Fast imaging of subsurface conductors using very low‐frequency electromagnetic data

The study presents a fast imaging technique for the very low‐frequency data interpretation. First, an analytical expression was derived to compute the vertical component of the magnetic field at any point on the Earth's surface for a given current density distribution in a rectangular block on the subsurface. Current density is considered as exponentially decreasing with depth, according to the skin depth rule in a particular block. Subsequently, the vertical component of the magnetic field due to the entire subsurface was computed as the sum of the vertical component of the magnetic field due to an individual block. Since the vertical component of the magnetic field is proportional to the real part of very low‐frequency anomaly, an inversion program was developed for imaging of the subsurface conductors using the real very low‐frequency anomaly in terms of apparent current density distribution in the subsurface. Imaging results from the presented formulation were compared with other imaging techniques in terms of apparent current density and resistivity distribution using a standard numerical forward modelling and inversion technique. Efficacy of the developed approach was demonstrated for the interpretation of synthetic and field very low‐frequency data. The presented imaging technique shows improvement with respect to the filtering approaches in depicting subsurface conductors. Further, results obtained using the presented approach are closer to the results of rigorous resistivity inversion. Since the presented approach uses only the real anomaly, which is not sensitive to very small isolated near‐surface conducting features, it depicts prominent conducting features in the subsurface.     

Two-dimensional, regularised inversion of VLF data

Very low frequency electromagnetic (EM) methods using VLF transmitters have found many applications in subsurface geophysical investigations. Surface measurements involving both the vertical component of the magnetic field (VLF-EM or VLF-Z) and of the apparent resistivity (VLF-R) are increasingly common. Although extensive VLF data sets have been successfully used for mapping purposes, modelling and interpretation techniques which asess the third (i.e. depth) dimension appear limited.Given a profile of VLF-R measurements the main purpose of the present study is to demonstrate an automatic method for the construction of a resistivity cross-section. The technique used is one of a new generation of regularised inversion methods. These techniques attempt to overcome the problem of equivalence/non-uniqueness in EM sounding data by constructing the resistivity distribution with the minimum amount of structure that fits the data.VLF data represent a special case of plane-wave EM sounding in that they conform, in practice, to a single-frequency technique. This fact imposes a limitation in the amount of vertical resolution that we can expect using such data. In the case of two-dimensional modelling and inversion, resolution through the cross-section is a resultant attribute from both vertical and lateral resistivity gradients within the subsurface. In order to provide insight into the practical application of regularised inversion techniques to VLF data, both synthetic and field examples are considered. Both sets of examples are primarily concerned with VLF data applied to near-surface fault mapping where the main aim is to assess the location, dip and depth extent of conductive subsurface features.     

Interpretation of ground VLF-EM data in terms of inclined sheet-like conductor models

The response of two-dimensional, inclined, sheet-like conductors with, low conductance values to plane wave electromagnetic fields in the very low frequency (VLF) range has been evaluated by using a numerical technique. The conductance values of the conductors considered are appropriate for those produced by water and/or clay-filled fracture and shear zones in the Precambrian crystalline rocks of the Canadian Shield. The surrounding host rock was assumed to be, resistive with resistivities in the 1–10 k.m range to reflect the high resistivities over the shield areas. No overburden was assumed in this analysis.The results of the computations are presented in the form of characteristic interpretation diagrams to interpret ground VLF data in the field, where facilities for direct numerical modelling may not be available. A method for interpreting ground VLF data using such characteristic diagrams has been proposed in this paper which requires a prior knowledge of the host rock resistivity and the inclination of the conductor. These two parameters may be derived from a VLF resistivity survey and from appropriate filtering of the VLF tilt angle response. The interpretation method was applied to a ground VLF anomaly obtained at a research site near Atikokan in NW Ontario, which yielded an interpretation compatible with information from geological mapping.Geological Survey of Canada Contribution No. 51888.     

Use of non-linear filtering for the regional–residual separation of potential field data

Regional–residual separation is essential in gravity and magnetic data interpretation and a variety of techniques have been proposed. Graphical determination of the regional allows geological information to be taken into account. Upward continuation can be used to obtain the regional field either empirically or using some hypothesis about the geology. In some cases, a matched filter can be designed and used to separate deep and shallow sources. Simple low pass filtering has also been used but without much success. Here we propose to use a non-linear filter approach to remove gravity and magnetic anomalies smaller than a given width. This technique attempts to mimic the graphical separation method. The results from synthetic models are presented as well as the results from a case study in eastern Canada and compared to regional gravity and magnetic anomalies obtained by other techniques. Contrary to the regional fields obtained by upward continuation, non-linear filtering does not have any physical meaning. However, its main advantage is that it gives a regional component of the gravity or magnetic field similar to the one obtained from a graphical separation.     

VLF ANOMALIES FROM A PERFECTLY CONDUCTING HALF PLANE BELOW AN OVERBURDEN*

A theoretical solution to the electromagnetic problem of a perfectly conducting half plane below a conducting overburden has been obtained. The VLF anomalies have been computed for different overburden conductivity and thickness and also for different dip angles of the half plane. In the computations the contribution to the secondary magnetic field from the electric Hertz potential has been neglected. The anomaly curves which are displayed as EM 16 readings, show a fairly complicated behaviour. This is mainly due to the phase shift and attenuation of the field caused by the conductivity of the overburden and the host rock. From the anomaly curves it is possible to define the apparent depth to the top of the conductor as the distance between the peak value and the cross-over of the real component. The apparent depth is usually larger than the actual depth, but it is possible to determine the actual depth to the conductor from the relation between the peak-to-peak anomaly and the apparent depth. When the peak-to-peak anomaly is fairly large, it is also possible to make estimates of the dip angle. However, a complete set of master curves will be a necessary tool for interpretation of VLF data when there is need to obtain more accurate estimates of the half plane parameters. In a specific case the theoretical calculations are shown to be in good agreement with measured data.     

INTERPRETATION OF VLF-EM IN-PHASE DATA USING CURRENT DENSITY PSEUDOSECTIONS1

The interpretation of VLF-EM surveys in terms of buried conductors can be assisted by the application of a linear filter to the observed in-phase component of the vertical magnetic field. One such scheme is examined critically by using the calculated response from a variety of synthetic models to compute theoretical current density pseudosections. The results confirm that this filter technique provides a useful complementary tool for studying the third (i.e. depth) dimension. For single, steeply dipping plates (> 45°) diagnostic information may be derived concerning the depth, size, lateral location, and direction of dip, since the current density maxima seems always to occur within the conductor or at least within one data interval. However, there are some limitations which do not appear to be widely recognized. For single plates the angle of dip cannot be resolved by the current density transformation. Pattern distortions can occur where targets are in close proximity, where the cross-sectional form of the conductor is complex or where the dip is shallow (< 45°). In these latter cases the current density maxima may not occur within the conductive structure and therefore cannot be used to infer depth of burial and/or conductor shape with the same degree of confidence.     

LINE CURRENT FILTERING OF FIXED-LOOP TRANSIENT ELECTROMAGNETIC DATA1

The VLF filtering technique of Karous and Hjelt has been applied to fixed-loop step-response transient electromagnetic data. This allows the data measured in each channel to be converted to an equivalent current-density pseudosection. For a conductive half-space, the maximum value of the equivalent current density starts near the transmitter loop and migrates outwards as a function of delay time. The rate of migration tends to increase as a function of delay time, with the increase being faster for a surficial conductive layer than it is for a half-space. Theoretical and field examples show that the currents tend to be more persistent in the relatively conductive areas, so that a pseudosection which is the average of the current densities at all delay times will highlight the more conductive zones. In resistive ground, it is not so critical to average the pseudosections as a particular delay time may give a better idea of the conductivity structure. For example, the latest possible delay time will reveal the most conductive features.     

An optimal Savitzky–Golay derivative filter with geophysical applications: an example of self-potential data

We propose a strategy in designing an optimal set of filter parameters, such as the order of interpolating polynomial and the filter length for a Savitzky–Golay derivative filter. The proposed strategy is based on the ‘principle of parsimony’ while satisfying the optimality conditions. The optimality conditions are based on the Durbin–Watson lag-1 test statistic and the Derringer–Suich desirability function. While the former checks for an appropriate data fitting, the latter, on the other hand, ensures minimal shape distortion of the reconstructed response. The proposed strategy of designing filter parameters is developed and validated through numerical experiments using Gaussian pulse as a test function which is contaminated with additive white Gaussian noise. In the numerical tests, the polynomial orders used were 3, 5 and 7, but the filter length for each polynomial was varying until the optimality conditions were satisfied. The Savitzky–Golay derivative filtering is used in obtaining the robust reconstruction of noisy geophysical anomaly and the robust estimation of its first- and second-order derivatives. We validated the proposed technique on the published self-potential anomaly data using a data-based interpretation technique where the reconstructed anomaly and its first- and second-order derivatives were used in estimating model parameters. The data-based interpretation using the proposed technique of Savitzky–Golay derivative filtering provides a close agreement with the published results.     

补偿向下延拓方法研究及应用

位场向下延拓是重、磁处理和解释的常用方法,但其不稳定性限制了其在资料处理及反演中的应用.本文基于补偿圆滑滤波思想以及空间域向下延拓迭代法,通过逐次补偿的办法实现位场的稳定向下延拓.同时,在频率域空间给出了该下延方法的频率域响应因子,并讨论了其低通滤波特性,理论模型和实际位场资料试验表明该方法向下延拓稳定性具有较高的延拓精度.将其应用于重力密度界面反演中,改进反演的稳定性,实际莫霍界面反演表明下延因子具备实用性.     

Nonlinear structure‐enhancing filtering using plane‐wave prediction*

Attenuation of random noise and enhancement of structural continuity can significantly improve the quality of seismic interpretation. We present a new technique, which aims at reducing random noise while protecting structural information. The technique is based on combining structure prediction with either similarity‐mean filtering or lower‐upper‐middle filtering. We use structure prediction to form a structural prediction of seismic traces from neighbouring traces. We apply a non‐linear similarity‐mean filter or an lower‐upper‐middle filter to select best samples from different predictions. In comparison with other common filters, such as mean or median, the additional parameters of the non‐linear filters allow us to better control the balance between eliminating random noise and protecting structural information. Numerical tests using synthetic and field data show the effectiveness of the proposed structure‐enhancing filters.     

Interpretation of VLF Resistivity Data for Ground Water Contamination Surveys

Very low frequency (VLF) military communications systems provide a primary field that can be used for shallow geophysical surveys to locate ground water contamination and vertical geologic contacts. Useful properties that can be easily obtained from the interaction of the earth and the primary field are the magnitude of the vertical secondary magnetic field, the surface impedence, and the phase angle between the electrical and magnetic horizontal components. The variations in the secondary magnetic field can be related to vertical geologic contacts, such as the edges of landfill trenches. The surface impedence yields an apparent terrain conductivity, which can be used to locate low-resistivity anomalies often associated with contaminated ground water. The phase angle gives information on vertical variations in resistivity, phase angles less than 45° indicating increasing resistivity with depth. The depth of penetration of the VLF field is about one skin depth. For a frequency of 20 kHz, the skin depth in meters is approximately equal to 3.67 where p is terrain resistivity in ohmmeters.     

Incorporation of a Non-linear Image Filtering Technique for Noise Reduction in Seismic Data

Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing. In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences. The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component. We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data. Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively.     

基于非平稳相似性系数的构造导向滤波及断层检测方法

不连续地质体（如断层）的自动检测一直以来都是叠后地震数据解释中的关键问题之一,尤其在三维情况中尤为重要.然而,大多数边缘检测和相干算法都对随机噪声很敏感,随机噪声衰减是叠后地震数据解释的另一个主要问题.针对构造保护去噪和断层检测问题,本文基于非平稳相似性系数完善一种构造导向滤波方法并且提出一种自动断层检测方法,形成了一套匹配的处理技术.该构造导向滤波既能够有效地衰减随机噪声又可以很好地保护地震资料中的断层等信息不被破坏,增强地震剖面中弯曲、倾斜同相轴的连续性.根据地震数据局部倾角走向,利用相邻道构建当前地震道的预测,通过预测道的叠加得到参考道,计算预测道与参考道之间的非平稳相似性系数可以设计出数据驱动的加权中值滤波.另一方面,预测道与原始道之间的非平稳相似性系数能够用于带有断层指示性的相干分析.这两种方法都基于构造预测和非平稳相似性系数,但是使用不同的调节参数和处理方案.理论模型和实际数据的处理结果证明了本文提出构造导向滤波和断层检测方法的有效性.     

Comparison between VLF and RMT methods: A combined tool for mapping conductivity changes in the sedimentary cover

We compare the resolution power of single frequency very low frequency (VLF) electromagnetic data (real and imaginary parts of the tipper) and multi-frequency RadioMagnetoTelluric (RMT) data in delineating conductive structures typical for the sedimentary cover over crystalline basement in Scandinavia. Using VLF field data from five parallel profiles reveals that the estimated models have responses that fit the observed data well, and the models show an overall agreement with more detailed models derived from broadband RMT data. It is suggested that VLF data be used as a fast mapping tool to fill in the gaps between profiles along which more detailed RMT measurements are made. A generic model with conductive clay lenses and sandy formations over crystalline basement is used to generate synthetic data for the two cases. Using regularized inversion the corresponding estimated models clearly shows the strength and the weakness of both methods. Being inductive methods, they both have difficulties in clearly resolving the depth transition from conductive to resistive units. Especially the single frequency VLF data can be interpreted with very smooth models at depth. However, both methods resolve very well the lateral boundaries of the clay lenses and the RMT data also constrain the thickness of the clays quite well compared with the VLF models, which are less distinct at depth. Single frequency scalar VLF data emphasize those conductive structures that have dominant strikes in the direction of the transmitter. Multi-frequency VLF (tensor VLF) measurements provide the tipper vector which depends upon the underlying conductivity structure only. Real conductivity structures have significant 3D components which can be delineated easily by tensor VLF measurements. We propose that new VLF instrumentation be developed with this in mind.     

Microlevelling procedures applied to regional aeromagnetic data: an example from the Transantarctic Mountains (Antarctica)

The extensive application of digital enhancement and filtering as a powerful tool for aeromagnetic interpretation, not only of high resolution but also of regional data, requires an improved levelling. Two microlevelling techniques were thus compared in order to find an effective but relatively simple procedure to remove, or at least to reduce, residual magnetic errors remaining after standard levelling processes. This study was carried out on regional aeromagnetic data recently acquired at high magnetic latitudes along the Transantarctic Mountains in Antarctica, where it is particularly critical to remove time-dependent magnetic variations. Two-dimensional FFT filters applied to the gridded data, namely the Butterworth and a directional cosine filter, proved to be more effective than previously proposed one-dimensional space-domain filters in the reduction of the 'residual corrugation' not removed by statistical levelling. Tectonic interpretation of trends detected in the total field magnetic anomaly map and in the 3D analytic signal improved after application of frequency-domain microlevelling. However, we also show that when interpreting microlevelled data, two factors must be considered: (i) the possible presence of real geological trends aligned along the flight lines; (ii) modifications in the results yielded by depth estimates of magnetic sources due to the FFT filters applied during the microlevelling procedure. Such changes were seen both in the well-established 2D FFT method, based on the slope of the energy spectrum, and in the more recent 3D Euler deconvolution technique. Overall our results indicate that microlevelling could profitably be applied to older gridded aeromagnetic data sets in Antarctica, thus improving the accuracy and geological significance of future regional magnetic compilations, as already seen in other continents.     

局部相关加权中值滤波技术及其在叠后随机噪声衰减中的应用

随机噪声的衰减和同相轴连续性的提高可以极大地改善地震资料解释的精度.本文提出一种新的滤波技术,既能够有效地衰减随机噪声又可以很好地保护地震资料中的断层等信息不被破坏,增强地震剖面中弯曲、倾斜同相轴的连续性.该方法结合新的加权中值滤波技术和两种构造信息保护滤波策略,实现基于预测数据体和基于倾角走向的加权中值滤波.通过设计...     

THE COLLOCATION APPROACH TO THE INVERSION OF GRAVITY DATA1

Gravity data inversion can provide valuable information on the structure of the underlying distribution of mass. The solution of the inversion of gravity data is an ill-posed problem, and many methods have been proposed for solving it using various systematic techniques. The method proposed here is a new approach based on the collocation principle, derived from the Wiener filtering and prediction theory. The natural multiplicity of the solution of the inverse gravimetric problem can be overcome only by assuming a substantially simplified model, in this case a two-layer model, i.e. with one separation surface and one density contrast only. The presence of gravity disturbance and/or outliers in the upper layer is also taken into account. The basic idea of the method is to propagate the covariance structure of the depth function of the separation surface to the covariance structure of the gravity field measured on a reference plane. This can be done since the gravity field produced by the layers is a functional (linearized) of the depth. Furthermore, in this approach, it is possible to obtain the variance of the estimation error which indicates the precision of the computed solution. The method has proved to be effective on simulated data, fulfilling the a priori hypotheses. In real cases which display the required statistical homogeneity, good preliminary solutions, useful for a further quantitative interpretation, have also been derived. A case study is discussed.     

VLF RESISTIVITY MAPPING AND VERTICALIZATION OF THE ELECTRIC FIELD1

For over 20 years, powerful VLF transmitters have been used as electromagnetic sources for subsurface investigations in mining exploration. Measurements initially concerned the vertical component of the magnetic field or the inclination of the field and were later extended to measurement of the horizontal electric field in the direction of the transmitter, to determine the resistivity of the terrain. Measurement of the electric field is usually performed with electric lines, grounded or not, with lengths of at least 5 m. This paper presents the concept of a VLF resistivity meter with a very short electric sensor (1 m) and the results obtained with it. This technique improves the measurement of the electric field, which is in principle a point value. It also permits a higher spatial sampling rate and, by closely linking the electric sensor with the magnetic sensor on a lightweight mount, makes it possible for the instrument to be used by a single operator. In addition, transformation of the electric field data, analogous to reduction to the pole in magnetism, is proposed to correct the horizontal deformation of the anomalies created by polarization of the primary field. Comparison with direct current electrical measurements shows highly satisfactory correlations. This transformation, validated for VLF, can be extended to any electrical or electromagnetic method using a uniform primary field, i.e. gradient array in direct current or low-frequency magnetotellurics. We call this verticalization of the electric field. Resistivity measurements and mapping using the VLF frequency range can be applied not only to mining but also to a wide range of shallow geophysical studies (hydrology, civil engineering, etc.) and are not limited to problems concerning the location of conductive targets     

基于抛物线密度模型的频率域三维界面反演及其在川滇地区的应用

密度界面反演作为了解地球内部结构的一种重要方法,长期以来都是重力学研究的主要内容.本文结合抛物线密度模型及频率域算法的优点,将抛物线密度函数应用于Parker-Oldenburg算法,经过理论推导得到了抛物线密度模型的频率域公式,从而建立了基于抛物线密度模型的三维密度界面重力异常正反演的算法和流程.理论模型数据试验表明本方法快速、有效,适用于大多数浅部比深部增加更快的实际地壳密度.研究中还利用该方法对川滇地区重力异常进行了反演,获得了该区的莫霍面深度分布,并与接收函数研究结果进行对比分析,进一步验证了本文方法的正确性和有效性.     

基于ARMA模型非因果空间预测滤波(英文)

常规频域预测滤波方法是建立在自回归(autoregressive,AR)模型基础上的,这导致滤波过程中前后假设的不一致,即首先利用源噪声的假设计算误差剖面,却又将其作为可加噪声而从原始剖面中减去来得到有效信号。本文通过建立自回归-滑动平均(autoregres sive/moving-average,ARMA)模型,首先求解非因果预测误差滤波算子,然后利用自反褶积形式投影滤波过程估计可加噪声,进而达到去除随机噪声目的。此过程有效避免了基于AR模型产生的不一致性。在此基础上,将一维ARMA模型扩展到二维空间域,实现了基于二维ARMA模型频域非因果空间预测滤波在三维地震资料随机噪声衰减中的应用。模型试验与实际资料处理表明该方法在很好保留反射信息同时,压制随机噪声更加彻底,明显优于常规频域预测去噪方法。