2D magnetic resonance tomography applied to karstic conduit imaging

Karstic conduits play a crucial role for water supply in many parts of the world. However, the imaging of such targets is generally a difficult task for most geophysical methods. Magnetic Resonance Sounding (MRS) is a geophysical method designed for imaging of water bearing structures. Initially, MRS was developed for characterizing horizontally stratified aquifers. However, when applying a 1D MRS measuring setup to the imaging of 2D–3D targets, the size of which may be much smaller than the loop, the accuracy and the lateral resolution may not be sufficient. We have studied the possibility of simultaneously processing several MRS aligned along a profile to perform a Magnetic Resonance Tomography (MRT). This work emphasizes the gain of resolution for 2D–3D imagery of MRT versus the interpolation of 1D inversion results of MRS along the same profile. Numerical modelling results show that the MRT response is sensitive to the size and location of the 2D target in the subsurface. Sensitivity studies reveal that by using the coincident transmitting/receiving (TX/RX) setup and shifting the loop around the anomaly area, the depth, section and position of a single karstic conduit with a size smaller than the MRS loop size can be resolved. The accuracy of the results depends on the noise level and signal level, the latter parameter being linked to the depth and volume of the karstic conduit and the water content in the limestone matrix. It was shown that when applying MRT to the localization of 2D anomalies such as karstic conduits, the inclination of the geomagnetic field, the orientation of the MRT profile and the angle of crossover of the conduit by the MRT profile must be taken into account. Otherwise additional errors in interpretation should be expected. A 2D inversion scheme was developed and tested. Both numerical and experimental results confirm the efficiency of the developed approach.     

Interpretation of magnetic resonance soundings in rocks with high electrical conductivity

Magnetic resonance sounding (MRS) is an electromagnetic method designed for groundwater investigations. MRS can be applied not only for studying fresh-water aquifers, but also in areas where intrusion of saline water is rendering the subsurface electrically conductive. In the presence of rocks with a high electrical-conductivity attenuation and a phase shift of the MRS signal may influence the efficiency of the MRS method. We investigated the performance of MRS for allowing us to propose a procedure for interpreting MRS data under these conditions. For numerical modeling, we considered a subsurface with a resistivity between 0.5 and 10 Ω m. The results show that the depth of investigation with MRS depends upon the electrical conductivity of groundwater and surrounding rocks, on the depth of the saline water layer, and on the amount of fresh water above the saline water. For interpreting MRS measurements, the electrical conductivity of the subsurface is routinely measured with an electrical or electromagnetic method. However, due to the equivalence problem, the result obtained with these methods may be not unique. Hence, we investigated the influence of the uncertainty in conductivity distribution provided by transient electromagnetic measurements (TEM) on MRS results. It was found that the uncertainty in TEM results has an insignificant effect on MRS.     

2D magnetic resonance tomography applied to karstic conduit imaging

Karstic conduits play a crucial role for water supply in many parts of the world. However, the imaging of such targets is generally a difficult task for most geophysical methods. Magnetic Resonance Sounding (MRS) is a geophysical method designed for imaging of water bearing structures. Initially, MRS was developed for characterizing horizontally stratified aquifers. However, when applying a 1D MRS measuring setup to the imaging of 2D–3D targets, the size of which may be much smaller than the loop, the accuracy and the lateral resolution may not be sufficient. We have studied the possibility of simultaneously processing several MRS aligned along a profile to perform a Magnetic Resonance Tomography (MRT). This work emphasizes the gain of resolution for 2D–3D imagery of MRT versus the interpolation of 1D inversion results of MRS along the same profile. Numerical modelling results show that the MRT response is sensitive to the size and location of the 2D target in the subsurface. Sensitivity studies reveal that by using the coincident transmitting/receiving (TX/RX) setup and shifting the loop around the anomaly area, the depth, section and position of a single karstic conduit with a size smaller than the MRS loop size can be resolved. The accuracy of the results depends on the noise level and signal level, the latter parameter being linked to the depth and volume of the karstic conduit and the water content in the limestone matrix. It was shown that when applying MRT to the localization of 2D anomalies such as karstic conduits, the inclination of the geomagnetic field, the orientation of the MRT profile and the angle of crossover of the conduit by the MRT profile must be taken into account. Otherwise additional errors in interpretation should be expected. A 2D inversion scheme was developed and tested. Both numerical and experimental results confirm the efficiency of the developed approach.     

Challenges of using electrical resistivity method to locate karst conduits—A field case in the Inner Bluegrass Region, Kentucky

Conduits serve as major pathways for groundwater flow in karst aquifers. Locating them from the surface, however, is one of the most challenging tasks in karst research. Geophysical methods are often deployed to help locate voids by mapping variations of physical properties of the subsurface. Conduits can cause significant contrasts of some physical properties that can be detected; other subsurface features such as water-bearing fractures often yield similar contrasts, which are difficult to distinguish from the effects of the conduits. This study used electrical resistivity method to search for an unmapped karst conduit that recharges Royal Spring in the Inner Bluegrass karst region, Kentucky, USA. Three types of resistivity techniques (surface 2D survey, quasi-3D survey, and time-lapse survey) were used to map and characterize resistivity anomalies. Some of the major anomalies were selected as drilling targets to verify the existence of the conduits. Drilling near an anomaly identified by an electrical resistivity profile resulted in successful penetration of a major water-filled conduit. The drilling results also suggest that, in this study area, low resistivity anomalies in general are associated with water-bearing features. However, differences in the anomaly signals between the water-filled conduit and other water-bearing features such as water-filled fracture zones were undistinguishable. The electrical resistivity method is useful in conduit detection by providing potential drilling targets. Knowledge of geology and hydrogeology about the site and professional judgment also played important roles in locating the major conduit.     

2D磁异常分步反演方法分析研究

2D磁异常分步反演方法是利用二维(剖面)磁测数据确定场源几何参数以及物性参数的一种反演方法,该方法的优点是构造的形态函数S不受场源磁化特征的影响,因此可以在未知场源物性参数的前提下,通过拟合依次反演得到磁性源形体横截面几何参数、磁化强度以及磁化方向.本文阐述了2D磁异常分步反演方法的原理及步骤,对形态函数S的特征及求取方法进行了讨论,分析了区域背景干扰(正常场)对反演结果的影响并提出了初步解决方案.在方法研究的基础上,进行了单一理论模型及组合理论模型的试算,得到了较好的反演结果.为了验证该方法的效果,对实测剖面进行了试算,得到了场源的边界及场源埋深信息,为进一步反演提供了有用的参考.     

Using constrained inversion of gravity and magnetic field to produce a 3D litho‐prediction model

Geologically constrained inversion of gravity and magnetic field data of the Victoria property (located in Sudbury, Canada) was undertaken in order to update the present three‐dimensional geological model. The initial and reference model was constructed based on geological information from over 950 drillholes to constrain the inversion. In addition, downhole density and magnetic susceptibility measured in six holes were statistically analysed to derive lower and upper bounds on the physical properties attributed to the lithological units in the reference model. Constrained inversion of the ground gravity and the airborne magnetic data collected at the Victoria property were performed using GRAV3D and MAG3D, respectively. A neural network was trained to predict lithological units from the physical properties measured in six holes. Then, the trained network was applied on the three‐dimensional distribution of physical properties derived from the inversion models to produce a three‐dimensional litho‐prediction model. Some of the features evident in the lithological model are remnants of the constraints, where the data did not demand a significant change in the model from the initial constraining model (e.g., the thin pair of diabase dykes). However, some important changes away from the initial model are evident; for example, a larger body was predicted for quartz diorite, which may be related to the prospective offset dykes; a new zone was predicted as sulfide, which may represent potential mineralisation; and a geophysical subcategory of metabasalt was identified with high magnetic susceptibility and high density. The litho‐prediction model agrees with the geological expectation for the three‐dimensional structure at Victoria and is consistent with the geophysical data, which results in a more holistic understanding of the subsurface lithology.     

强剩磁强退磁条件下的二维井中磁测反演

强剩磁、强退磁改变了总磁化强度的大小和方向,给磁测资料解释带来困难.为此,本文利用二维井中磁测数据反演磁化强度矢量的二维分布.首先利用井中磁测的磁异常模量反演磁化强度大小的分布.然后,在已知磁化强度大小分布的前提下,拟合磁场分量,反演磁化强度方向的分布.其中,磁化强度大小和方向均用共轭梯度法求解,并通过预优矩阵改善磁化强度大小的反演效果.理论模拟说明,该方法能准确获得磁化强度矢量分布.磁化强度矢量反演结果包括感磁、剩磁及退磁的影响,这为研究强剩磁、高磁化率矿床提供了一种有效方法.     

Estimating free parameters in 2D inversion: example of gravity inversion in a rifted basement

We advance a principle directed to assigning numerical values to free parameters usually present in inversion methods. It may be formulated as: ‘Optimum estimates of free parameters in an inversion procedure must lead, in tests using synthetic data, to solutions whose geometrical expression reflects the main qualitative or semiquantitative geological characteristic of the study area.’ To this end, the interpreter should (i) specify a typical anomalous source geometry which incorporates the most relevant geological information for the study area, (ii) compute the corresponding gravity anomaly and (iii) invert the anomaly for the source geometry finding the numerical values of the free parameters that lead to a solution closest to the typical source. Application of the above methodology to synthetic and real data from the basement relief of a rift basin has asserted its efficacy.     

大地电磁、重力、磁法和地震初至波走时的交叉梯度二维联合反演研究

为了准确的探测和描绘地下复杂的地质结构,同时克服地球物理单一方法反演的多解性和单一参数反演模型的不一致性等问题,近年来基于交叉梯度联合反演的综合地球物理解释已经得到了广泛的关注和应用.本文首先研究了两种地球物理方法的交叉梯度联合反演算法,在此基础上,推导并实现了多种地球物理方法（大地电磁,重力,磁法,地震初至波走时）的多交叉梯度约束的二维联合反演算法;其次,我们设计了结构不一致模型和复杂模型,针对多物性联合反演算法的准确性和有效性进行了模拟试算,并对复杂模型的单独反演结果和联合反演结果进行了交叉梯度值和物性交会图的对比;最后,本文将成熟的卫星资料多光谱综合分析技术应用到联合反演中,将多物性参数反演模型结果图通过RGB（红-绿-蓝）模式进行合成,得到融合的RGB合成图.结果表明：通过对结构不一致模型和复杂模型的联合反演结果和单独反演结果的对比分析,可以得出联合反演得到的结果更接近真实模型,并从得到的交叉梯度值进一步证明了联合反演模型相似度高,也从物性交会图中得到联合反演的物性相关性更好的结论,反向证明了算法的正确性.最终从得到的RGB合成图像,我们可以更直观的分析反演结果,更有利于准确划分地下模型结构.

     

Gravity and magnetic data inversion for 3D topography of the Moho discontinuity in the northern Red Sea area, Egypt

The main goal of our study is to investigate 3D topography of the Moho boundary for the area of the northern Red Sea including Gulf of Suez and Gulf of Aqaba. For potential field data inversion we apply a new method of local corrections. The method is efficient and does not require trial-and-error forward modeling. To separate sources of gravity and magnetic field in depth, a method is suggested, based on upward and downward continuation. Both new methods are applied to isolate the contribution of the Moho interface to the total field and to find its 3D topography. At the first stage, we separate near-surface and deeper sources. According to the obtained field of shallow sources a model of the horizontal layer above the depth of 7 km is suggested, which includes a density interface between light sediments and crystalline basement. Its depressions and uplifts correspond to known geological structures. At the next stage, we isolate the effect of very deep sources (below 100 km) and sources outside the area of investigation. After subtracting this field from the total effect of deeper sources, we obtain the contribution of the Moho interface. We make inversion separately for the area of rifts (Red Sea, Gulf of Suez and Gulf of Aqaba) and for the rest of the area. In the rift area we look for the upper boundary of low-density, heated anomalous upper mantle. In the rest of the area the field is satisfied by means of topography for the interface between lower crust and normal upper mantle. Both algorithms are applied also to the magnetic field. The magnetic model of the Moho boundary is in agreement with the gravitational one.     

Transport of suspended solids from a karstic to an alluvial aquifer: the role of the karst/alluvium interface

This study focuses on the coupled transport of dissolved constituents and particulates, from their infiltration on a karst plateau to their discharge from a karst spring and their arrival at a well in an alluvial plain. Particulate markers were identified and the transport of solids was characterised in situ in porous and karstic media, based on particle size analyses, SEM, and traces. Transport from the sinkhole to the spring appeared to be dominated by flow through karst: particulate transport was apparently conservative between the two sites, and there was little difference in the overall character of the particle size distribution of the particulates infiltrating the sinkhole and of those discharging from the spring. Qualitatively, the mineralogy of the infiltrating and discharging material was similar, although at the spring an autochthonous contribution from the aquifer was noted (chalk particles eroded from the parent rock by weathering). In contrast, transport between the spring and the well appears to be affected by the overlying alluvium: particles in the water from the well, showed evidence of considerable size-sorting. Additionally, SEM images of the well samples showed the presence of particles originating from the overlying alluvial system; these particles were not found in samples from the sinkhole or the spring. The differences between the particulates discharging from the spring and the well indicate that the water pumped from the alluvial plain is coming from the karst aquifer via the very transmissive, complex geologic interface between the underlying chalk formation and the gravel at the base of the overlying alluvial system.     

磁化强度矢量反演新方法及其在卡拉塔格铜多金属矿床找矿中的应用

磁异常的反演是地球物理勘探的重要手段,三维磁化率反演是磁异常定量解释中的一种重要方法.由于剩磁的存在使得磁化方向与地磁场方向产生偏差,从而影响了磁异常反演与解释的精度.本文基于磁异常模量反演和磁化强度矢量反演方法得到了一种新的磁化强度矢量反演方法.与以往的磁化强度矢量反演方法相比,该方法以磁异常模量反演得到的磁化率模型为约束,采用L_p范数正则化方法求解,提高了磁化强度矢量反演的精度和效率.本文通过模拟试验的反演计算,验证了这种磁化强度矢量反演方法的有效性.最后,将本文方法应用于新疆东天山卡拉塔格地区航磁数据的解释,获得了地下空间不同磁性差异的磁性体的空间分布特征,为进一步分析研究区隐伏矿床提供了重要信息.     

Internal structure of Ustica volcanic complex (Italy) based on a 3D inversion of magnetic data

A ground magnetic study of Ustica Island was performed to provide new insights into subsurface tectonic and volcanic structures. The total-intensity anomaly field, obtained after a data-reduction procedure, shows the presence of a W–E-striking magnetic anomaly in the middle of the island and another two intense anomalies, which seem to continue offshore, in the southwestern and the northeastern sides, respectively. The detected anomalies were analyzed by a quadratic programming (QP) algorithm to obtain a 3D subsurface magnetization distribution. The volcano magnetization model reveals the presence of intensely magnetized volumes, interpreted as the feeding systems of the main eruptive centers of the island, which roughly follow the trend of the main regional structural lineaments. These findings highlight how regional tectonics has strongly affected the structural and magmatic evolution of the Ustica volcanic complex producing preferential ways for magma ascent.     

自动构建大地电磁二维反演的测点中心网格

在大地电磁二维反演中,如果网格不均匀或者测点在网格中的位置不恰当,则将出现测点偏离现象,影响反演的精度.此外,由于正演精度和稳定性的需要,反演中网格间距不能差别太大,需要具有一定的光滑性.本文提出了几种自动构建测点中心网格的方法来消除测点偏离现象,并以正则化约束条件来保证网格的光滑程度.本文还提出了一套网格质量检验指标.算例对比研究表明,对于不同的测点集,最佳网格构建的方法可能不相同,但其中“最平模型约束动态配点法”、“最光模型约束动态配点法”拥有最强的适应能力,它们在各种情况下所构建的网格一般同时具备较光滑的网格间距变化和较小的测点偏离程度.此外,采用高质量（光滑性好、测点偏离程度低）网格在一定程度上不仅可提高反演结果的可靠性,还能提高反演的计算效率.本文的方法为获得高质量的大地电磁二维反演网格提供了简单有效的途径.     

The use of reference models from a priori data to guide 2D inversion of electrical resistivity tomography data

Clay-rich till plains cover much of the UK. Such sites are attractive locations for landfills, since clay aquitards lower the risk of landfill leachate entering groundwater. However, such tills often contain sand and gravel bodies that can act as leachate flow routes. Such bodies may not be detected by conventional site investigation techniques such as drilling boreholes and trial pitting. A method of guided inversion, where a priori data are used to construct structural reference models for use in inverting electrical resistivity tomography data, was proposed as a tool to improve the detection of sand and gravel bodies within clay-rich till sequences.
Following a successful 2D guided inversion synthetic modelling study, a field study was undertaken. Wenner 2D electrical resistivity tomography lines, resistivity cone penetrometry bores and electromagnetic induction ground resistivity data were collected over a site on the East Yorkshire coast, England, where sand and gravel lenses were known to exist from cliff exposures. A number of equally valid geoelectrical models were constructed using the electromagnetic and resistivity cone data. These were used as structural reference models in the inversion of the resistivity tomography data. Blind inversion using an homogenous reference model was also carried out for comparison.
It was shown for the first time that the best solution model produced by 2D inversion of one data set with a range of structural reference models could be determined by using the l ₂ model misfit between the solution models and associated reference models (reference misfit) as a proxy for the l ₂ misfit between the solution models and the synthetic model or 'best-guess' geoelectrical model (true misfit). The 2D methodology developed here is applicable in clay-rich till plains containing sand and gravel bodies throughout the UK.     

Optimizing a layered and laterally constrained 2D inversion of resistivity data using Broyden's update and 1D derivatives

Dense profile-oriented resistivity data allows for 2D and 3D inversions. However, huge amounts of data make it practically impossible to do full 2D or 3D inversions on a routine basis. Therefore, a number of approximations have been suggested over the years to speed up computations. We suggest using a combination of Broyden's update on the Jacobian matrix with derivatives calculated using a 1D formulation on a parameterized 2D model of locally 1D layered models. The approximations bring down the effective number of 2D forward responses to a minimum, which again gives us the ability to invert very large sections. Broyden's update is not as useful with a parameterized problem as is the case with a smooth minimum structure problem that has been the usual application. 1D derivatives, however, seem to be very effective when initiating a full 2D solution with Broyden's update. We compare the different methods using two different kinds of data on two synthetic models and on two field examples. The most effective and reliable optimization combines 1D derivatives with a full 2D solution and Broyden's update. When using Broyden's update the Jacobian matrix needs to be reset every once in a while. We do this whenever the difference in data residual from the previous iteration is less than 5%. This combined inversion method reduces the computation time approximately a factor of 3 without losing model resolution.     

裂陷盆地基底双界面模式二维重力反演

裂陷盆地基底的起伏表现为非光滑的几何形态,传统的重力反演结果并不能很好地反映这种特点.此外,大多数情况下,重力观测面并不位于盆地上界面,应为单独的起伏观测面,盆地应为上界面和基底组成的双界面模式.基于此,本文研究了起伏观测面上裂陷盆地基底双界面模式二维重力反演方法.研究中假设沉积盆地的沉积层与基底的密度差随深度按双曲线规律变化.将沉积盆地的沉积层剖分成相邻的垂直柱体,其水平尺寸是已知的,顶面与沉积层上界面重合,底面深度代表基底的深度,即为要反演的参数.反演中引入全变差函数作为盆地模型的约束,使得反演结果呈现非光滑形态,符合裂陷盆地基底特征.为减小反演多解性,引入已知深度点作为约束.建立由重力数据拟合、已知深度约束及全变差函数组成的目标函数,采用非线性共轭梯度算法使目标函数最小化.模型试算结果表明该方法可反演裂陷盆地基底起伏,并通过调整正则化参数的值可反演坳陷盆地基底起伏.将该反演方法用于珠江口盆地惠州凹陷和运城-临汾裂陷盆地实际资料处理,其结果较好地反映了裂陷盆地基底起伏特征,为研究盆地构造、油气勘探等提供重要参考.     

Reservoir parameter classification of a Miocene formation using a fractal approach to well logging,porosimetry and nuclear magnetic resonance

A methodology for rock classification is presented that considers lithology and reservoir parameters on the basis of a combined fractal analysis of well logs and mercury porosimetry results with nuclear magnetic resonance outcomes. A sandy‐shaly thinly‐bedded Miocene gas bearing formation in the Carpathian Foredeep is investigated. Fractal correlation dimensions D₂ calculated for standard logs are used to distinguish sandstone as the most homogeneous lithological group with the highest porosity. The fractal analysis also confirmed observations of gas accumulations in sandstone, shaly sandstone and sandy claystone as rocks of high porosity. The results of two laboratory methods are combined to improve reservoir properties assessment and evaluate movable media in pore space; this technique was based on the similarity of mercury porosimetry results plotted as cumulative intrusion volume versus pressure or pore diameter and also the curves of cumulative porosity and transverse relaxation time distributions using nuclear magnetic resonance. Close values of porosity from logs, recorded in situ and in laboratory measurements, provide the link between fractal analysis and porosimetry and nuclear magnetic resonance measurements.     

Using wavelet‐domain adaptive filtering to improve signal‐to‐noise ratio of nuclear magnetic resonance log data from tight gas sands

In tight gas sands, the signal‐to‐noise ratio of nuclear magnetic resonance log data is usually low, which limits the application of nuclear magnetic resonance logs in this type of reservoir. This project uses the method of wavelet‐domain adaptive filtering to denoise the nuclear magnetic resonance log data from tight gas sands. The principles of the maximum correlation coefficient and the minimum root mean square error are used to decide on the optimal basis function for wavelet transformation. The feasibility and the effectiveness of this method are verified by analysing the numerical simulation results and core experimental data. Compared with the wavelet thresholding denoise method, this adaptive filtering method is more effective in noise filtering, which can improve the signal‐to‐noise ratio of nuclear magnetic resonance data and the inversion precision of transverse relaxation time T₂ spectrum. The application of this method to nuclear magnetic resonance logs shows that this method not only can improve the accuracy of nuclear magnetic resonance porosity but also can enhance the recognition ability of tight gas sands in nuclear magnetic resonance logs.     

An application of the distributed hydrologic model CASC2D to a tropical montane watershed

Increased stormflow in the Quebrada Estero watershed (2.5 km²), in the northwestern Central Valley tectonic depression of Costa Rica, reportedly has caused flooding of the city of San Ramón in recent decades. Although scientifically untested, urban expansion was deemed the cause and remedial measures were recommended by the Programa de Investigación en Desarrollo Humano Sostenible (ProDUS). CASC2D, a physically-based, spatially explicit hydrologic model, was constructed and calibrated to a June 10th 2002 storm that delivered 110.5 mm of precipitation in 4.5 h visibly exceeded the bankfull stage (0.9 m) of the Quebrada flooding portions of San Ramón. The calibrated hydrograph showed a peak discharge 16.68% (2.5 m³ s⁻¹) higher, an above flood stage duration 20% shorter, and time to peak discharge 11 min later than the same observed discharge hydrograph characteristics. Simulations of changing land cover conditions from 1979 to 1999 showed an increase also in the peak discharge, above flood stage duration, and time to peak discharge. Analysis using a modified location quotient identified increased urbanization in lower portions of the watershed over the time period studied. These results suggest that increased urbanization in the Quebrada Estero watershed have increased flooding peaks, and durations above threshold, confirming the ProDUS report. These results and the CASC2D model offer an easy-to-use, pragmatic planning tool for policymakers in San Ramón to assess future development scenarios and their potential flooding impacts to San Ramón.