Edge Detection in Potential-Field Data by Enhanced Mathematical Morphology Filter

Enhancement on the edges of the causative source is an indispensable tool in the interpretation of potential-field data. There are a number of methods for recognizing the edges, most of which involve high-pass filters based on derivatives of potential-field data. A new edge-detection method is presented, called the enhanced mathematical morphology (EMM) filter. The EMM filter uses the ratio of the erosion of the total horizontal derivative to the dilation of total horizontal derivative to recognize the edges of the sources, and can display the edges of the shallow and deep bodies simultaneously. The EMM filter does not require the computation of vertical derivatives, which makes this method computationally stable. The EMM filter is tested on synthetic and real potential field data in China. Compared to other edge-detection filters, the new method is able to recognize the source edges more clearly, and the outputs are more insensitive to noise.     

应用加强解析信号倾斜角进行位场数据的边界检测

边界检测在地球物理位场数据解释中占有重要位置.现有的传统边界识别方法有的不能同时显示不同振幅的异常边界,有的虽然能均衡不同振幅的异常,但识别出来的边界信息中含有一些额外的错误的边界信息,尤其是当测量的异常中同时含有正异常和负异常时.目前已有的去除额外错误边界信息的方法存在着一定的人为主观性.为了解决这些问题,本文定义了加强解析信号倾斜角来进行地质体边界识别.通过模型试验证明了该方法不仅能同时清晰地识别深部和浅部地质体的边界,而且能有效地避免引入一些错误边界信息.最后将该方法应用到四川盆地的重力异常数据中,并取得了良好边界结果.     

位场各阶垂向导数换算的新正则化方法

位场垂向导数大量应用于位场数据处理与解释中.当前广泛采用的位场各阶垂向导数换算方法为基于Laplace方程并结合波数域和空间域方法的具有递推特性的ISVD(integrated second vertical derivative)算法.本文在位场垂向导数换算的正则化方法和径向平均功率谱的基础上,提出一种位场各阶垂向导数换算的新正则化方法.新正则化方法仅需通过分析位场径向平均功率谱来确定一个截止波数,即可稳定换算位场各阶垂向导数.理论模型和实测数据实验结果表明:(1)新正则化方法物理意义明确、计算简单,且各阶垂向导数换算的稳定性和精度明显优于ISVD算法;(2)在用新正则化方法求得各阶垂向导数的基础上,利用泰勒级数法可以获得大深度、高精度的位场向下延拓结果.     

基于Theta法改进的均衡滤波器在位场边界识别中的应用——以庐枞矿集区为例

利用观测数据确定地质体的边界位置是位场数据解译中的一项重要工作,传统的边界识别滤波器通常不能均衡深、浅部的地质体边界,近些年相关研究开始致力于发展均衡边界滤波器.本文基于Theta图法定义了新的边界识别滤波器,详述了滤波器波数域及空间域的主要计算公式,通过模型验证,该滤波器显著压制了Theta图法对深部地质体边界的放大作用,较好地平衡了深部和浅部边界.通过与传统的边界识别滤波器对比,本文定义的滤波器能够清晰且更加收敛地圈定出地质体的水平边界位置.以长江中下游成矿带庐枞矿集区为例,开展了1∶5万重磁数据的处理分析,并结合物性资料进行了讨论,结果表明:重磁数据的检测结果精确刻画了郯庐断裂带的位置;庐枞盆地的磁力数据检测边界整体与盆地的地质边缘一致,明确了边界断裂在深部倾向盆地内部;识别出庐枞盆地外围一系列环形边界,这些边界封闭区域与最新勘探发现的深部岩体及铁铜矿化体相对应,对于指导区域深部找矿工作有着重要的意义.     

The application of spatial derivatives to non‐potential field data interpretation

Source/body edge detection is a common feature in the processing and interpretation of potential field data sets. A wide range of spatial derivatives is available to enhance the information contained in the basic data. Here the ability of these procedures to assist with the mapping interpretation of non‐potential field data is considered. The study uses airborne electromagnetic (conductivity) data but also provides a general context for other conductivity/resistivity data, provided the non‐potential field nature of active and thus spatially‐focused, measurements is acknowledged. The study discusses and demonstrates the application of a range of common spatial derivative procedures, including the analytic signal and upward continuation, to both magnetic and conductivity data. The ability of the tilt derivative to provide enhanced mapping of conductivity data is considered in detail. Tilt and its associated functions are formed by taking combinations of vertical and horizontal derivatives of the data set. Theoretical forward modelling studies are first carried out to assess the performance of the tilt derivative in relation to the detection and definition of concealed conductivity structure. The tilt derivative embodies automatic gain control that normalizes the detection and definition of both weak and strong conductivity gradients across an appropriate subsurface depth range. The use of high‐order spatial derivatives inevitably results in a degree of noise (cultural perturbation) amplification that is survey and technique specific. Both of these aspects are considered using practical case studies of jointly obtained magnetic and conductivity data at a variety of spatial scales.     

空间域滤波在求二维重磁接触面参数中的应用

1975年、1976年格林和斯坦利发表了求二维接触面参数的一个方法。本文试图在他们工作的基础上,用空间域滤波来代替格林和斯特利用差商求水平导数和用希尔伯特变换求垂直导数的方法。文中给出了应用空间域滤波计算重、磁异常水平和垂直导数的方法。模型试验证实了理论上的推断。与差商和希尔伯特变换方法相比,优点在于它既能同时滤掉高频干扰,又能使求得的垂直导数和水平导数具有相同的精度,进而提高反演结果的精确度。     

Step-Edge Detection Filters for the Interpretation of Potential Field Data

Edge detection is a useful tool in the interpretation of potential field data, and the existing edge detection filters are almost functions of first-order horizontal and vertical derivatives. We propose step-edge detection filters to improve the resolution of edge detection results, which use the functions of different-order derivatives to accomplish the edge detection task. We demonstrate the proposed filters on synthetic potential field data, and the results show that the new methods can recognize the edges of the sources more precisely and clearly. We also discuss the application effect of different step-edge detection filters. Lastly, we apply the proposed filters to real potential field data, and the recognized edges of the stratigraphic markers are more precise and clear.     

位场解析信号振幅极值位置空间变化规律研究

通过对单一边界、双边界、多边界以及点(线)质量模型重力异常解析信号振幅和重力异常垂向导数解析信号振幅的极值位置空间变化规律研究表明,重力异常垂向导数解析信号振幅和化极磁力异常解析信号振幅的极值位置相同,且与重力异常解析信号振幅的极值位置空间变化规律相似.利用位场解析信号振幅极大值位置能够准确识别单一直立边界地质体的边缘位置,但不能准确识别其它任何形体的边缘位置,其识别结果的偏移量大小随地质体的埋深、水平尺寸以及倾斜程度等变化.虽然重力异常垂向导数解析信号振幅比重力异常解析信号振幅的峰值更加尖锐、横向识别能力更强,其极大值位置更靠近地质体上顶面边缘位置,但均受地质体埋深的影响较大;随着埋深的增加,位场解析信号振幅的极大值位置会快速收敛到形体的"中心位置",其轨迹类似"叉子状";且对多边界模型会出现"极大值位置盲区"而无法识别其边缘位置.通过这些理论研究表明,位场解析信号振幅只能识别单一边界地质体的边缘位置;而不宜用来识别多边界地质体的边缘位置,但可以用来识别多边界地质体的"中心位置".     

改进的均衡滤波器在位场数据边界识别中的应用

边界识别是进行位场数据解释时一项必不可少的任务.现有的边界识别滤波器存在识别边界发散和深部地质体边界模糊的缺点.本文提出增强型均衡滤波器,可有效地改善上述缺点.该滤波器是利用不同阶导数之间的组合来进行地质体边界的识别,并在运算中引入一种计算高阶垂直导数的稳定算法.通过理论模型试验证明增强型均衡滤波器能使浅部与深部地质体的边界同时清晰地显示,且相对于其它边界识别滤波器能更加准确和清晰地识别出地质体的边界.最后将增强型均衡滤波器应用于实测位场数据的解释,根据其识别结果可容易地划分出断裂的水平位置及不同地层之间的界线,并能发现更多的细节信息.     

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.     

基于磁异常的边界特征增强方法对比研究

基于磁异常进行场源边界识别(如断裂划分)是磁法勘探解释工作的重要内容.由于受到斜磁化、场源埋深、异常叠加以及噪声等多种因素的影响,基于磁异常直接进行场源的边界识别往往难以准确识别出场源体的边界,所以,人们研究了各种场源边界特征增强的方法技术,以便于进行场源边界的识别工作.近年来,国内外出现了很多新的边界特征增强方法,但有些方法的边界特征增强效果与已有方法相近,有的方法效果有待深化检验,存在验证方法的理论模型过于简单,未全面细致地分析出它们的优缺点等问题.针对上述情况,本文运用多种复杂、贴近实际的理论模型,深入对比分析了包括解析信号模法和倾斜角法等在内的15种具有代表性的边界增强方法,分析了它们在不同磁化方向、不同场源埋深、不同场源形态、异常叠加和噪声干扰等多种因素影响下的边界增强效果,重点归纳总结出它们的优缺点和适用条件,以为实际应用时的方法选择提供参考.通过模型实验,我们认为解析信号模垂向导数法、总水平导数法、解析信号模倾斜角法是在多种因素影响下,适用性较强、应用效果较好的三种方法.     

ACCURATE DETERMINATION OF THE DIP ANGLE OF A GEOLOGICAL CONTACT USING THE GRAVITY METHOD*

From a gravity profile over a truncated horizontal plate, the horizontal derivative and, by means of the Hilbert Transform, the vertical derivative are obtained. When the horizontal derivative is plotted against the vertical derivative, the axis of symmetry of the resulting curve is inclined at the angle of dip of the face of the truncated plate. The depths to the upper and lower surfaces of the plate can be obtained uniquely from the symmetrical figure. Because of the derivatives being used, the method avoids the difficulties which arise from other methods of interpretation which depend upon a knowledge of the position of the origin of the gravity field data. The entire procedure for interpretation can be accommodated on a programmable calculator. An illustrative example is given.     

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.     

Filtering potential field data by modifying its amplitude and phase in the space domain

Potential field datasets are commonly broken down in the space domain into amplitude (total gradient, or analytic signal amplitude) and phase (tilt angle) components as part of the data processing and interpretation procedure. However, it is possible to reconstruct the data again in the space domain from the amplitude and phase, and if they have been modified then a filtered dataset will be produced. For example, modified derivatives and filters which are based on them (such as the tilt angle and the theta map) can be produced. In addition, the modification of the data amplitude prior to the reconstruction of the signal allows controllable automatic gain control filters to be designed. The procedures are demonstrated on aeromagnetic and gravity data from Southern Africa.     

CONSTRUCTION OF COMPONENT MAPS FROM AEROMAGNETIC TOTAL FIELD ANOMALY MAPS1

Total field anomalies as defined from normal aeromagnetic surveys give good approximations of the anomalous components along the direction of the main geomagnetic field, which is generally much larger than the anomalous field. Using the relations between vertical and horizontal components of the field, the total field anomaly is related to any vertical or horizontal component and the corresponding horizontal and vertical derivatives. An example from the Siljan impact structure indicates that such directional filters may be applied to extract useful information from magnetic maps.     

Computation of apparent resistivity profiles from VLF-EM data using linear filtering1

A simple filter is developed which transforms VLF-EM real magnetic field transfer functions into apparent resistivities. It is based on the relationship between the horizontal derivative of the surface electric field and the vertical magnetic field at the surface of a two-dimensional earth model. The performance of this simple autoregressive filter is tested for modelled and real survey data. The technique yields profiles of apparent resistivity very similar, both in magnitude and in wavelength, to those which would have been obtained using VLF-EM resistivity measurements or d.c. resistivity profiling. This low-pass filter has the advantage of reducing high-wavenumber noise in the data; therefore only the major features of the VLF-EM profile are displayed.     

An analytic signal approach to the interpretation of total field magnetic anomalies1

The analytic signal (AS) is defined as the square root of the sum of the squares of the vertical and the two horizontal derivatives of the total magnetic field ΔT. This paper verifies theoretically that peaks of the AS correlate directly with their magnetic causative bodies and are positioned symmetrically over them, i.e. the main feature of the AS is that it is independent of the inclination of the magnetic field. This avoids the difficulties that are often faced in the conventional process of reduction to pole for ΔT, when the direction of magnetization of the causative bodies is not known. In addition, the AS has characteristics similar to the derivative features of the magnetic field, so that it is very sensitive to edge effects of the causative magnetic bodies. The theoretical derivations are tested by comparison with calculations on models, and, in a field example from Hunan Province, China, the AS is applied successfully to the interpretation of ΔT, whereas the conventional process of reduction to pole fails, due to the reverse magnetization of the causative body.     

基于三维构造张量的位场边界识别滤波器

地质体构造边界位置的确定是位场数据解释中的一项重要工作,现有很多基于位场梯度张量数据的边界检测滤波器,但存在识别边界位置模糊且无法均衡深浅地质体异常的缺点.本文定义了位场数据的三维构造张量,并提出基于位场构造张量的边界滤波器.为了同时显示不同振幅异常的边界位置,对新定义的滤波器进行归一化处理.在高阶均衡滤波器的计算中需要计算位场的垂向高阶导数,本文引入一种计算的稳定算法,基于拉普拉斯方程利用位场水平导数求解垂向导数,可减小垂向导数计算中产生的误差.将定义的滤波器应用到合成的重磁数据中证明了新方法相比传统的滤波器能更加清晰、准确地圈定边界位置,而且针对同时含有正负异常的地质情况,可避免产生额外的错误边界.最后将新的滤波器应用到实测的重磁数据的解释中,结果显示基于构造张量的滤波器可更准确清晰地划分出断裂的边界位置,发现更多的构造细节.     

THE ANALYSIS AND DESIGN OF TWO-DIMENSIONAL FILTERS FOR TWO-DIMENSIONAL DATA *

Some of the methods such as regional removal and second derivative calculations which can be used to outline anomalies on potential data maps can be thought of as a filtering operation. The analysis and design of such two-dimensional filters by means of direct and inverse two-dimensional Fourier transforms have been considered. An analysis of several published sets of second derivative coefficient sets indicates that, in general, they are not a good approximation to the theoretical second derivative filter. Alternate methods of designing regional removal and second derivative filters are discussed. The properties of various two-dimensional filters are further illustrated by means of maps obtained from the convolution of several of these filters with a set of observed field data. These maps show the large changes in anomaly shape which can result from the inclusion or rejection of various wavelength components.     

位场数据归一化总水平导数垂向导数边缘识别方法(英文)

位场数据边缘识别技术常常用来识别地质体的边缘位置.本文提出了一种新的位场数据边缘识别方法--归一化总水平导数垂向导数,它具有边缘探测和边缘增强两种功能.该方法首先计算位场数据的总水平导数THDR和总水平导数THDR的n阶垂向导数VDRn,并对n阶垂向导数VDRn采用取大于0的阈值技术得到总水平导数峰值PTHDR,该值可以用来进行边缘探测;其次,计算总水平导数峰值PTHDR与总水平导数THDR的比,并用最大值进行归一化得到归一化总水平导数垂向导数,该值可以用来进行边缘增强;最后,通过理论模型和实际资料检验了方法的有效性和可靠性.