test the applicability of the proposed method.     

Solute transport scales in an unsaturated stony soil

Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include information from different scales of heterogeneities.     

Depth determination from a non-stationary magnetic profile for scaling geology

The conventional spectral analysis method for interpretation of magnetic data assumes stationary spatial series and a white‐noise source distribution. However, long magnetic profiles may not be stationary in nature and source distributions are not white. Long non‐stationary magnetic profiles can be divided into stationary subprofiles following Wiener filter theory. A least‐squares inverse method is used to calculate the scaling exponents and depth values of magnetic interfaces from the power spectrum. The applicability of this approach is demonstrated on non‐stationary synthetic and field magnetic data collected along the Nagaur–Jhalawar transect, western India. The stationarity of the whole profile and the subprofiles of the synthetic and field data is tested. The variation of the mean and standard deviations of the subprofiles is significantly reduced compared with the whole profile. The depth values found from the synthetic model are in close agreement with the assumed depth values, whereas for the field data these are in close agreement with estimates from seismic, magnetotelluric and gravity data.