We are developing an innovative low-noise directional borehole radar system. Harsh and changing Operating environments are a challenge to the low-noise sensitive electronic design. Additionally a system with such high sensitivity is susceptible to temperature changes and to component parameter variations. Therefore a calibration module was developed to calibrate the overall measurement system with a test signal generator. This calibration includes channel matching for accurate direction detection and sampling clock correction. After a brief introduction, testing and calibration methods are introduced. Additionally measurement results and figures depicting the practical results achieved thus far are included.
Co-seismic interferometric analysis was performed to investigate the spatial and temporal evolution of ground deformation related to the aftershock sequence of the Athens 1999 earthquake (Mw = 6.0). Differential interferograms (DInSAR) spanning different periods after the main seismic event showed variable ground deformation associated with the evolution of the post-seismic displacement field. Using ERS SAR images, four co-seismic differential interferograms were generated for the period from September to December of 1999, and spanning 16, 32, 67 and 102 days after the occurrence of the main shock. It was found that the cumulative ground deformation detected by DInSAR analysis was exponentially decreasing, following the declining rate of the post-seismic activity. The observed propagation of the ground deformation maxima towards the SE direction is consistent with the presence of clustered aftershock activity to the east of the epicentral area. The aforementioned evolution of deformation was also recognized by the observed expansion of the displacement field to the east.
Multichannel Analysis of Surface Waves utilizes a multichannel recording system to estimate near-surface shear (S)-wave velocities from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity (vS) section is constructed by aligning 1D models at the midpoint of each receiver spread and using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. The receiver spread length sets the theoretical lower limit and any vS structure with its lateral dimension smaller than this length will not be properly resolved in the final vS section. A source interval smaller than the spread length will not improve the horizontal resolution because spatial smearing has already been introduced by the receiver spread.
Schlumberger and AMT surveys over 2D resistivity structures are often interpreted using 1D automatic inversion. However, the models obtained using such approach have inherent limitations which must be known. Therefore, the study of model limitations and of alternative interpretations is a very important issue. Using synthetic data sets constructed from a relatively complex conductive graben, we examined the advantage of joint inversion over inversion using individual data sets. The data sets consist of apparent resistivity curves generated by arrays extended parallel and perpendicular to strike. In this case the AMT survey appears to have an advantage over the resistivity survey, since the dc data are more affected by lateral effects. As might be expected, neither of the methods is effective in resolving deep structures, located beneath the conductive target, when applied separately. The use of a 1D joint inversion of the data yields a better estimate imaging of the true resistivity distribution. 1D joint inversion of the averaged AMT and dc apparent resistivity curves, seems to be the most effective method to determine the resistivity structure. Some of the conclusions derived from the synthetic example are used as guidelines in the interpretation of real field data acquired over a graben, northern Portugal.
An innovative sensor technique has been developed to detect water leaks in supply pipes, especially in cases where the existing prevailing methods do not offer reliable solution, such as in PVC pipelines or for minor leaks. The presented system uses a Continuous Wave (CW) Doppler sensing unit operating at 2.45 GHz, consisting of a low power transmitter, a homodyne receiver and a digital signal processing unit. The operation principle is the detection of the Doppler frequency shift of the reflected electromagnetic wave by slightly moving water that leaks out of a pipe. A first prototype has already been developed and tested in test sites as well as in real water leaking conditions. The system has additionally been compared to the commercially available water leaking methods, verifying its reliability and accuracy in the detection of water leaks.
By considering arbitrary source–receiver configurations, compressional primary reflections can be imaged into time or depth-migrated seismic sections so that the migrated wavefield amplitudes are a measure of angle-dependent reflection coefficients. Several migration algorithms were proposed in the recent past based on the Born or Kirchhoff approach. All of them are given in form of a weighted diffraction-stack integral operator that is applied to the input seismic data. The result is a migrated seismic section where at each reflection point the source wavelet is reconstructed with an amplitude proportional to the reflection coefficient at that point. Based on the Kirchhoff approach, we derive the weight function and the diffraction stack integral operator for a two and one-half (2.5-D) seismic model and apply it to a set of synthetic seismic data in noisy environment. The result shows the accuracy and stability of the 2.5-D migration method as a tool for obtaining important information about the reflectivity properties of the earth's subsurface, which is of great interest for amplitude vs. offset (angle) analysis. We also present a new application of the Double Diffraction Stack (DDS) inversion method to determine three important parameters along the normal ray path, i.e., the angle and point of emergence at the earth surface, and also the radius of curvature of the hypothetical Normal Incidence Point (NIP) wave.
The 2001 Bhuj earthquake (Mw 7.7) formed several medium to large sand blow craters due to extensive liquefaction of the sediments comprising the Banni plain and Great Rann of Kachchh. We investigated two large closely spaced sand blow craters of different morphologies using Ground Penetrating Radar (GPR) with a view to understand the subsurface deformation, identify the vents and source of the vented sediments. The study comprises velocity surveys, GPR surveys using 200 MHz antennae along three selected transects that is supplemented by data from two trenches excavated. The GPR was able to provide good data on stratigraphy and deformation up to a depth of 6.5 m with good resolution. The GPR successfully imaged the subsurface characteristics of the craters based on the contrasting lithologies of the host sediments and the sediments emplaced in the craters. The GPR also detected three vertical vents of ∼ 1 m width continuing throughout the profile which are reflected as high amplitude vertical events. We conclude that the large sand blows during the 2001 Bhuj earthquake were produced due to liquefaction of sediments in the subsurface at > 6.5 m depth and that the clay-rich sediments of the Banni plain have behaved as the fine grained cap over it. The present study provides a modern analogue for comparing the liquefaction features of past great earthquakes (for example, the 1819 earthquake) that have occurred in the Kachchh region to understand the phenomena of liquefaction.
This paper presents a methodology in geophysics applied to the study of porous aquifers. This methodology is based on an improved “very low frequency-resistivity” equipment, on greater importance being attached to the local geological heterogeneity of the environment, and also on a method of data processing which is simple but well adapted to a large number of studies concerning prospecting, protection and management of underground water.The radio magnetotelluric-resistivity equipment (RMT-R) is derived from the classical VLF-resistivity equipment. Its increased reception band (12–240 kHz) allows us to realize rapid frequency soundings.In the example to be discussed, a geostatistical analysis of semivariance, made on a series of more than 600 measurements, shows a spatially structured geophysical heterogeneity, both for the values of resistivity and for those of phase. The correlation between this geophysical heterogeneity and the lithological heterogeneity of the environment is confirmed by mechanical soundings (geological test holes). The indirect relations between this geophysical heterogeneity and the hydraulic behaviour of the aquifer system can be estimated and are confirmed, on this specific site, by the observation of the piezometric levels.The results of our study illustrate the positive contribution RMT-R can make to hydrogeology. Above all they show that those porous environments, frequently considered as homogeneous, cannot be considered as such either hydrogeologically or geophysically.
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.
We present the problem of tracing rays in 2D and 3D heterogeneous isotropic media as a set of optimization problems. Each optimization problem is obtained by applying Fermat's principle to an approximation of the travel time equation from a fixed source to a fixed receiver. We assume a piecewise linear ray path that simplifies the computations of the problem, in the same way Mao and Stuart suggested in a very recent paper. Here, instead, the reflector geometry and the velocity function are computed by using nonuniformly biharmonic splines. On the other hand, to solve the optimization problem we use the Global Spectral Gradient method. This recent developed optimization scheme is a low storage optimization technique that requires very few floating point operations. It only requires the gradient of the travel time function, and it is global because it converges independently of the initial guess, that is, it does not require a close initial ray path. These three properties of the optimization method and the assumption of piecewise linear rays make this ray tracing scheme a very fast, global and effective method when estimating velocities via tomography. Moreover, in a homogeneous stratified or dipped media, any solution of the optimization problem is the best solution, i.e., it is the global minimum, no matter what numerical approach is used. We present some numerical results that show the computational advantages and the performance of this ray tracing in homogeneous and heterogeneous media.
Sinkholes in dolomitic areas are notoriously difficult geophysical targets, and selecting an appropriate geophysical solution is not straightforward. Electrical resistivity imaging, or tomography (RESTOM) is well suited to mapping sinkholes because of the ability of the technique for detecting resistive features and discriminating subtle resistivity variations. RESTOM surveys were conducted at two sinkhole sites near Pretoria, South Africa. The survey areas are located in the dolomites of the Lyttelton Formation, which forms part of the Malamani Subgroup and Chuniespoort Group of the Transvaal Supergroup. The survey results suggest that RESTOM is an ideal geophysical tool to aid in the detection and monitoring of sinkholes and other subsurface cavities.
2D resistivity methods can provide useful information about moisture distributions within porous historic stonework, especially when used in conjunction with simulated driving rain. Moisture is known to be a highly important factor in the deterioration of porous stone. We report here on a series of experiments on historic walls within the centre of Oxford, UK, which illustrate varying degrees of deterioration (including the formation of gypsum-rich black crusts and exfoliating hollows). Using medical electrodes we have been able to carry out non-invasive and non-destructive 2D resistivity surveys before and after simulated rainfall to investigate the progress of wetting and drying. We have applied tentative calibrations to convert resistivity values to moisture contents. Our results show that rainfall penetrates in predictable ways, with clearly defined wetting and drying fronts. Stone blocks with highly weathered surfaces exhibit the most rapid and high levels of water uptake, but also dry out more quickly than crusted or sound blocks. Thus, positive feedbacks may be encouraged whereby more water is cycled through damaged blocks, thereby enhancing the potential for further damage.
In 2D-multielectrode electrical surveys using the pole–pole array, the distance to `infinite electrodes' is actually finite. As a matter of fact, the available cable length generally imposes a poor approximation of theoretical location of these electrodes at infinity. This study shows that in most of the cases, the resulting apparent resistivity pseudosection is strongly distorted. Numerical simulation validated by field test also shows that a particular finite array provides results that are as close as possible to the ones of the ideal pole–pole array. This is achieved when two conditions that are weaker than an infinite location are fulfilled: (i) the `infinite electrodes' are placed symmetrically on both sides of the in-line electrodes with a spread angle of 30° and (ii) the length of `infinite lines' is at least 20 times the greatest distance between in-line electrodes. The electrical 2D image obtained with this enhanced array is the least distorted one with respect to the pole–pole image. The apparent resistivities are generally underestimated, but this deviation is almost homogeneous. Though the shift cannot be determined a priori, the interpretation of such an image with direct or inverse software designed for pole–pole data provides an accurate interpretation of the ground geometry.
Real time 2D inversion for an induction logging instrument may be achieved using a fast forward modeling and special inversion strategy. The fast forward modeling employs a low-frequency approximation of an induction response known as Doll's geometric factor. Modeling geometric factors is much faster than modeling the electromagnetic field in the frequency domain. To transform real data into the Doll's limit, multi-frequency skin-effect correction is applied. The correction technique involves an asymptotic theory of the integral equation for a 2D boundary value problem. The inversion is based on separating the parameter space into subspaces of lower dimension. Initially, adaptive overlapping windows split logging data into manageable portions. Each window consists of three subwindows: the predictor, corrector and upgrader. Further separation of parameters is introduced by Doll's approximation: the low-frequency response is linear with respect to formation conductivity. This allows us to split inversion for conductivity and geometric parameters. The next level of splitting inversion is achieved by independently determining parameters of the near borehole zone and remote formation areas. This is done by utilizing different subsets of sensors. The inversion does not require initial guess: layers are introduced dynamically, if necessary. The resolution is improved in sequential iterations by adding finer details to the previously obtained models. The final selection of parameters satisfies a variety of a priori constraints formulated as target resistivity distributions. The technique for imposing constraints is based on the analysis of data mapping into the model space. Interpretation of synthetic and real data confirms the viability of the method.
2D and 3D high-resolution seismic investigations were performed on submerged coastal archaeological sites at Iskele and near to Karantina Island in the Bay of Izmir in western Turkey. Tectonic subsidence of the coastline has submerged a number of archaeological features associated with an important Early Bronze Archaic settlement (Liman Tepe) and the classical Ionian city of Clazomenae. Seismic surveys were focused on imaging of an Archaic harbour structure and other submerged Hellenistic and Roman architectural features. Seismic data were acquired with the SEAMAP-3D ultra-high-resolution 3D marine seismic acquisition system developed for detailed archaeological site investigation.
Two nearly parallel seismic profiles were acquired in the Kristineberg area, located in the western part of the Skellefte ore district, in northern Sweden. A novel approach in the acquisition was that all shots from each profile were recorded onto both lines, resulting in a third CDP line halfway between the two profiles. The combination of geometry, acquisition parameters and geological complexity of the area required specific processing techniques to produce a stacked section that could be correlated with the two in-line processed seismic profiles. The processing sequence included a carefully designed frequency filter, optimized stack methods and pseudo 3D processing by applying cross-dip corrections. Due to the long offsets between the profiles, the resulting stacked section does not provide any information in the upper 1.2 s. Below 1.2 s, the upper crust shows a north-dipping event that correlates well with observations on the in-line data. Sub-horizontal reflectivity is also observed in the upper 4 s of the stack, similar to what is observed on the profile west of the cross-profile. Cross-dip analysis shows that the north-dipping event observed in all three profiles has a westerly dip component. Our study shows that additional information on the sub-surface may be obtained through cross-profile acquisition and processing.
An analytical solution of the stochastic wave equation is presented to model 2D heterogeneous geological environments. In the formulation, a plane-harmonic seismic wave propagates in a medium having random elastic properties in the horizontal and vertical directions. The 2D random field representation is introduced in the stiffness properties of the medium by assuming it has log-normal probability density functions. The constitutive stress and displacement laws with the momentum balance equation for total stress yield a partial differential equation, which is developed using a perturbation approach by assuming a 2D random geological medium having material heterogeneity randomly distributed in the horizontal (x) and vertical (z) directions. The method yields a double integral representation of the displacement wave vector based on the Green's tensor and the Fourier–Stieltjes increments. The double integral is reduced to one integral representation by removing the singularities. The final form of the integral is used to construct the stochastic wave field displacement components expressed in terms of a single integral that is appropriate for calculations.
An important problem of marble-quarry management is assessing the quality and the homogeneity of quarry blocks before excavation. In this study, we decided to image the limestone, which we studied in a marble quarry, in terms of layer thickness, discontinuities and cavities using the ground-penetrating-radar (GPR) method. The method was successfully applied to detect and map the fractures with the cavities in a marble layer according to depth in the Ankara City Polatli Town (Turkey) region, which represents upper Miocene–Pliocene lacustrine carbonate rocks.This paper is based on interactive transparent 3D visualisation of the 2D GPR profiles to determine changes in layer thickness and discontinuities. In addition, this paper indicates the importance of the appropriate opacity-function construction to obtain transparent 3D visualisation. Firstly we acquired and processed parallel 2D GPR profile data, then we assigned two different amplitude–colour ranges using a limited number of colours to determine the layer thickness and its discontinuities separately. We obtained a 3D volume using parallel 2D GPR data and displayed a limited amplitude range by arranging an opacity function. Therefore, we obtained transparent 3D blocks for thickness and discontinuities, and we formulated an interactive 3D display to image the horizontal, vertical and inclined discontinuities and their directions in the x–y plane versus depth. The GPR results were compared with the petrographical investigation on the basis of textural and mineralogical compositions. The vesicular textures within carbonate platform were supported by the GPR results.
Tumuli are artificially erected small hills that cover monumental tombs or graves. In this work, the surface three-dimensional (3D) Electrical Resistivity Tomography (ERT) method, composed of dense parallel two-dimensional (2D) tomographies, was used to investigate the properties of the tumuli filling material and to resolve buried archaeological structures inside the tumuli.The effectiveness of the method was investigated by numerical modeling and through 3D inversion of synthetic apparent resistivity data. A resistivity model that simulates the inhomogeneous tumulus material and the tombs that are buried inside the tumulus was assumed. The Dipole–Dipole (DD), Pole–Dipole (PD), Pole–Pole (PP), Gradient (GRAD), Midpoint-Potential-Referred (MPR) and Schlumberger Reciprocal (SCR) arrays, which are suitable for multichannel resistivity instruments, were tested. The tumulus topography (pyramid or capsized cup) was incorporated into the inversion procedure through a distorted finite element mesh. The inversion procedure was based on a smoothness constrained Gauss–Newton algorithm in which the Active Constraint Balancing (ACB) method was also applied in order to enhance the least-squares resolving power and stability.Synthetic modeling showed that the different tumulus layers and the horizontal contact of the artificial tumulus material with the natural background soil were reconstructed by all of the tested electrode arrays. Generally, PD and the GRAD arrays comprise the optimum choices to investigate the subsurface properties of a tumulus and locate buried tombs. The MPR model was inferior to the GRAD model, while the DD, PP and SCR models had the poorest resolution. It was also shown that the inversion models are practically independent from the survey direction and the topography shape of the tumulus.The real field data collected employing the PD array along a small tumulus from the archaeological site of Vergina in northern Greece enhanced the synthetic modeling results. The inversion model outlined a number of archaeological structures that exhibit a high possibility to correlate with graves. Overall, this work signifies that the surface 3D ERT method can provide a valuable tool in the non-destructive archaeological exploration of tumuli.
We present a novel methodology for 3D gravity/magnetic data inversion. It combines two algorithms for preliminary separation of sources and an original approach to 3D inverse problem solution. The first algorithm is designed to separate sources in depth and to remove the shallow ones. It is based on subsequent upward and downward data continuation. For separation in the lateral sense, we approximate the given observed data by the field of several 3D line segments. 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. It allows retrieving unknown 3D geometry of anomalous objects in terms of restricted bodies of arbitrary shape and contact surfaces. For restricted objects, we apply new integral equations of gravity and magnetic inverse problems. All steps of our methodology are demonstrated on the Kolarovo gravity anomaly in the Danube Basin of Slovakia.Highlights► New methodology for 3D interpretation of gravity/magnetic anomalies is suggested. ► It includes original algorithms for separation of sources and 3D inversion. ► We retrieve 3D geometry of restricted objects of arbitrary shape and contact surfaces. ► All steps of our technology are demonstrated on a real gravity anomaly.
When investigating topographically irregular layers in the near surface with shear waves, it is of particular importance to consider the 3D-nature of wave propagation. Depending on the layer geometry and on the spatial arrangement of source- and receiver-points significant lateral ray bending can occur causing side-swipe traveltime effects and complicated polarisation patterns. As an example we present a study where 3D-shear wave refraction measurements were applied in order to reconstruct the geometry of a silted ancient harbour basin at the archaeological site of Miletus (West Turkey). Seismic signals were generated with a three-component vector force and recorded with three-component geophones arranged in 2D-arrays of 1 m grid spacing. Since a correct identification of refracted S-wave arrivals is a precondition to traveltime interpretation we investigated a method to decompose these wavefields with respect to their polarisation and azimuth of propagation. Taking advantage of the 2D-geophone arrangement we applied the following processing approach: In case of general lateral heterogeneity a decomposition can be performed by applying the curl and divergence operations to the vector wavefields recorded in 2D-arrays. The separated tangential and normal components to the wavefront in a plane are finally enhanced by combining the different force components in order to eliminate the radiation characteristics of the source. The decomposed wavefield was then the basis for 3D-refractor imaging through a newly formulated map migration of the refracted traveltime field. This technique was developed to map coherent basement structure on the meter-scale. Supplemental tomographic inversion using the refractor topography model as input provided a plausible velocity model, exhibiting characteristic anomalies such as a prominent low velocity zone overlain by a high velocity layer in the refractor. The seismic velocity structure suggests that the harbour basin was locally filled with natural or anthropogenic debris on which an antique harbour wall could have been founded.
Muro Leccese (Lecce) contains one the most important Messapian archaeological sites in southern Italy.The archaeological interest of the site arises from the discovery of the remains of Messapian walls, tombs, roads, etc. (4th–2nd centuries BC) in the neighbourhood. The archaeological remains were found at about 0.3 m depth.At present the site belongs to the municipality, which intends to build a new sewer network through it. The risk of destroying potentially interesting ancient archaeological structures during the works prompted an archaeological survey of the area. The relatively large dimensions of the area (almost 10,000 m2), together with time and cost constraints, made it necessary to use geophysical investigations as a faster means to ascertain the presence of archaeological items. Since the most important targets were expected to be located at a soil depth of about 0.3 m, a ground-penetrating radar (GPR) survey was carried out in an area located near the archaeological excavations. Unfortunately the geological complexity did not allow an easy interpretation of the GPR data.Therefore a 3D electrical resistivity tomography (ERT) scan was conducted in order to resolve these interpretation problems.A three-way comparison of the results of the dense ERT measurements parallel to the x axis, the results of the measurements parallel to the y axis and the combined results was performed.Subsequently the synthetic model approach was used to provide a better characterization of the resistivity anomalies visible on the ERT field data.The 3D inversion results clearly illustrate the capability to resolve in view of quality 3D structures of archaeological interest. According to the presented data the inversion models along one direction (x or y) seems to be adequate in reconstructing the subsurface structures.Naturally field data produce good quality reconstructions of the archaeological features only if the x-line and y-line measurements are considered together. Despite the increased computational time required by the 3D acquisition and 3D inversion schemes, good quality results can be produced.
Owing to their nature landfills are challenging targets for high resolution Near Surface Geophysics.Herein it is described an integrated high resolution geophysical survey over the Ilhavo landfill sealed about a decade ago.The first aim of the survey is to investigate the time evolution of the contamination plume of the landfill since operations stopped and sealing took place.The second, and main objective, is the study of the landfill itself, that is, to carry out a high resolution 3D geophysical survey over it in order to investigate the thickness and effectiveness of the top cover, the thickness and sealing conditions of the landfill bottom and, finally, to investigate its internal structure.To fulfill these objectives an integrated 3D constant offset GPR and resistivity survey was designed. The interpretation of the geophysical data was carried out together with local borehole and hydrogeological information, so that, the ambiguity and uncertainty of the interpretation was reduced considerably and the usefulness of the methods were assessed.
Kirchhoff–Helmholtz (KH) theory is extended to synthesize two-way elastic wave propagation in 3D laterally heterogeneous, anisotropic media. I have developed and tested numerically a specialized algorithm for the generation of three-component synthetic seismograms in multi-layered isotropic and transversely isotropic (TI) media with dipping interfaces and tilted axes of symmetry. This algorithm can be applied to vertical seismic profile (VSP) geometries and works well when the receiver is located near the reflector interface. It is superior to ray methods in predicting elliptical polarization effects observed on radial and transverse components. The algorithm is used to study converted-wave propagation for determining fracture-related shear-wave anisotropy in realistic reservoir models. Results show that all wavefront attributes are strongly affected by the anisotropy. However, it is necessary to resolve a trade-off between the effects of fractures and formation dip prior to converted-wave interpretation. These results provide some assurance that the present scheme is sufficiently versatile to handle shear wave behaviour due to various generalized rays propagating in complex geological models.
A high resolution, cross-borehole, 3D electrical resistivity tomography (ERT) study of solute transport was conducted in a large experimental tank. ERT voxels comprising the time sequence of electrical images were converted into a 3D array of ERT estimated fluid conductivity breakthrough curves and compared with direct measurements of fluid conductivity breakthrough made in wells. The 3D ERT images of solute transport behaviour were also compared with predictions based on a 3D finite-element, coupled flow and transport model, accounting for gravity induced flow caused by concentration differences.
The present paper deals with the 3D modeling of a resistivity data set, carried out over the Chaves graben where the hot springs, with a temperature reaching 78°C, have a great economic importance. The main objective of the modeling was to incorporate the partial knowledge obtained from previous ID and 2D interpretations into a three dimensional model. The 3D models of three rectangles and two dipole-dipole surveys, which were performed to detect conductive zones associated with the hydrothermal circulation, depict the general form of the graben and the spatial configuration of the low resistivity zones (10–15 μ m). The achieved models exhibit several characteristics similar to those of previous 1D and 2D interpretations and are consistent with geological information and new findings related to the bed-rock depth (1200 to 1500 m), the northern and southern borders of the conductive zones and its connection with the fault systems.
Hidden mineshafts located in urban areas are a significant problem across much of the industrialized world. Electrical resistivity tomography (ERT) is a technique that can detect and characterize hidden mine entries by exploiting resistivity contrasts between the shaft and surrounding materials, resulting from either compositional or structural differences. A case study is presented in which both surface and crosshole 3D ERT surveys are used to image a hidden backfilled mineshaft at a built environment site, situated on Carboniferous Lower Coal Measures strata in the UK.Backfilled shafts generally present the greatest challenge for detection using geophysical methods, as contrasts between the fill and bedrock are typically low compared to air or water-filled conditions. Nevertheless, the shaft in this case was identified by both the surface and crosshole 3D surveys. The shaft appeared as a strongly resistive anomaly relative to background materials, which we interpreted as resulting from the disturbed fabric of the fill materials rather than any significant compositional differences. The study highlighted the respective strengths and weaknesses of the surface and crosshole ERT methodologies for this type of problem. The surface survey, which covered a non-rectangular area to accommodate irregular boundaries and other physical obstructions, provided a relatively rapid means of investigating the study site. However, this method had a limited depth of investigation and was constrained in its coverage by the locations of buildings. By contrast, the 3D crosshole method was able to image the shaft to the level of the deepest borehole electrodes. Although crosshole ERT is too expensive to be used for large-scale mineshaft surveys, this study clearly demonstrates its suitability for targeted investigations where surface methods cannot be deployed, such as scanning beneath surface structures or in situations where it is essential for resolution to be maintained with depth.
Geothermal reservoirs are usually located at a depth range of 2 to 5 km, so to efficiently utilize such resources an advanced prospecting method is needed to detect these deep geologic structures. This study aimed to three-dimensionally characterize geothermal reservoirs by a combination of Magnetotelluric (MT) survey, inversion analysis of apparent resistivity, and interpolation of the resistivity data obtained. The western side of Mt. Aso crater, southwest Japan, was chosen as the case study area. Three hot springs exist there and a fault is assumed to go in the direction connecting them. A MT survey was carried out at 26 sites and the data processed by a remote reference method to reduce artificial noises. Based on skewness and Mohr circle analyses of the impedance tensor, the local geologic structure at each site could be approximated as horizontally layered and therefore, a one-dimensional inversion analysis was applied to the MT raw data. The resultant resistivity column data were then interpolated by the three-dimensional optimization principle method. The resistivity distributions obtained clarified continuous conductors with especially low resistivity (less than 10 Ω·m) at the hot springs along the fault. Because the resistivity decreases largely with an abundance of clay minerals, the conductors could be considered to correspond with the cap rocks. Thus, two geothermal reservoirs, whose shapes were estimated to be pillar, were detected under the cap rocks in an elevation range of − 1000 to − 3000 m. By comparing the resistivity distributions with the temperature distributions based on fluid-flow calculations at a steady state using FEM, the validity of the location and dimension of the estimated reservoirs were confirmed.
This paper presents a general and comprehensive way to evaluate the geometric factors used for the computation of apparent resistivities in the context of DC resistivity mapping and non-destructive investigations, in laboratory or in the field. This technique enables one to consider 3-dimensional objects with arbitrary shape. The expression of the geometric factor results from the early definition of apparent resistivitiy. It is expressed as the ratio of the resistances obtained from measurements to the resistances induced in the medium with unitary resistivity considering the same object geometry and electrode set-up. In this work, a finite element code is used for the computation of the geometric factor. In this code, the electrodes do not need to be located on the nodes of the mesh. This option makes the finite element mesh generation task easier. A first synthetical example illustrates how the present approach could be applied to apparent resistivity mapping in an environment with a complex underground topography. A second example, based on real data in a water tank, illustrates the simulation of a resistivity survey on a structure with finite extent, e.g. a laboratory sample. In both examples, topographic artefacts and effects of material sample shapes are successfully taken into account and reliable apparent resistivity descriptions of the structures are obtained. The effectiveness of the method for the detection of heterogeneities in apparent resistivity maps is highlighted.
A set of geophysical data collected in an area in Iran are analyzed to check the validity of a geological map that was prepared in connection to a mineral prospecting project and also to image the spatial electrical resistivity distribution. The data set includes helicopter electromagnetic (HEM), airborne magnetic and ground electrical resistivity measurement. Occam approach was used to invert the HEM data to model the resistivity using a layered earth model with fixed thicknesses. The algorithm is based on a nonlinear inverse problem in a least-squares sense.The algorithm was tested on a part of an HEM dataset acquired with a DIGHEM helicopter EM system at Kalat-e-Reshm, Semnan in Iran. The area contains a resistive porphyry andesite that is covered by Eocene sedimentary units. The results are shown as resistivity sections and maps confirming the existence of an arc like resistive structure in the survey area. The resistive andesite seems to be thicker than it is indicated in the geological maps. The results are compared with the reduced to the pole (RTP) airborne magnetic anomaly field data as well as with two ground resistivity profiles. We found reasonable correlations between the HEM 1D resistivity models and 2D models from electrical resistivity tomography (ERT) inversions. A 3D visualization of the 1D models along all flight lines provided a useful tool for the study of spatial variations of the resistivity structure in the investigation area.Highlights► We compare a geological map from a mineralization prospecting with geophysical data. ► HEM, airborne magnetic and ERT data are utilized for an integrated interpretation. ► We model the HEM data in 1D and image the electrical resistivity in 3D.
Rainfall-induced landslides pose a common problem in areas with slopes steeper than the friction angle of the soil. A series of such landslides in North Switzerland inspired a detailed geophysical and geotechnical site investigation prior to a monitoring experiment.High-resolution 2D and 3D electrical resistivity tomography (ERT) was used to derive a detailed subsurface image, which was verified by direct penetration tests, boreholes and laboratory analysis of soil samples with respect to grain size distribution and plasticity. Resolution analysis of ERT configurations proved a combination of Wenner–, Schlumberger– and Dipole–Dipole data to be a reasonable compromise between measurement time and model accuracy. Furthermore, a statistical approach to reducing subjectivity in the interpretation of 3D resistivity models is suggested. Applying this classification scheme to field data yields a model in very good agreement with the geotechnical model. The 3D resistivity model is then interpreted quantitatively using laboratory data and a constitutive relation accounting for clay and silt contents. The dominant influence of saturation on resistivity predicted by this model is confirmed and exemplified during repeated surveys in a dry and a wet period. In wet summer 2004, a silty sand layer of high water saturation is confined between two less permeable layers, the sandstone bedrock below and a clayey sand layer on top. This layer may locally form an aquifer, which becomes rapidly saturated during heavy rainfalls and contributes to the risk of failure. The combined ERT and geotechnical survey helped to optimize the design of the forthcoming monitoring experiment and may be used as a guideline for the investigation of similar slope conditions.
Evolution models of the planet Mars show that a significant quantity of water may reside beneath the surface as ground ice. This permafrost, which at mid-latitudes could be 1 to 2 km deep, forms a better penetrating medium for radio waves than warmer dry ground. A GPR system is planned to be integrated inside the surface-drag guiderope of the Mars 96 balloon mission to detect the permafrost, estimate its thickness, and to evaluate the water quantity. We have developed a GPR system for operation within an experimental guiderope. This implies techniques and technologies adapted for deep sounding, compatible with the Mars 96 mission weight and volume constraints, cold temperatures, and shock resistance. This also provides a basis for electromagnetic compatibility, antenna, propagation studies, and simulations.In this paper, we present an impulse radar system using repetitive-trace coherent integration to improve the signal-to-noise ratio, and a variable gain receiver to increase the dynamic range as the echo depth increases. The outermost shell of the guiderope assembly forms a loaded dipole antenna. Preliminary experiments were carried out on a glacier and on a sand dune to obtain representative experimental GPR profiles. We present the processing and the interpretation of these profiles in combination with modelling of the medium and numerical simulation of the GPR signal propagation. Finally, using possible geological models of the Martian subsurface, we estimate the radar received power and discuss the capability of the GPR for imaging the Martian permafrost.
A major plan for Portugal Mainland is being envisaged to use old open pits from abandoned uranium mining sites as “Waste Containment Deposits”. These areas will store mining waste from other adjacent mines. The old mining sites classification to this kind of usage is carried out accordingly to its location, accessibility, geological and hydrogeological conditions. Mining waste deposition in the open pits may however cause environmental problems related with geological and hydrogeological features that must be predicted and prevented before a particular site is chosen. Therefore, the identification of faults and conductive zones that may promote groundwater circulation and the spread of contaminated waters is of great importance, since the surrounding area is highly populated. The possible negative environmental impacts of the presence of such potential waste disposal sites are therefore being assessed using geophysical methods and geological outcrop studies in several geological and hydrogeological critical areas. The abandoned Quinta do Bispo uranium mine is one of such places. This old open pit, chosen as one of the sites to be used in the near future as a “Waste Containment Deposit” (accordingly to the above mentioned criteria), needs to be characterized at depth to prevent any possible negative environmental impacts. Thus, the acquisition, processing and interpretation of electromagnetic, electrical and both seismic refraction and reflection have been carried out. 2D schematic models have been constructed, showing alteration and faults zones at depth. These fault zones control groundwater circulation and therefore, future water circulation problems with negative environmental impact may be predicted and prevented.
Gravity data acquired in the Shamakhy–Gobustan and Absheron oil- and gas-bearing regions were filtered using a Hartley transform (HT) and Butterworth filter. The HT, originally introduced by Hartley [Hartley, R.V.L., 1942. A more symmetrical Fourier analysis applied to transmission problems. Proc. IRE, 30(2), pp. 144–150], is an integral transform method similar to the Fourier transform (FT) with a number of properties being similar to the properties of FT. The HT is a real transform. It is an alternative procedure to the discrete FT since one complex operation is equal to four real operations. The experiments show that the discrete HT is twice as fast as the discrete FT. The power spectrum of the HT analysis of the Bouguer gravity values in the Shamakhy–Gobustan and Absheron regions suggests that a gravity field may be separated into long- and short-wavelength components. The power spectrum indicates a depth of 24.5 km for the long component and 3.2 km for the short one. No relationship has been revealed between the gravity anomalies and the surface tectonics. The regional anomalies are interpreted to be related with elevation and the sinking of the crystalline basement.
A system is presented for measuring the resistivity of highly conducting samples with low-frequency AC-bridges. A sample in the bridge coil is modelled as a sphere placed in a spatially uniform, alternating magnetic field. Model calculations are made using both generally valid formulae and their low-frequency approximations. The calculations show that the out-of-phase response of the bridges and the resistivity of a spherical sample are linearly related at a reasonable accuracy (error below 5%), when the sample has a susceptibility K < 0.2 (SI) and a response parameter W < 2. The latter condition can always be fulfilled by reducing sample size. Using a theoretic relation, which is empirically verified, the low-frequency response of spherical samples is tied to that of non-permeable cylindrical samples with different dimension ratios. The system is calibrated with the aid of lead and bismuth spheres. For cylindrical and spherical samples with low K-values the measuring errors can be kept below 10% in the resistivity range 10−2–10−7 μm.
An automatic procedure for the seismic zonation of a territory is presented. The results consist of deterministic computation of acceleration time series distributed on a regular grid over the territory. For the estimation of the accelerations, complete synthetic seismograms are computed by the modal summation technique. A first rough zonation can be accomplished by considering a map showing the distribution of peak ground acceleration. In this work the new procedure has been applied to the Italian territory. The structural and source models necessary to compute the synthetic signals have been fixed after an extensive bibliographic research. Seismogenic areas have been defined in the framework of the GNDT (Gruppo Nazionale per la Difesa dai Terremoti of the Consiglio Nazionale delle Ricerche, Rome) research activities dedicated to the definition of the kinematic model of Italy. Information on historical and recent seismicity has been taken from the most updated Italian earthquake catalogues. The estimated peak ground accelerations have been found to be compatible with available data, both in terms of intensity (historical earthquakes) and accelerations (recent earthquakes).
Slowly decaying transients were measured during a TEM survey over crystalline metamorphic rocks in the vicinity of the village of Chernorud, on the western shore of Lake Baikal. Once converted to apparent resistivities, these transients resulted in values of about 2–5 Ω m. Because neither in-field nor laboratory DC resistivity measurements indicate conductive rocks, the TEM results are confusing. It is hypothesized that the anomalous transients were caused by the relaxation of the magnetization of extremely fine ferri- and/or ferromagnetic particles concentrated in the near-surface layer. In 1997, in the soil thrown out of a gopher burrow, slags and charcoal fragments were found which suggested ancient metallurgical activity. Despite the slags being electrically poorly conductive, once placed into a small coil, they produced slowly decaying transients caused by magnetic viscosity effects. On the basis of their chemical and mineral composition, the Chernorud site slags proved to be identical to those which are known to have been formed during the production of iron in ancient bloomery furnaces. An excavation carried out at the site of the gopher burrow resulted in the discovery of a large bloomery furnace, much slag, charcoal, and baked clay fragments. In 1999, reconnaissance magnetic field and galvanic resistivity profiling measurements were conducted, focused on the site's archaeological potential. Data were taken over a 96×100 m area at 4 m intervals along parallel profiles spaced at 4 m. The magnetic field contour and surface maps exhibited an isometrically shaped positive anomaly with an amplitude of 40–50 nT, that was 30–40 m in diameter. The bloomery and other archaeometallurgical structures fall within the central part of the magnetic anomaly. The galvanic profiling has revealed a resistivity high (1000–1500 Ω m against 300–500 Ω m) which might be attributed to ancient human activity. Radiocarbon dating of three charcoal fragments sampled during the excavation from different depth intervals has given uncalibrated ages of 1915±35, 2050±35 and 2180±30 years BP. These results make it apparent that the Iron Age on the western shore of Lake Baikal started about 700–900 years earlier than is generally accepted. Occurrence of slags over an area of no less than 15 ha suggests that iron production in the Barun-Khal valley was performed on a large scale.
For a fixed, central ray in an isotropic elastic or acoustic media, traveltime moveouts of rays in its vicinity can be described in terms of a certain number of parameters that refer to the central ray only. The determination of these parameters out of multi-coverage data leads to very powerful algorithms that can be used for several imaging and inversion processes. Assuming two-dimensional propagation, the traveltime expressions depend on three parameters directly related to the geometry of the unknown model in the vicinity of the central ray. We present a new method to extract these parameters out of coherency analysis applied directly to the data. It uses (a) fast one-parameter searches on different sections extracted from the multi-coverage data to derive initial values of the sections parameters, and (b) the application of a recently introduced Spectral Projected Gradient (SPG) optimization algorithm for the final parameter estimation. Application of the method on a synthetic example shows an excellent performance of the algorithm both in accuracy and efficiency. The results obtained so far indicate that the algorithm may be a feasible option to solve the corresponding, harder, full three-dimensional problem, in which eight parameters, instead of three, are required.
Imaging with acoustic and optical televiewers results in continuous and oriented 360° views of the borehole wall from which the character, relation, and orientation of lithologic and structural planar features can be defined for studies of fractured-rock aquifers. Fractures are more clearly defined under a wider range of conditions on acoustic images than on optical images including dark-colored rocks, cloudy borehole water, and coated borehole walls. However, optical images allow for the direct viewing of the character of and relation between lithology, fractures, foliation, and bedding. The most powerful approach is the combined application of acoustic and optical imaging with integrated interpretation. Imaging of the borehole wall provides information useful for the collection and interpretation of flowmeter and other geophysical logs, core samples, and hydraulic and water-quality data from packer testing and monitoring.
Electrical, seismic, and electromagnetic methods can be used for noninvasive determination of subsurface physical and chemical properties. In particular, we consider the evaluation of water salinity and the detection of surface contaminants. Most of the relevant properties are represented by electric conductivity, P-wave velocity, and dielectric permittivity. Hence, it is important to obtain relationships between these measurable physical quantities and soil composition, saturation, and frequency. Conductivity in the geoelectric frequency range is obtained with Pride's model for a porous rock. (The model considers salinity and permeability.) White's model of patchy saturation is used to calculate the P-wave velocity and attenuation. Four cases are considered: light nonaqueous phase liquid (LNAPL) pockets in water, dense nonaqueous phase liquid (DNAPL) pockets in water, LNAPL pockets in air, and DNAPL pockets in air. The size of the pockets (or pools), with respect to the signal wavelength, is modeled by the theory. The electromagnetic properties in the GPR frequency range are obtained by using the Hanai–Bruggeman equation for two solids (sand and clay grains) and two fluids (LNAPL or DNAPL in water or air). The Hanai–Bruggeman exponent (1/3 for spherical particles) is used as a fitting parameter and evaluated for a sand/clay mixture saturated with water.
The geotechnical structures of permeability, porosity and shear strength within the near-surface sediments of Tokyo area are imaged by analytically inverting the acoustic wave velocity and attenuation fields. The acoustic velocity and attenuation fields were previously measured by a Pseudo Random Binary Sequence (PRBS)-based crosswell acoustic tomography device. A quadratic equation of permeability derived from the Biot theory is used for the permeability inversion of the measured acoustic velocity–attenuation fields. The porosity and shear modulus images are also extracted from the velocity and attenuation fields using the newly derived quadratic dispersion equation and an empirical shear modulus–porosity–depth of burial relation. The acoustically measured images of permeability, porosity and shear modulus are favorably compared with the engineering tests performed on the cores and boreholes.
This paper studies the influence of a pore-space microstructure on the physical properties of double-porosity carbonate rocks. Starting from a unified microstructure model for double porosity media and applying the self-consistent method of the Effective Medium Approximation, we have calculated the elastic-wave velocities, electrical and thermal conductivities as functions of primary and secondary porosities, and secondary pore shapes. The double porosity medium is treated as a heterogeneous material composed of a homogeneous isotropic matrix that corresponds to a solid frame with primary small-scale pores and secondary pores represented by large-scale inclusions. Both pore-systems are completely saturated with water. Pores are arbitrarily orientated, and randomly distributed in the matrix. The shapes of secondary pores are approximated by three-axial ellipsoids. By varying the ellipsoid aspect ratios we model different secondary porosity types. The simulations performed demonstrate the different character of the dependences of the acoustic-wave velocities and electrical conductivity upon the inclusion shapes, matrix and secondary porosity values. The thermal conductivity has low sensitivity to the secondary pores for all considered shapes. Based on the responses of the acoustic and electrical parameters to the shapes of the secondary pores, we propose a new geophysical classification of the secondary porosity into four types: vugs (quasi-spherical inclusions), quasi vugs (oblate ellipsoids), channels (prolate ellipsoids), and cracks (strongly flatted inclusions). Additionally, we have calculated the rock physical properties for mixture of two types of the secondary pores. We show that in this case the joint analysis of acoustic-wave velocities and electrical conductivity allows each secondary-porosity type to be identified.
The Low-level Acoustic Combustion Source (LACS) which can fire its pulses at a high rate, has been tested successfully as a seismic marine source on shallow ice-age sediments in Byfjorden at Bergen, Norway. Pseudo-Noise pulsed signals with spiky autocorrelation functions were used to detect the sediments. Each transmitted sequence lasted 10 s and contained 43 pulses. While correlation gave a blurry result, deconvolution between the near-field recordings and the streamer recordings gave a clear seismic section. Compared to the section acquired with single air-gun shots along the same profile, the LACS gave a more clear presentation of the sediments and basement.
Acoustic wavelengths in soils range from meters to millimeters, depending on their frequencies. The spatial and temporal scales of pulse transmission through soils are well suited to investigate transient and presumably heterogeneous water infiltration into and redistribution within soils.Acoustic pulses were transmitted through a column of an undisturbed and partially water-saturated loess soil with height and diameter of 0.8 and 0.3 m, respectively. The maximum frequency of the arriving pulses was 10 kHz, which corresponds to a wavelength of about 50 mm. Both travel velocities and absorption of the acoustic waves reacted in the expected ways on soil moisture variations; however, the two temporal reaction patterns differed considerably. Brutsaert's [J. Geophys. Res. 69 (1964) 243] model was successfully applied to the data. Dye tracers visualized the patterns of water distribution. Their scale compares well with theoretical considerations on the flow paths and the results from the acoustic investigations.
Acoustic-wave based sub-bottom profiler (SBP) and electromagnetic-wave based ground penetrating radar (GPR) are two complementary geophysical tools that were used to map bathymetry and sediment sublayers in shallow waters. Near shore regions in Great Lakes, inland lakes, and rivers in Wisconsin, USA were examined using both geophysical tools. In areas with high silt and clay contents, such as Lake Superior, the SBP was able to image the sediment sublayers, whereas in the areas with sand cover and vegetation, the GPR provided sediment stratigraphic information. The higher vertical and horizontal resolutions of the SBP surveys provided more accurate and detailed bathymetry information than GPR surveys. In the Yahara River, SBP surveys imaged blurring contrasts between sublayers due to the gradual deposition of sediments; however, GPR provided sharp delineations of sediment layers but was only able to image the top two sublayers because of the high silt and clay electromagnetic wave attenuation. To confirm these findings, Shelby tubes and hydraulic jetting were used to collect ground-truth information. Sublayer thicknesses are estimated by evaluating acoustic and electromagnetic wave velocities using a mixture-based equation. In Lake Michigan, both techniques show similar sediment stratigraphy, indicating that the average sediment particle size ranges between silt and fine sand. Three-dimensional maps of bathymetry and subbottom sediments are also constructed. Overall it is shown that the combination of GPR and SBP techniques compensates each survey's strengths in an effective methodology for imaging bathymetry and sub-bottom profiles in shallow water environments.
A towed sledge system has been utilised to generate and receive Love waves at the seabed. Due to unique deployment procedures, the system is capable of acquiring data both rapidly and efficiently over an extensive area. An experiment was undertaken to assess the capability of the system to measure the lateral variation of the shear wave velocity in unconsolidated near-surface sediments along a 4-km survey line. The site chosen was known to display significant variations in sediment characteristics over relatively short distances and could therefore provide a suitable test. A parametric approach was used to obtain phase-velocity dispersion curves from the Love wave data sets. This approach enabled the fk-spectra to be resolved to a sufficiently high level using a limited number of receivers. Finally, the shear wave velocity profile for each record was estimated with respect to a reference model using a non-linear least squares inversion algorithm. Results indicated that the shear wave velocity field varied significantly along the survey line. The shear wave velocity at a depth of 30 cm below the seabed changed from 30 to 55 m/s over the length of the survey line. The velocity variations correlated well to geotechnical data acquired from the area, suggesting that Love waves acquired from only five seafloor receivers can successfully be used to construct near-surface models of seafloor shear wave velocity in unconsolidated near-surface sediments, with a lateral resolution of up to 25 m and a depth measurement range of up to 4 m.
Two underground coal mines in the Sydney Coalfield, Nova Scotia, Canada have encountered gas outbursts from sandstone formations overlying the coal seams. These have consistently occurred while driving mine roadways into virgin ground at and below mining depths of 700 m. In this investigation, triaxial compression tests were conducted on samples of the outburst-prone sandstone from one of these mines, the Phalen Colliery, while simultaneously measuring gas permeability, acoustic emissions and ultrasonic P-wave velocity and attenuation. Experimental results characterized these sandstone properties over the full range of axial stresses up to compressive failure. These data were intended to assist with (i) evaluating the potential for degassing the sandstone and (ii) evaluating the results of in-seam seismic surveys, which were conducted to map the sandstone ahead of mining. At the estimated in situ conditions in virgin rock at 700 m depth, the sandstone permeability is expected to be in the 0.005 to 0.04 mD range, the P-wave velocity is approximately 4000 m/s and the attenuation quality factor in the 20 to 25 range. Near mine openings at 700 m depth, where the lateral confining pressures are reduced, the permeability can be several orders of magnitude higher in the 4 to 15 mD range, the P-wave velocity is 3800 m/s and the attenuation quality factor is in the 10 to 15 range. Experimental data suggests that microcracking in the sandstone prior to compressive failure does not significantly enhance permeability but there may be local pockets of higher permeability within the sandstone.
Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic–viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown–Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown–Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz–clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks.
It is known that sedimentary rocks demonstrate velocity dispersion in the acoustic log frequency range. In this paper we have calculated the waveforms of sonic log for a borehole located in a viscoelastic medium. The acoustic field in the borehole has been obtained for acoustic multipole sources. To describe the viscoelastic properties of a rock we used the Cole–Cole model. This model describes the dispersion of acoustic wave velocities and quality factors in a wide frequency range. To solve the acoustic log direct problem we have applied the double integral Fourier transform (RAI method). The results obtained have shown the feasibility of S-wave velocity dispersion estimation from acoustic dipole waveform processing.Highlights► Acoustic log waveforms for a borehole located in a viscoelastic medium. ► We have used the Cole-Cole model to describe the viscoelastic properties of rocks. ► S-wave velocity dispersion estimation from the acoustic dipole waveform processing.
Geophysical monitoring is used principally to interpret the locations and amounts of ground condition changes. To achieve these objectives, differences are computed and examined using time-lapse images calculated under the time-invariant static assumption, that any material property changes during the data measurement can be practically ignored. These monitored data, however, can be contaminated with noise and frequently generate false anomalies of ground condition changes. Furthermore, the assumption of the static model can be invalid if the material property changes significantly during data acquisition. To alleviate these problems, we developed a new least-squares inversion algorithm that allows for the subsurface properties to continuously change in time. We define the subsurface structure and the entire monitoring data in the space–time domain, allowing us to obtain a four-dimensional space–time model using just one inversion process. We introduce the regularizations not only in the space domain but also in time, resulting in reduced inversion artifacts and improved stability of the inverse problem. We demonstrated the performance of the proposed algorithm through numerical experiments that assumed several scenarios of ground condition changes and data acquisition sequences. Finally, the applicability to field data was proven by applying the developed algorithm to the monitoring data of crosshole resistivity tomography jointly performed with a dye tracer flooding experiment. This experiment had a small enough scale that we could not ignore the change of material properties during the data measurement.