Introduction to ground surface self-potential tomography

A new approach to self-potential (SP) data interpretation for the recognition of a buried causative SP source system is presented. The general model considered is characterized by the presence of primary electric sources or sinks, located within any complex resistivity structure with a flat air-earth boundary. First, using physical considerations of the nature of the electric potential generated by any arbitrary distribution of primary source charges and the related secondary induced charges over the buried resistivity discontinuity planes, a general formula is derived for the potential and the electric field component along any fixed direction on the ground surface. The total effect is written as a sum of elementary contributions, all of the same simple mathematical form. It is then demonstrated that the total electric power associated with the standing natural electric field component can be written in the space domain as a sum of cross-correlation integrals between the observed component of the total electric field and the component of the field due to each single constitutive elementary charge. By means of the cross-correlation bounding inequality, the concept of a scanning function is introduced as the key to the new interpretation procedure. In the space domain, the scanning function is the unit strength electric field component generated by an elementary positive charge. Next, the concept of charge occurrence probability is introduced as a suitable function for the tomographic imaging of the charge distribution geometry underground. This function is defined as the cross-correlation product of the total observed electric field component and the scanning function, divided by the square root of the product of the respective variances. Using this physical scheme, the tomographic procedure is described. It consists of scanning the section, through any SP survey profile, by the unit strength elementary charge, which is given a regular grid of space coordinates within the section, at each point of which the charge occurrence probability function is calculated. The complete set of calculated grid values can be used to draw contour lines in order to single out the zones of highest probability of concentrations of polarized, primary and secondary electric charges. An extension to the wavenumber domain and to three-dimensional tomography is also presented and discussed. A few simple synthetic examples are given to demonstrate the resolution power of the new SP inversion procedure.     

3D geoelectric tomography and archaeological applications1

Following a previous paper in which the principles of a 3D ground-surface tomographic processing of self-potential data were established, we extend the method to active source geoelectric surveying. The main purpose of the new tomographic approach is to obtain a physical image reconstruction of the induced electric charges distributed over buried resistivity discontinuities. The information is produced in a probabilistic sense, as the mathematical formulation underlying the method treats only the intrinsic physical nature of the generated electric field underground and the method of its ground-surface detection, independently of the geometry of the unknown structures. In practice, a 3D tomography is realized by cross-correlating a set of distributed electric-field ground-surface data with a scanning function, representing a unit positive point charge located anywhere in the lower half-space. The resolution of the method is tested on the synthetic response of a 3D structural simulation of an archaeological target, consisting of an infinitely resistive prismatic body immersed in a half-space, including surface inhomogeneities and layering. Finally, the field response of a 3D structure consisting of a hypogeal dromos-chamber tomb inside the Sabine Necropolis at Colle del Forno, close to Rome, is presented and discussed.     

Electric field variations measured continuously in free air over a conductive thin zone in the tilted Lias-epsilon black shales near Osnabrück,Northwest Germany

Common studies on the static electric field distribution over a conductivity anomaly use the self-potential method. However, this method is time consuming and requires nonpolarizable electrodes to be placed in the ground. Moreover, the information gained by this method is restricted to the horizontal variations of the electric field. To overcome the limitation in the self-potential technique, we conducted a field experiment using a non conventional technique to assess the static electric field over a conductivity anomaly. We use two metallic potential probes arranged on an insulated boom with a separation of 126 cm. When placed into the electric field of the free air, a surface charge will be induced on each probe trying to equalize with the potential of the surrounding atmosphere. The use of a plasma source at both probes facilitated continuous and quicker measurement of the electric field in the air. The present study shows first experimental measurements with a modified potential probe technique (MPP) along a 600-meter-long transect to demonstrate the general feasibility of this method for studying the static electric field distribution over shallow conductivity anomalies.Field measurements were carried out on a test site on top of the Bramsche Massif near Osnabrück (Northwest Germany) to benefit from a variety of available near surface data over an almost vertical conductivity anomaly. High resolution self-potential data served in a numerical analysis to estimate the expected individual components of the electric field vector.During the experiment we found more anomalies in the vertical and horizontal components of the electric field than self-potential anomalies. These contrasting findings are successfully cross-validated with conventional near surface geophysical methods. Among these methods, we used self-potential, radiomagnetotelluric, electric resistivity tomography and induced polarization data to derive 2D conductivity models of the subsurface in order to infer the geometrical properties and the origin of the conductivity anomaly in the survey area. The presented study demonstrates the feasibility of electric field measurements in free air to detect and study near surface conductivity anomalies. Variations in Ez correlate well with the conductivity distribution obtained from resistivity methods. Compared to the self-potential technique, continuously free air measurements of the electric field are more rapid and of better lateral resolution combined with the unique ability to analyze vertical components of the electric field which are of particular importance to detect lateral conductivity contrasts. Mapping Ez in free air is a good tool to precisely map lateral changes of the electric field distribution in areas where SP generation fails. MPP offers interesting application in other geophysical techniques e.g. in time domain electromagnetics, DC and IP.With this method we were able to reveal a ca. 150 m broad zone of enhanced electric field strength.     

Gravity probability tomography: a new tool for buried mass distribution imaging

Following the probability tomography principles previously introduced to image the sources of electric and electromagnetic anomalies, we demonstrate that a similar approach can be used to analyse gravity data. First, we give a coherent derivation of the Bouguer anomaly concept as a Newtonian-type integral for an arbitrary mass distribution buried below a non-flat topography. A discretized solution of this integral is then derived as a sum of elementary contributions, which are cross-correlated with the gravity data function in the expression for the total power associated with the Bouguer anomaly. To image the mass distribution underground we introduce a mass contrast occurrence probability function using the cross-correlation product of the observed Bouguer anomaly and the synthetic field due to an elementary mass contrast source. The tomographic procedure consists of scanning the subsurface with the elementary source and calculating the occurrence probability function at the nodes of a regular grid. The complete set of grid values is used to highlight the zones of highest probability of mass contrast concentrations. Some synthetic and field examples demonstrate the reliability and resolution of the new gravity tomographic approach.     

自电位层析成像的理论与实验研究

为研究自电位异常场的物理机制，本文根据Patella半无限空间自电位层析成像的理论方法，对有限边界条件下的图像重建进行了研究，根据四边形界面处自电位的测量数据，重建出异常电荷的二维概率分布.文中对图像重建进行了数值模拟，分析了改进成像精度的措施，并对受压岩石的破裂过程开展了实验模拟研究，成像结果表明，实验中发现的岩石破裂的裂隙同正电荷出现的最大概率区域的位置基本一致，反映了裂隙尖端处正负电荷分离的微观过程.     

Looking inside Mount Vesuvius by potential fields integrated probability tomographies

First, we outline the theory of the three-dimensional (3D) probability tomography for any generic vector or scalar geophysical field and define an approach to the integrated tomography of any pair of geophysical data sets collected in the same area. Then, we discuss the results of the application of the 3D probability tomography to the Mount Vesuvius volcanic complex, considering gravity, magnetic and self-potential survey data. The most important feature resulting from the integrated tomography regards the Mt. Vesuvius plumbing system. A unique central conduit is outlined at the intersection between a W–E- and a N—S-trending vertical boundary planes. The top terminal part of this conduit appears completely filled with magnetized and less dense volcanic material. This new information, combined with previous indications about the probable existence of a magma reservoir at 8–10 km of depth, strengthen the hypothesis that Mount Vesuvius is still to be considered a highly hazardous volcano.     

A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.     

岩石破裂过程中的超低频电磁异常

震前电磁场和大地自电位的异常是重要的地震前兆现象．在零磁空间对超低频段的磁场和自电位的变化进行了岩石破裂的实验研究，细致地揭示出电场、磁场出现异常变化的全过程，对深入认识超低频电磁信号的微观机理具有重要的意义．实验发现，岩石受力后应变、电位和磁场的缓慢变化在空间分布上是首先在近破裂源处出现，继而随裂纹的发展而改变位置；在时间序列上先出现自电位异常，然后是超低频磁场的变化；在异常形态上，超低频电磁信号呈现出早期、中期、晚期3个阶段的明显差异．研究表明，岩石微破裂引起裂隙尖端处的电荷分离. 静电荷在局部区域的积累和运移，导致了自电位的脉冲状变化；而在主破裂阶段，积累电荷的急速运动形成瞬间电流，激发了脉冲式的磁场异常．本文详细介绍了这一综合实验的技术步骤和观测结果，并对地震电磁前兆的微观机理进行了探讨．      

ULF electric and magnetic anomalies accompanying the cracking of rock sample

The anomalies of electric-magnetic field and self-potential before earthquakes are important precursory phenom-ena.A simulating experiment study on the variations in ultra-low frequency(ULF)magnetic field and self-poten-tial during rock cracking was carried out in a magnetic field-free space.The results revealing in detail the whole process of the occurrences of electric and magnetic anomalises are significant for understanding the microscopic mechanism of ULF electric and magnetic signals.The experiment indicated that at the initial stage the slow changes in strain.self-potential and magnetic field with small amounts appeared firstly near the source of initial cracking,and then extended as the crack developed on.In the time domain,the self-potential anomaly emerged first and ULF magnetic field changes arose then.The shape of the ULF electric and magnetic anomaly varied ob-viously in early-,mid-and late-term of the test.The authors attributed the pulse-like changes of self-potential to the generationj and movement of the accumulated electric charges during the cracking caused by charge separation on the crack tips within the sample.While the magnetic pulses of shorter-period at the last stage of the test,may be induced by instantaneous electric current of the accumulated charege during the cracking acceleration.The technical method and the observational results of this experiment are given in detail and the microscopic mechanism of elec-tric and magnetic precursors before earthquake are discussd in the present paper as well.     

二次电流场多次叠加概率成像

基于地下电流场的积分公式,离散化的二次电流场被分解为电性不连续界面上的一系列点电荷电场的代数和.单位正点电荷电场被引入作为空间扫描函数（SDS）,积累电荷出现的概率（COP）函数定义为二次电流场与SDS的互相关.为对概率成像结果进行定量分析解释,提出了规范的积累电荷出现的概率（NCOP）函数.通过应用有限元算法对2D地电模型进行二次电流场合成,实现了二次电流场的多次叠加概率成像.结果表明对均匀半空间中赋存地质异常体的电性结构,概率成像方法对地下异常体的空间位置有较好的指示作用.     

Reconstruction of the Water Table from Self-Potential Data: A Bayesian Approach

Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number , especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.     

Hydrothermal system beneath Aso volcano as inferred from self-potential mapping and resistivity structure

We conducted self-potential (SP) surveys sequentially from part to part over the central cones of Aso volcano since August 1998 by December 2001. The compiled SP map revealed large SP anomalies on the central cones. The main feature of the SP map is a ‘W-shaped’ profile along the NS-transect over the central cones. It is probable that this characteristic SP profile is produced by the combination of hydrothermal upwelling in the middle and topographic effect. A positive anomaly showing a large concentric pattern has appeared after correcting the topographic effect.To evaluate this SP anomaly, we implemented a numerical code that calculates electric potential produced by arbitrarily positioned current sources and sinks in any three-dimensional resistivity structure. A layered structure obtained from a time-domain electromagnetic (TDEM) field experiment was used for the resistivity model. The estimated current source is 300 A, being located in a conductive layer around the sea level. Meanwhile, sinks were estimated to sit on a circular area corresponding to the marginal part of the conductive layer.Water and heat budget study gives a lower limit of water mass transfer from depth to the bottom of the crater lake of Nakadake. This value was used to estimate the equivalent current in either case of electro-kinetic (EK) [Mizutani, H., Ishido, T., 1976. A new interpretation of magnetic field variation associated with the Matsushiro earthquakes, J. Geomag. Geoelectr., 28, 179–188.] or rapid fluid disruption (RFD) process [Johnston, M.J.S., Byerlee, J.D., Lockner, D., 2001. Rapid fluid disruption: A source for self-potential anomalies on volcanoes, J. Geophys. Res. 106(B3), 4327-4335.]. This comparison suggests that the former process is preferable to explain the observed SP anomaly. From these results we infer a large-scale hydrothermal system beneath the central cones of Aso volcano, in which the fluid flow initiates from the surrounding area, converging to the central vent to transport the heat and materials up to the crater lake of Nakadake through a vapor-filled conduit.     

On the electrical reflectivity tensor in d.c. electric field modelling

We use the integral equation for a d.c. electric field, published in the literature, to introduce the concept of the electrical reflectivity tensor into d.c. electric field modelling. It is shown that in d.c. electric field modelling, the electric reflectivity tensor can be obtained in exactly the same way as in electromagnetic modelling. As a result, for a d.c. electric field, the quasi‐linear and the quasi‐analytical approximations, as well as the quasi‐analytical series, can be constructed in exactly the same way as in electromagnetic modelling. If the primary field is uniform, and if the anomalous body is a uniform circular cylinder or a uniform sphere, the reflectivity tensor is zero order (constant), relating to the free surface charge density. Thus, for some homogeneous bodies that have simple shapes and are embedded in a uniform primary field, the electrical reflectivity tensor is not only a mathematical mechanism for obtaining approximate solutions, but also a physical reality. Indeed, the free surface charge density is defined as the change of the electric displacement vector across the boundary surface under consideration. If the primary field is caused by a point source, and if the anomalous body is a uniform sphere, the reflectivity tensor is second order, varying slowly within the sphere. The relationship to the free surface charge density can be established only when both the reflectivity tensor and the free surface charge density are approximated by the first terms of their series solutions. If the point source is far from the centre of the sphere, the corresponding reflectivity tensor reduces to zero order, and is independent of the observation position within the sphere, i.e. it is a constant. Therefore, the basic idea of the quasi‐analytical approximation, i.e. taking the reflectivity tensor outside the integral operator, is justified in the case considered here.     

The European Upper Mantle as Seen by Surface Waves

We derive a global, three-dimensional tomographic model of horizontally and vertically polarized shear velocities in the upper mantle. The model is based on a recently updated global database of Love- and Rayleigh-wave fundamental-mode phase-anomaly observations, with a good global coverage and a particularly dense coverage over Europe and the Mediterranean basin (broadband stations from the Swiss and German seismic networks). The model parameterization is accordingly finer within this region than over the rest of the globe. The large-scale, global structure of our model is very well correlated with that of earlier shear-velocity tomography models, based both on body- and surface-wave observations. At the regional scale, within the region of interest, correlation is complicated by the different resolution limits associated to different databases (surface waves, compressional waves, shear waves), and, accordingly, to different models; while a certain agreement appears to exist for what concerns the grand tectonic features in the area, heterogeneities of smaller scale are less robustly determined. Our new model is only one step towards the identification of a consensus model of European/Mediterranean upper-mantle structure: on the basis of the findings discussed here, we expect that important improvements will soon result from the combination, in new tomographic inversions, of fundamental-mode phase-anomaly data like ours with observations of surface-wave overtones, of body-wave travel times, of ambient “noise”, and by accounting for an a-priori model of crustal structure more highly resolved than the one employed here.     

Hydrologic response of upland catchments to wildfires

To which extent do wildfires affect runoff production, soil erosion and sediment transport in upland catchments? This transient effect is investigated here by combining data of long term precipitation, sediment yield and wildfire records with a fine resolution spatially distributed modeling approach to flow generation and surface erosion. The model accounts for changes in the structure and properties of soil and vegetation cover by combining the tube-flux approach to topographic watershed partition with a parsimonious parametrization of hydrologic processes. This model is used to predict hydrologic and sediment fluxes for nine small catchments in Saint Gabriel mountains of southern California under control (pre-fire) and altered (post-fire) conditions. Simulation runs using a 45 years record of hourly precipitation show the passage of fire to significantly modify catchment response to storms with a major effect on erosion and flood flows. The probability of occurrence of major floods in the post-fire season is shown to increase up to an order of magnitude under same precipitation conditions. Also, the expected anomaly of sediment yield can increase dramatically the desertification hazard in upland wildfire prone areas. One should further consider the role of firefloods produced by the combined occurrence of wildfires and storms as a fundamental source of non-stationarity in the assessment of hydrologic hazard.     

Resistivity anomaly imaging by probability tomography

Probability tomography is a new concept reflecting the inherently uncertain nature of any geophysical interpretation. The rationale of the new procedure is based on the fact that a measurable anomalous field, representing the response of a buried feature to a physical stimulation, can be approximated by a set of partial anomaly source contributions. These may be given a multiplicity of configurations to generate cumulative responses, which are all compatible with the observed data within the accuracy of measurement. The purpose of the new imaging procedure is the design of an occurrence probability space of elementary anomaly sources, located anywhere inside an explored underground volume. In geoelectrics, the decomposition is made within a regular resistivity lattice, using the Frechet derivatives of the electric potential weighted by resistivity difference coefficients. The typical tomography is a diffuse image of the resistivity difference probability pattern, that is quite different from the usual modelled geometry derived from standard inversion.     

Image‐ray Tomography

Seismic tomography is a well‐established approach to invert smooth macro‐velocity models from kinematic parameters, such as traveltimes and their derivatives, which can be directly estimated from data. Tomographic methods differ more with respect to data domains than in the specifications of inverse‐problem solving schemes. Typical examples are stereotomography, which is applied to prestack data and Normal‐Incidence‐Point‐wave tomography, which is applied to common midpoint stacked data. One of the main challenges within the tomographic approach is the reliable estimation of the kinematic attributes from the data that are used in the inversion process. Estimations in the prestack domain (weak and noisy signals), as well as in the post‐stack domain (occurrence of triplications and diffractions leading to numerous conflicting dip situations) may lead to parameter inaccuracies that will adversely impact the resulting velocity models. To overcome the above limitations, a new tomographic procedure applied in the time‐migrated domain is proposed. We call this method Image‐Incident‐Point‐wave tomography. The new scheme can be seen as an alternative to Normal‐Incidence‐Point‐wave tomography. The latter method is based on traveltime attributes associated with normal rays, whereas the Image‐Incidence‐Point‐wave technique is based on the corresponding quantities for the image rays. Compared to Normal‐Incidence‐Point‐wave tomography the proposed method eases the selection of the tomography attributes, which is shown by synthetic and field data examples. Moreover, the method provides a direct way to convert time‐migration velocities into depth‐migration velocities without the need of any Dix‐style inversion.     

3-D multi-parameter type traveltime tomography in a spherical coordinate frame: comparison of double and triple class simultaneous inversions

It is now common practice to perform simultaneous traveltime inversion for the velocity field and the reflector geometry in reflection/refraction tomography, or the velocity field and the hypocenter locations in regional earthquake tomography, but seldom are all three classes of model parameters updated simultaneously. This is mainly due to the trade-off between the different types of model parameters and the lack of different seismic phases to constrain the model parameters. Using a spherical-coordinate ray tracing algorithm for first and later(primary reflected) arrival tracing algorithm in combination with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model parameters in regional or global tomographic studies. In this paper we incorporate the multistage irregular shortest-path ray tracing algorithm(in a spherical coordinate system) with a subspace inversion solver to formulate a simultaneous inversion algorithm for triple model parameters updating using direct and later arrival time information.Comparison tests for two sets of data(noise free and added noise) indicate that the new triple-class parameter inversion algorithm is capable of obtaining nearly the same results as the double-class parameter inversion scheme. Furthermore,the proposed multi-parameter type inversion method is not sensitive to a modest level of picking error in the traveltime data, and also performs well with a relatively large uncertainty in earthquake hypocentral locations. This shows it to be a feasible and promising approach in regional or global tomographic applications.     

The long wavelength component of mantle convection

Theoretical models of mantle convection predict that the major temperature fluctuations within the mantle are confined to narrow horizontal boundary layers and vertical plumes. These fluctuations result in heterogeneities in seismic body wave velocities which could, in principle, be detected by seismic tomographic techniques. However, recent tomographic images of the spatial variations of temperature in the mantle are considerably “out of focus” in that only the longest wavelength components can be resolved. To assess this partial recovery of the total tomographic image, theoretical temperature fields have been generated with a numerical model of high Rayleigh number mantle convection and then Fourier analysed in two dimensions. Upon re-synthesizing the model temperature fields, the Fourier series expansions were truncated at various levels of resolution. The truncated expansions, containing only the long wavelength components of the model temperature fields, are compared to both the complete field and the tomographic images of the mantle. At the current level of resolution it seems unlikely that seismic tomography could distinguish between layered and whole-mantle convection. Estimates, based on current tomographic data, of long wavelength fluctuations of temperature and surface topography are predicted, in the case of whole-mantle convection, to represent approximately 10% of the total temperature variation, and approximately 50% of the total topographic relief. Thus topography at the core-mantle boundary may be more accurately inferred from seismic tomography than may the characteristic lateral temperature fluctuation which drives the convective circulation.     

4D tropospheric tomography using GPS slant wet delays

Tomographic techniques are successfully applied to obtain 4D images of the tropospheric refractivity in a local dense network of global positioning system (GPS) receivers. We show here how GPS data are processed to obtain the tropospheric slant wet delays and discuss the validity of the processing. These slant wet delays are the observables in the tomographic processing. We then discuss the inverse problem in 4D tropospheric tomography making extensive use of simulations to test the system and define the resolution and the impact of noise. Finally, we use data from the Kilauea network in Hawaii for February 1, 1997, and a local 4 × 4 × 40 voxel grid on a region of 400 km² and 15 km in height to produce the corresponding 4D wet refractivity fields, which are then validated using forecast analysis from the European Center for Medium Range Weather Forecast (ECMWF). We conclude that tomographic techniques can be used to monitor the troposphere in time and space.