Showing papers in "Geophysical Prospecting in 1996"

Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method1

Abstract: A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.

Practical techniques for 3D resistivity surveys and data inversion1

Abstract: Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole-pole array is used to make the potential measurements. The number of measurements required can be reduced to about one-third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness-constrained least-squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half-space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi-Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.

Bayesian inference, Gibbs' sampler and uncertainty estimation in geophysical inversion

Abstract: The posterior probability density function (PPD), σ(m|d obs ), of earth model m, where d obs are the measured data, describes the solution of a geophysical inverse problem, when a Bayesian inference model is used to describe the problem. In many applications, the PPD is neither analytically tractable nor easily approximated and simple analytic expressions for the mean and variance of the PPD are not available. Since the complete description of the PPD is impossible in the highly multi-dimensional model space of many geophysical applications, several measures such as the highest posterior density regions, marginal PPD and several orders of moments are often used to describe the solutions. Calculation of such quantities requires evaluation of multidimensional integrals. A faster alternative to enumeration and blind Monte-Carlo integration is importance sampling which may be useful in several applications. Thus how to draw samples of m from the PPD becomes an important aspect of geophysical inversion such that importance sampling can be used in the evaluation of these multi-dimensional integrals. Importance sampling can be carried out most efficiently by a Gibbs' sampler (GS). We also introduce a method which we called parallel Gibbs' sampler (PGS) based on genetic algorithms (GA) and show numerically that the results from the two samplers are nearly identical. We first investigate the performance of enumeration and several sampling based techniques such as a GS, PGS and several multiple maximum a posteriori (MAP) algorithms for a simple geophysical problem of inversion of resistivity sounding data. Several non-linear optimization methods based on simulated annealing (SA), GA and some of their variants can be devised which can be made to reach very close to the maximum of the PPD. Such MAP estimation algorithms also sample different points in the model space. By repeating these MAP inversions several times, it is possible to sample adequately the most significant portion(s) of the PPD and all these models can be used to construct the marginal PPD, mean) covariance, etc. We observe that the GS and PGS results are identical and indistinguishable from the enumeration scheme. Multiple MAP algorithms slightly underestimate the posterior variances although the correlation values obtained by all the methods agree very well. Multiple MAP estimation required 0.3% of the computational effort of enumeration and 40% of the effort of a GS or PGS for this problem. Next, we apply GS to the inversion of a marine seismic data set to quantify uncertainties in the derived model, given the prior distribution determined from several common midpoint gathers.

Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements1

Abstract: Spectral induced polarization as well as complex electrical measurements are used to estimate, on a non-invasive basis, hydraulic permeability in aquifers. Basic laboratory measurements on a variety of shaly sands, silts and clays showed that the main feature of their conductivity spectra in the frequency range from 10-3 to 103 Hertz is a nearly constant phase angle. Thus, a constant-phase-angle model of electrical conductivity is applied to interpret quantitatively surface and borehole spectral induced polarization measurements. The model allows for the calculation of two independent electrical parameters from only one frequency scan and a simple separation of electrical volume and interface effects. The proposed interpretation algorithm yields the true formation factor, the cation exchange capacity and the surface-area-to-porosity ratio, which corresponds to the inverse hydraulic radius. Using a Kozeny–Carman-like equation, the estimation of hydraulic permeability is possible.

A physical model for shear-wave velocity prediction

Abstract: The clay-sand mixture model of Xu and White is shown to simulate observed relationships between S-wave velocity (or transit time), porosity and clay content. In general, neither S-wave velocity nor S-wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well-log applications. In principle, the model can predict S-wave velocity from lithology and any pair of P-wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P-wave velocity are the most reliable. The robust relationship between S- and P-wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P-wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs. Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksoz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P- and S-wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the v P - v s relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P-wave velocity in shaly sands than in less compliant cleaner sandstones.

Estimation of multivalued arrivals in 3D models using wavefront construction—Part I1

Abstract: A new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S- and P-velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple-event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

Full frequency‐range transient solution for compressional waves in a fluid‐saturated viscoacoustic porous medium1

Abstract: An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies. lntroduction The acoustics of porous media, within the framework of petroleum geophysics, have been receiving more attention in recent years. Regional exploration seismology aimed at the discovery of hydrocarbon reservoirs is based on simplified rheological models and ray representations of the wavefield. In the past, these approximations were sufficient, since the degree of resolution required was not high. In the present time, when most reservoirs are delimited, the need to increase the resolution and use not only the traveltimes but also the information contained in the amplitude and phase of the seismic wavefield has gradually emerged. The new exploration scenario is confined to reservoir areas and involves the presence of oil wells and data from seismic logs and well seismics, which have enough resolution to 'see' the effects of bulk properties, porosity, permeability' fluid content and fluid-solid interaction on the seismic pulse. In this case, the correct

Integrating long‐offset transient electromagnetics (LOTEM) with seismics in an exploration environment1

Abstract: The applications of electromagnetics have increased in the past two decades because of an improved understanding of the methods, improved service availability, and the increased focus of exploration in the more complex reservoir characterization issues. For electromagnetic methods surface applications for hydrocarbon Exploration and Production are still a special case, while applications in borehole and airborne research and for engineering and environmental objectives are routine. In the past, electromagnetic techniques, in particular deep transient electromagnetics, made up a completely different discipline in geophysics, although many of the principles are similar to the seismic one. With an understanding of the specific problems related to data processing initially and then acquisition, the inclusion of principles learned from seismics happened almost naturally. Initially, the data processing was very similar to seismic full-waveform processing. The hardware was also changed to include multichannel acquisition systems, and the field procedures became very similar to seismic surveying. As a consequence, the integration and synergism of the interpretation process is becoming almost automatic. The long-offset transient electromagnetic (LOTEM) technique will be summarized from the viewpoint of its similarity to seismics. The complete concept of the method will also be reviewed. An interpretation case history that integrates seismic and LOTEM from a hydrocarbon area in China clearly demonstrates the limitations and benefits of the method.

Part II: Tracing and interpolation1

Abstract: The numerical tracing of short ray segments and interpolation of new rays between these ray segments are central constituents of the wavefront construction method. In this paper the details of the ray tracing and ray-interpolation procedures are described. The ray-tracing procedure is based on classical ray theory (high-frequency approximation) and it is both accurate and efficient. It is able to compute both kinematic and dynamic parameters at the endpoint of the ray segments, given the same set of parameters at the starting point of the ray. Taylor series are used to approximate the raypath so that the kinematic parameters (new position and new ray tangent) may be found, while a staggered finite-difference approximation gives the dynamic parameters (geometrical spreading). When divergence occurs in some parts of the wavefront, new rays are interpolated. The interpolation procedure uses the kinematic and dynamic parameters of two parent rays to estimate the initial parameters of a new ray on the wavefront between the two rays. Third-order (cubic) interpolation is used for interpolation of position, ray tangent and take-off vector from the source) while linear interpolation is used for the geometrical spreading parameters.

Ground radar simulation for archaeological applications1

Abstract: This work presents a new modelling scheme for the simulation of electromagnetic radio waves, based on a full-field simulator. Maxwell's equations are modified in order to include dielectric attenuation processes, such as bound- and free-water relaxation, ice relaxation and the Maxwell-Wagner effect. The new equations are obtained by assuming a permittivity relaxation function represented by a generalized Zener model. The convolution integral introduced by the relaxation formulation is circumvented by defining new hidden field variables, each corresponding to a different dielectric relaxation. The equations are solved numerically by using the Fourier pseudospectral operator for computing the spatial derivatives and a new time-splitting integration algorithm that circumvents the stiffness of the differential equations. The program is used to evaluate the georadar electromagnetic response of a Japanese burial site, in particular, a stone coffin-like structure.

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

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

A new method for geoelectrical investigations underwater1

Abstract: A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type ; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.

Multiple suppression by 2D filtering in the parabolic tau-p domain: a wave-equation-based method1

Abstract: The filter for wave-equation-based water-layer multiple suppression, developed by the authors in the x-t, the linear τ-p, and the f-k domains, is extended to the parabolic τ-2 domain. The multiple reject areas are determined automatically by comparing the energy on traces of the multiple model (which are generated by a wave-extrapolation method from the original data) and the original input data (multiples + primaries) in τ-p space. The advantage of applying the data-adaptive 2D demultiple filter in the parabolic τ-p domain is that the waves are well separated in this domain. The numerical examples demonstrate the effectiveness of such a dereverberation procedure. Filtering of multiples in the parabolic τ-p domain works on both the far-offset and the near-offset traces, while the filtering of multiples in the f-k domain is effective only for the far-offset traces. Tests on a synthetic common-shot-point (CSP) gather show that the demultiple filter is relatively immune to slight errors in the water velocity and water depth which cause arrival time errors of the multiples in the multiple model traces of less than the time dimension (about one quarter of the wavelet length) of the energy summation window of the filter. The multiples in the predicted multiple model traces do not have to be exact replicas of the multiples in the input data, in both a wavelet-shape and traveltime sense. The demultiple filter also works reasonably well for input data contaminated by up to 25% of random noise. A shallow water CSP seismic gather, acquired on the North West Shelf of Australia, demonstrates the effectiveness of the technique on real data.

A numerical laboratory for simulation and visualization of seismic wavefields1

Abstract: Computational seismic modelling (CSM) plays an important role in the geophysical industry as an established aid to seismic interpreters. Numerical solution of the elastic wave equations has proved to be a very important tool for geophysicists in both forward modelling and migration. Among the techniques generally used in CSM, we consider the finite-element method (FEM) and investigate its computational and visualization requirements. The CSMFEM program, designed for this purpose and developed on an IBM 3090 computer with vector facility, is described in detail. It constitutes a numerical laboratory for performing computer experiments. Two Newmark type algorithms for time integration are compared with other time integration schemes, and both direct and iterative methods for solving the corresponding large sparse system of linear algebraic equations are analysed. Several numerical experiments to simulate seismic energy propagation through heterogeneous media are performed. Synthetics in the form of common shot gathers, vertical seismic profiles and snapshots are suitably displayed, since with the large amounts of data obtained from CSM research, methods for visualization of the computed results must be developed. The FEM is compared with other numerical tools, such as finite-difference and pseudo-spectral methods.

High‐speed photography of the bubble generated by an airgun1

Abstract: High-speed photography has been used visually to study the shape, surface, turbulence and behaviour of an underwater oscillating bubble generated by an airgun. The source was a BOLT airgun with a chamber volume of 1.6cu.in., placed in a 0.85m3 tank at 0.5m depth. Near-field signatures were also recorded in order to compare the instant photographs of the oscillating bubble with the pressure field recorded about 25 cm from the gun. Estimations of the bubble-wall velocity and bubble radius estimated from high-speed film sequences are also presented, and are compared with modelled results. The deviation between the modelled and measured bubble radii was at most 9%. In order to check the capacity for transmission of light through the bubble, a concentrated laser beam was used as illumination. We found that the air bubble is a strong scattering medium of laser light, hence the bubble is opaque.

Interpretation of slingram conductivity mapping in near-surface geophysics: using a single parameter fitting with 1D model1

Abstract: Electrical conductivity mapping is a prerequisite tool for hydrogeological or environmental studies. Its interpretation still remains qualitative but advantages can be expected from a quantitative approach. However a full 3D interpretation is too laborious a task in comparison with the limited cost and time which are involved in the majority of such field studies. It is then of value to define the situations where lateral variations are sufficiently smooth for a 1D model to describe correctly the underlying features. For slingram conductivity measurements, criteria allowing an approximate 1D inversion are defined: these mainly consist of a limited rate of variation over three times the intercoil spacing. In geological contexts where the weathering has generated a conductive intermediate layer between the underlying sound rock and the soil, this processing can be applied to determine the thickness of the conductive layer from the apparent resistivity map when the other geoelectrical parameters are known. The examples presented illustrate this application.

Shallow velocity-depth model imaging by refraction tomography1

Abstract: A tomographic imaging technique combined with coherence inversion is proposed for constructing a near-surface model from refraction events. A model obtained from coherence inversion serves as a good background model for the tomographic reconstruction. A simultaneous iterative reconstruction technique (SIRT) algorithm was used for this purpose. This is a simple algorithm and can be easily adapted to irregular acquisition geometry and limited angular aperture. Using synthetic data it was shown that the proposed procedure can be used for determination of local velocity anomalies in a shallow subsurface. The technique was also tested on a real data set.

Ray tracing based on Fermat's principle in irregular grids1

Abstract: A new method to trace rays in irregular grids based on Fermat's principle of minimum time is introduced. Besides the usual transmitted and reflected waves, refracted, diffracted and converted waves can also be simulated. The proposed algorithm is fast and stable, and respects the reciprocity principle between source and receiver better than procedures adopting the shooting method. It is particularly suited to form part of a traveltime inversion procedure. The use of irregular grids allows adaptation of the earth discretization to the available acquisition geometry and ray distribution, to obtain more stable and reliable tomographic images.

Electromagnetic mapping of electrical conductivity beneath the Columbia basalts1

Abstract: Sedimentary rocks beneath the Columbia River Basalt Group are recognized as having potential for oil and gas production, but the overlying layered basalts effectively mask seismic reflections from the underlying sediments. Four electromagnetic (EM) methods have been applied on profiles crossing Boylston Ridge, a typical east-west trending anticline of the Yakima Fold Belt, in an attempt to map the resistivity interface between the basalts and the sediments and to map variations in structure and resistivity within the sediments. The EM surveys detected strong variations in resistivity within the basalts, and in particular the continuous magnetotelluric array profiling (EMAP) revealed resistivity lows beneath the surface anticlines. These low resistivity zones probably coincide with fracturing in the core of the anticlines and they appear to correlate well with similar zones of low seismic velocity observed on a nearby seismic profile. The controlled-source EM surveys (in-loop transient, long-offset transient, and variable-offset frequency-domain) were designed in anticipation of relatively uniform high resistivity basalts, and were found to have been seriously distorted by the intrabasalt conductors discovered in the field. In particular, the resistivity sections derived from 1D inversions were found to be inconsistent and misleading. The EMAP survey provided the most information about themore » subsurface resistivity distribution, and was certainly the most cost-effective. However, both controlled-source and EMAP surveys call for accurate 2D or 3D inversion to accommodate the geological objectives of this project. [References: 18]« less

Papua New Guinea MT: looking where seismic is blind1

Abstract: Hydrocarbon exploration in the Papuan fold belt is made extremely difficult by mountainous terrain, equatorial jungle and thick karstified Miocene limestones at the surface. The high-velocity karstified limestones at or near the surface often render the seismic technique useless for imaging the subsurface. In such areas magnetotellurics (MT) provides a valuable capability for mapping subsurface structure. The main structural interface which can be mapped with MT, due to the large electrical contrast, is the contact between the resistive Darai limestone and the underlying conductive sediments of the Ieru Formation. In some areas the base of the Darai can be mapped with reasonable accuracy by fitting 1D models to the observed MT data. However, in many cases where 2D and 3D effects are severe, 1D interpretations can yield dramatically incorrect results. Numerical and field data examples are presented which demonstrate the severity of the 1D errors and the improvements in accuracy which can be achieved using a 2D inverse solution. Two MT lines over adjacent anticlines, both with well control and seismic data, are used to demonstrate the application of 1D and 2D inversions for structural models. In both cases the seismic data provide no aid in the interpretations. The example over the Hides anticline illustrates a situation where 1D inversion of either TE or TM mode provides essentially the same depth to base of Darai as 2D inversion of both TE and TM. Both models provide base Darai depth estimates which are within 10% of that measured in the well. The example over the Angore anticline illustrates the inadequacy of 1D inversion in structurally complex geology complicated by electrical statics. The TE mode fits a 1D Darai thickness of 800 metres while the TM mode fits a 1D Darai thickness of 3500 metres, bracketing the thickness of 2450 metres observed in the well. The final 2D inversion model provides a depth estimate of 2250 metres. Four MT lines along the Angore anticline have been interpreted using 2D inversion. A high degree of correlation exists between lineaments observed on an airborne radar image and zones of low resistivity within the high-resistivity material interpreted as Darai limestone. These low-resistivity zones are interpreted as fault zones. Three-dimensional modelling has been used to simulate 3D statics in an otherwise 2D earth. These data were used to test the Groom-Bailey (GB) decomposition for possible benefits in reducing static effects and estimating geoelectric strike in the Papua New Guinea (PNG) field data. It has been found that the GB decomposition can provide improved regional 2D strike estimates in 3D contaminated data. However, in situations such as PNG, where the regional 2D strike is well established and hence can be fixed, the GB decomposition provides apparent resistivities identical to those simply rotated to strike.

Event-oriented velocity estimation based on prestack data in time or depth domain1

Abstract: A 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event-oriented local approach of the layer-stripping type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half-offset systems. Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. The authors adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common-shot depth domain or the common-offset depth domain, then a depth-time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracing, and with respect to the original depth-migration velocity field. By this means, they expect the input events for velocity updating to become less sensitive to migration velocity errors. An interactive updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray-theoretical depth conversion, andmore » reflection-point derivatives are calculated accurately and efficiently from information pertaining to single rays.« less

Velocity sensitivity in transversely isotropic media

Abstract: We consider the problem of determining and predicting how the wave speeds in particular directions for a transversely isotropic (TI) medium depend on particular combinations of the density-normalized moduli A ij . The expressions for the q P and q SV velocities are known to depend on four moduli. Normally, we can only determine three independent parameters from q P data, or two from q SZ data, as the others have much lower sensitivity. The resolvable parameters are conveniently described by axial and off-axis parameters: for q P rays, P 0° = A 11 , P 90° = A 33 and P 45° =(A 11 A 33 )/4 (A 13 2 A 55 )/2; and for q SV rays, S 0° = S 90° = A 55 and S 45°= (A 11 A 33 )/4- A 13 /2. These parameters control the magnitude of the squared-velocities on the axes and at approximately 45°. For an arbitrary TI medium, if the medium is perturbed in a way that preserves a particular parameter, then slowness points in the associated direction and mode witl be approximately preserved in the new medium. we refer to these parameters as ‘push-pins’, i.e. if a parameter is fixed, the associated part of the slowness surface is pinned in place. Because, these five push-pins only contain four independent moduli, we can only fix at most three push-pins. Perturbing one of the other parameters inevitably perturbs the other. Numerical results illustrating the linkage between two push-pins, when three are fixed, are presented. So-called anomalous TI media occur when the roles of the q P and q SV waves are reversed: in some directions the faster ray has transverse polarization. That, in turn, requires anomalous velocities at the push-pins, i.e. S 0° > P 0° , S 45° > P 45° and/or S 90° > P 90° (equivalent to the usual anomalous conditions A 11 A 55 , A 33 A 55 ). In the Appendix, we confirm that anomalous sensitivities of the velocities at the five push-pins only occur in such media, although the push-pins still apply if interpreted appropriately. Truly anomalous sensitivities, in which push-pins play no role, only occur in media near the boundary between normal and anomalous.

Seismic inversion through Tabu Search1

Abstract: Highly non-linear seismic trace inversion problems can be solved efficiently by an implementation of Tabu Search, a meta-heuristic method related to artificial intelligence. The implementation under consideration is a deterministic, global search that combines the advantages of a local search, giving a quick descent to local misfit minima, with an ability to cross misfit barriers in the model space. Once Tabu Search has found an area of low misfit, it performs an extensive exploration of its deepest points. This property makes it possible to use Tabu Search for a semiquantitative resolution and uncertainty analysis of the inverse problem.

Advances in the combined interpretation of seismics with magnetotellurics1

Abstract: Five examples, obtained during exploration for hydrocarbons in the Pannonian Basin of Hungary, are used to show how the interpretation of seismic sections can be usefully complemented by results from MT surveys. Selection of the most appropriate MT quantities, considered to be proper ‘MT attributes’ for the purpose of visualization as well as recognition of the subsurface structures and the different inversions of MT data is essential for practical integration of seismic and MT surveys. A new technique providing a semiquantitive MT-attribute pseudosection for the purpose of visualization of the subsurface structures is proposed. The procedure utilizes derivative functions of the phase of MT impedance for visualization and derives estimated depths from the Bostick transformation of Cagniard apparent resistivities. On the basis of the MT-attribute pseudosections, constructed from the phase derivatives and transformed resistivity data, depths are estimated for interfaces between geological formations with significant resistivity contrast. In particular examples, the interface between the Tertiary sediments and the older basement rocks as well as tectonic fracture zones with decreased resistivity can be resolved.

Linearized elastic parameter sections

Abstract: Contrasts in elastic parameters can be estimated directly from seismic data using offset-dependent information in the PP reflection coefficient. A linear approximation to the PP reflection coefficient including three coefficients is fitted to the data, and relative contrasts in various elastic parameters are obtained from linear combinations of the estimated coefficients. Linearized elastic parameter sections for the contrasts in P-wave impedance, P-wave velocity, density, plane-wave modulus, and the change in bulk modulus and shear modulus normalized with the plane-wave modulus are estimated. If the average P- to S-wave velocity ratio is known, linearized parameter sections including the contrast in the average P- to S-wave velocity ratio and a fluid factor section can be computed. Applied to synthetic data, visual comparison of the estimated and true elastic parameter sections agree qualitatively, and the results are confirmed by an analysis of the standard deviation of the estimated parameters. The parameter sections obtained by inversion of a shallow seismic anomaly in the Barents Sea are promising, but the reliability is uncertain because neither well data nor regional trends are available.

A few case histories of subsurface imaging with EMAP as an aid to seismic processing and interpretation1

Abstract: The electromagnetic array profiling (EMAP) exploration method can be combined with a direct one-dimensional inversion process for conversion to depth to produce a subsurface resistivity cross-section. This cross-section may then be interpreted in parallel with a seismic cross-section to enhance the prediction of rock type and structure. In complex thrust environments and areas of shallow carbonate rocks, the EMAP method is often used to provide additional data either to help the seismic processor and/or to aid the seismic interpretation. In particular, the electromagnetic (EM) data can be used to build an independent seismic velocity file for depth migration. Three EMAP test areas in the western United States are used to demonstrate such a use of EMAP as an expioration tool. The first shows how a velocity file is estimated from resistivity data for seismic depth migration processing in a complex thrust environment. In the second example, the method is applied in layer-cake geology with high seismic velocity rocks at the earth's surface. The third example is another complex thrust environment, but in this case the velocity file derived from the resistivity data is used for stacking the seismic data.

3D Modelling of the electromagnetic response of geophysical targets using the FDTD method1

Abstract: A publicly available and maintained electromagnetic finite-difference time domain (FDTD) code has been applied to the forward modelling of the response of 1D, 2D and 3D geophysical targets to a vertical magnetic dipole excitation. The FDTD method is used to analyze target responses in the 1 MHz to 100 MHz range, where either conduction or displacement currents may have the controlling role. The response of the geophysical target to the excitation is presented as changes in the magnetic field ellipticity. The results of the FDTD code compare favorably with previously published integral equation solutions of the response of 1D targets, and FDTD models calculated with different finite-difference cell sizes are compared to find the effect of model discretization on the solution. The discretization errors, calculated as absolute error in ellipticity, are presented for the different ground geometry models considered, and are, for the most part, below 10% of the integral equation solutions. Finally, the FDTD code is used to calculate the magnetic ellipticity response of a 2D survey and a 3D sounding of complicated geophysical targets. The response of these 2D and 3D targets are too complicated to be verified with integral equation solutions, but show the proper low- andmore » high-frequency responses.« less

Plane‐layered models for the analysis of wave propagation in reservoir environments1

Abstract: The long-wavelength propagation and attenuation characteristics of three geological structures that frequently occur in reservoir environments are investigated using a theoretical model that consists of a stack of fine and viscoelastic plane layers, with the layers being either solid or fluid. Backus theory properly describes fine layering and a set of fluid-filled microfractures, under the assumption that interfaces between different materials are bonded. The effects of saturation on wave attenuation are modelled by the relative values of the bulk and shear quality factors. .The anisotropic quality factor in a fine-layered system shows a variety of behaviours depending on the saturation and velocities of the single constituents. The wave is less attenuated along the layering direction when the quality factors are proportional to velocity, and vice versa when inversely proportional to velocity. Fractured rocks have very anisotropic wavefronts and quality factors, in particular for the shear modes which are strongly dependent on the characteristics of the fluid filling the microfractures. '$7hen the size of the boundary layer is much smaller than the thickness of the fluid layer, the stack of solid-fluid layers becomes a layered porous media of the Biot type. This behaviour is caused by the slip-wall condition at the interface between the solid and the fluid. As in Biot theory, there are two compressional waves, but here the medium is anisotropic and the slow wave does not propagate perpendicular to the layers. Moreover, this wave shows pronounced cusps along the layering direction, like shear waves in a very anisotropic single-phase medium.

Transient electromagnetic vs. seismic prospecting—a correspondence principle1

Abstract: A correspondence principle is derived that relates the Green's functions (point-receiver responses to point-source excitations) for 2D transient diffusive electro-magnetic fields with electric field in the vertical plane to 2D seismic waves (in the acoustic approximation) with particle velocity in the vertical plane in arbitrarily inhomogeneous media. The constituent medium parameters in the two cases are related via two global proportionality constants. The kernels in the integral operators that express the diffusion phenomenon in terms of the wave phenomenon are of a smoothing nature. The fact that they are explicitly known can be of importance to the inverse operation. The correspondence principle is the fundamental tool in comparing the spatial resolving powers in the two methods of geophysical prospecting.