Three-dimensional gravity and magnetic data acquisition and study on its joint gradient Euler deconvolution method

Three-dimensional(3 D)gravitational and magnetic exploration is performed using aerial measurement tools,however,this has difficulties with measuring-height design and the construction of a joint-interpretation scheme.At present,the height in such experiments is set according to the measurement scale,and the distribution characteristics of anomalies are not fully considered.Here,we present the idea of using the attenuation characteristics of a singular-value spectrum to evaluate the contributions of various measurement heights and multi-height combinations for inversion to correctly and reasonably design appropriate measuring heights and the number of various measurement heights to be set.The jointgradient Euler-deconvolution method can accurately obtain the distribution of geological bodies from 3 D gravitational and magnetic data at an improved resolution,and experimental tests confirm these findings.Therefore,an actual 3 D aeromagnetic-data-acquisition and inversion test were carried out in the vicinity of the Zhurihe Iron Mine in Inner Mongolia.The fl ight-height diff erence was set to 60 m,and the specifi c distribution of lodes was obtained by the joint-gradient Euler-deconvolution method.This provides a reliable basis for future detailed exploration and proves that the methods presented in this paper have good practicalapplication eff ects and prospects.

STABILIZATION EFFECT OF FRICTIONS FOR TRANSONIC SHOCKS IN STEADY COMPRESSIBLE EULER FLOWS PASSING THREE-DIMENSIONAL DUCTS

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.

Combination of Tilt-Angle and Euler Deconvolution Approaches to Determine Structural Features from Aeromagnetic Data Modeling over Akonolinga-Loum Area (Centre-East, Cameroon)

Aeromagnetic data for center-east Cameroon between the latitudes 3.5° to 4.5°N and longitudes 12° to 12.5°E are used to further study the subsurface area of this part of the geological Province of Central Africa and the Congo Craton. The GIS and GEOSOFT v6.5 softwares are used to treat the data. This analysis enabled us to explore our study area from surface right to the base. The Tilt Angle method is used to delineate geological structures and to estimate the depth. The Euler’s deconvolution method is used to estimate the specific depth of structural contacts. We estimate the northern boundary of the Congo Craton and southern boundary of the Pan-African starting from 3°7'N of West to 3°75'N of East. Its depth is estimated around 2.6 km for deep and 0.1 km for shallow while the direction is WSW-ENE and the NW slope varies from 30° to 60°. We obtain that main and minor lineaments exist throughout, from the surface to the base of the area with their principal direction being SW-NE. We also obtain the vertical gradient contact and the quasihorizontal contact. This is proof of the subduction of the Pan-African belt under the Congo Craton due to the intense collision which caused the rejuvenation of the crust. The main consequence of this collision is the formation of pudding and fold structures, beginning from the superficial part right to the base and which caused the intrusion of schistose, chlorite-schist, quartzite in the micaschist and the intrusions of gneiss and garnetiferous schist in the migmatite. In our study, we highlight the presence of 37 major and 523 minor lineaments that localize the circulation of minerals. The probable slope of the lineaments in the northern part of the region varies from 30° to 60° in a SE direction while in the southern part, and it varies from 30° to 60° in a NW direction.

Field source characteristic of gravity variation in Hexi region before Menyuan Ms6.4 earthquake based on the Euler deconvolution

This study adopted the Euler deconvolution method to conduct an inversion and interpretation of the depth and spatial distribution pattern of field source that lead to gravity variation. For this purpose, mobile gravity data from four periods in the Hexi region between 2011 and 2015 were obtained from an observation network. With a newly established theoretical model, we acquired the optimum inversion parameters and conducted calculation and analysis with the actual data. The results indicate that one is the appropriate value of the structure index for the inversion of the mobile gravity data. The inversion results of the actual data showed a comparable spatial distribution of the field source and a consistent structural trend with observations from the Qilian-Haiyuan Fault zone between 2011 and 2015. The distribution was in a blocking state at the epicenter of the Menyuan earthquake in 2016. Our quantitative study of the field source provides new insights into the inversion and interpretation of signals of mobile gravity variation.

Depth Estimation of Geothermal Heat Structures by Euler Deconvolution of Gravity Data at Eburru Area, Kenya

Gravity survey was done at the Eburru area to estimate the source depth locations and delineate the fault boundaries using 3D Euler deconvolution. Gravity data was collected using CG-5 gravimeter. Gravity data reductions were done by applying drift correction, latitude correction, free air correction, Bouguer correction and terrain correction to the observed raw data to obtain complete bouguer anomaly (CBA). The CBA data was transferred to Oasis montaj software for Euler deconvolution processing. The 3D Euler deconvolution was carried out to determine and estimate the depth of the density bodies. Euler deconvolution locates the gravity anomaly source and estimates its depth from the gravity observation level. Euler deconvolution was preferred to other filtering methods in this study as solutions are only determined over identified analytic signal peaks, the window size varies according to anomaly size and the final solution involves only a few more precise depth estimates. The Euler deconvolution was performed using structural indices of 0.5, 1.0 and 2.0. Results from this analysis indicated that the CBA values in this study area range from gravity values of -272 mGal to -286 mGal and residual Bouguer anomaly amplitude range between -3 mGal and 3.4 mGal. The 0.5, 1.0 and 2.0 structural indices generated five solutions at depth range of 433 m - 2269 m, 801 m - 1433 m and 1170 m - 2246 m respectively occurring almost at the same locations on gravity highs. The deep structures were observed to occur in the northern part of the study area, and interpreted to be dense intruding masses likely to be trapped by the overlying cap rock at these depths. These could be geothermal heat sources that can be exploited to generate geothermal energy.

The Use of Edge Enhancement Methods and Euler Deconvolution to Estimate an Ore Deposit Depth from Gravity Data

The Hercynian massif of the central Jebilet (Morocco) is characterized by the outcrop of many gossans with great economic importance. This work focuses on interpreting gravity data of Benslimane gossan, located about thirty kilometres to the North-West of Marrakech. The residual gravity map of the study area highlights several anomalies which coincide with the mining and geological contexts. Applying edge detection methods, for example, tilt angle derivative (TDR), the total horizontal derivative of the tilt angle derivative (HDR_TDR) and the 3D Euler deconvolution, allowed us to estimate the depth of the Benslimane deposit. As a result, the average depth of the ore deposit was estimated to exceed 200 m. The results are promising, and the processing methods must be applied to the other gossan in the Jebilet massif for further exploration studies.

Estimating Field Source Parameters of Gravity Change in North China Based on the Euler Deconvolution Method

Based on the absolute and relative gravity observations in North China from 2009 to 2014,spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theoretical model to get the best estimates of parameters. Gravity field change caused by the depth and distribution in North China is calculated by back analysis. The results show the structural index that equals 1 is suitable for inversion of the gravity variation data. The inversion results indicate that the depths of anomaly field sources are spread over the Hetao fault. The research method of this paper can be used in the quantitative study on the field source and may shed new light on the interpretations of gravity change, and also provide quantitative basis for earthquake prediction index criterions based on the gravity change.

Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

Improved Euler method for the interpretation of potential data based on the ratio of the vertical fi rst derivative to analytic signal

We propose a new automatic method for the interpretation of potential fi eld data, called the RDAS–Euler method, which is based on Euler＇s deconvolution and analytic signal methods. The proposed method can estimate the horizontal and vertical extent of geophysical anomalies without prior information of the nature of the anomalies（structural index）. It also avoids inversion errors because of the erroneous choice of the structural index N in the conventional Euler deconvolution method. The method was tested using model gravity anomalies. In all cases, the misfi t between theoretical values and inversion results is less than 10%. Relative to the conventional Euler deconvolution method, the RDAS–Euler method produces inversion results that are more stable and accurate. Finally, we demonstrate the practicability of the method by applying it to Hulin Basin in Heilongjiang province, where the proposed method produced more accurate data regarding the distribution of faults.

用Euler反褶积方法反演台湾海峡磁异常

用Ｅｕｌｅｒ反褶积方法反演台湾海峡磁异常，选取的窗口不能大，而决定取舍反褶积解的误差限又不能小，这势必对解的质量有较大影响．为此，不仅用了不同延深的单体模型，而且进行了多体模型实验．结果表明，复杂分布的磁性体，用Ｅｕｌｅｒ反褶积方法确定磁性体的轮廓可能是困难的，但可确定磁性体的水平位置和深度，从而降低了对资料精度和计算参数选取的要求．在磁异常比较复杂的地区．

Tilt-Euler方法在位场数据处理及解释中的应用

通过探讨斜梯度欧拉反褶积(Tilt-Euler)方法及性质,对理论模型和实测重力资料进行分析,结果表明Tilt-Euler在无场源构造指数的条件下能快速推断出场源边界和深度分布,并能自动估算出构造指数,计算简便,实用性强,这对于大面积航空磁测和航空重力资料处理解释具有重要意义。

拖曳式海洋三分量磁力梯度仪的数据处理方法与应用

拖曳式海洋三分量磁力梯度仪能够同时获得地磁三分量和磁力梯度数据,与传统的拖曳式总场磁力仪相比具有降低船磁干扰和抵抗地磁日变影响等优点,也存在灵敏度误差、零点偏移误差、正交性误差和位置误差等校准处理的难点。在实际航次中用拖曳式海洋三分量磁力梯度仪实测得到一条剖面数据,经校准后与G880磁力仪重复线测量的地磁总场数据进行外符合精度评价,表明其具有较高的稳定性和可靠性。根据三分量磁力梯度数据计算得到其张量不变量以及磁边界走向图,并结合欧拉反褶积计算,对测线上的磁源体进行了有效识别和解释。结果显示拖曳式海洋三分量磁力梯度仪能够有效获得地磁总场、分量及梯度等多参量信息,可为海洋地磁场测量提供更有效的技术手段。

iTilt-Euler法在重力数据处理及断裂解释中的应用

为改善欧拉反演结果的收敛性,本文采用不依赖于构造指数的改进Tilt-Euler(iTilt-Euler)进行计算,并利用水平总梯度倾斜角峰值(TAHG)约束法约束反演数据,优化计算结果。模型试算结果表明,采用TAHG法约束的iTilt-Euler反演结果的收敛性得到了有效提高,且为深源地质体的位置和深度提供了更多信息。在肯尼亚ANZA盆地某区块重力数据处理中的应用表明,TAHG法约束下的iTilt-Euler反演解连续性较好,主要呈NW向,其次是NE向,且NW向展布的解延伸长、深度大,反映为控制区内构造单元边界的基底断裂,被NE向展布的盖层断裂所切割。此外,研究区东南部发育一条NNE向的深断裂,切割了NW向及NE向断裂,推测其可能控制了区域构造单元的东南边界。应用结果表明,iTilt-Euler法和TAHG法可为断裂解释提供可靠的研究手段,具有较好的实用性。

基于方向tilt-Euler的三维磁数据快速反演

三维磁异常快速反演是磁法勘探进行地质解释的一项重要内容.本文在方向tilt梯度基础上进行导数处理,并进行合理改进,得到了6个改进的方向tilt梯度导数,丰富了不同方向上的磁异常信息.对常规欧拉反褶积方程进行三个方向求导,所构成的方程组与6个改进的方向tilt梯度导数进行结合,从而构建出了两个基于方向tilt梯度导数的快速反演方程组(方向tilt-Euler法),用于反演场源的位置参数.另外,将三个方向导数下的欧拉反褶积进行平方和及均方根处理,得到了场源构造指数的求解公式.单一模型试验表明,6个改进的方向tilt梯度导数异常基本不受磁化方向影响,可从不同方向上反映磁异常信息,方向tilt-Euler能够准确地反演出场源的位置及构造指数.叠加模型试验证实了方向tilt-Euler法相对于tilt-Euler法,具有反演解聚集度更强、连续性更好、反演准确度更高、受噪声影响更小及无虚假反演解等优点.将本文方法应用于内蒙古塔木素航磁资料处理中,获得了丰富的地下磁源分布信息,为了解该地区隐伏断裂构造及岩体分布等提供了有效依据.

欧拉反演方法分析及实用技术改进

欧拉反演是重磁资料反演解释的重要方法。在深入研究的基础上,针对欧拉反演存在的问题提出了具体的技术措施:水平梯度滤波准则、距离约束评价准则、聚集度约束评价准则等方法,从而使三维欧拉反演的适用能力得到很大加强,使欧拉反演方法技术进入实用化阶段。

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2～5km、5～10km、10～20km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.

欧拉反褶积在重磁位场中应用与发展

介绍了欧拉反褶积方法原理,概述了国内外近几十年地球物理学者对欧拉反褶积方法进行的一系列改进及相关问题研究取得的主要进展和成就,并着重分析了构造指数的选取和欧拉解的稳定性等问题。通过分析指出了构造指数的正确选取、多场源混合叠加干扰和高阶次背景场研究及欧拉解的稳定性仍是今后欧拉反褶积方法研究重点和发展的主要方向,这对解决欧拉反褶积在重磁位场资料解释实用化中具有重要意义。

磁张量数据的边界识别和解释方法

本文利用方向解析信号进行磁张量数据的边界识别和解释,该方法最大优势是在进行反演时不用给出异常体形状的先验信息,且得到结果受磁化方向干扰小。文中给出了方向解析信号的定义,以及进行边界识别的基本公式,并将方向解析信号与欧拉方程联合进行异常的解释。通过对不同形状地质体产生的磁张量异常进行试验,表明该法能很好地完成张量数据的边界识别和解释。将其用于M区实测数据计算,获得了地下磁性体的分布特征。

中国东北地区重力场研究——利用改进的三方向小子域滤波划分主构造线及大地构造单元

利用重力异常进行大地构造单元的划分是区域重力资料处理与解释的重要任务.为了精细地划分中国东北地区大地构造单元及其分界线位置,对三方向小子域滤波进行了改进,探讨了改进的三方向小子域滤波的合理性.利用小子域及改进的三方向小子域滤波对研究区布格重力异常进行处理,并与欧拉反褶积反演结果进行对比分析.结果表明,改进的三方向小子域滤波在识别平面断裂的应用中具有更好的效果.综合分析东北地区布格重力异常特征、小子域和改进的三方向小子域滤波结果,划分出延续性较好、规模较大的断裂18条.对研究区重力异常进行了分区,描述了一、二级异常的分区特点,给出了东北地区大地构造单元的基本格架.黑河齐齐哈尔—白城等重要构造线平面位置的确定突破了传统的重力异常分区模式,指出东北地区NE向构造具有走滑特征,且走滑距离具有由西向东逐渐增大的特点.

重力梯度张量解析信号的欧拉反褶积

利用重力梯度张量数据高精度的特点以及解析信号在确定异常体位置上的优势,将重力梯度张量解析信号代替位场的导数完成重力梯度张量解析信号的欧拉反褶积;通过在1个窗口内对1组数据点解3个欧拉方程来自动识别构造指数,从而规避了传统欧拉反褶积方法中需要事先确定构造指数的问题,同时减少了背景场的影响。研究结果表明:使用重力梯度张量的解析信号,其欧拉反褶积的解收敛性很好,能准确地判断地下异常体源的位置,有效规避背景场的影响,反演效果较好。