bluuebunny/crossref_metadata_2025 huggingface dataset:
EXAMINATION OF A SPECTRAL METHOD FOR MEASURING THE EFFECTS OF ANISOTROPY1
Authors: MACBETH COLIN , CRAMPIN STUART
Published: April 2006

Abstract

The most diagnostic effect of anisotropy on shear waves is shear‐wave splitting. This phenomenon creates a distinctive signature in the 3D particle motion. Methods to extract the effects of anisotropy from shear‐wave data attempt to measure details of this motion. Many techniques have been published recently which process the shear waves in the time or frequency domain. Here we examine the way in which information on the interference effects between the split shear waves is contained within the frequency domain, and suggest some criteria which may be used in future processing algorithms. The time‐delay between the split shear waves, and the polarization direction of the leading shear wave can be converted into easily measured features from analysis of the Fourier spectrum of the shear‐wave signal on each component of motion. These features arise in the spectral interference patterns which are formed by the interaction between the two closely‐spaced and similar waveforms. The interference patterns are interpreted for synthetic and observed seismogram data.
NEAR‐SOURCE PULSE PROPAGATION: APPLICATION TO Q‐DETERMINATION1
Authors: JONGMANS D.
Published: April 2006

Abstract

Among the approaches generally used to measure attenuation from field data, the study of the first pulse broadening appears to be one of the more promising methods to estimate the quality factor Q for different geological formations including soils. Using a numerical scheme, we studied the evolution of the pulse shape in the neighbourhood of the source in order to establish the limits of the method. It was found that the pulse width variations depend strongly upon source depth. At short distances from the source, the pulse shape is controlled mainly by the near‐field terms and/or the onset of surface waves. The investigations proved that the pulse‐broadening method is reliable for distances greater than about 1.2 wavelengths. From numerical experiments, the maximum error in Q‐determination is found to be 10% in the half‐space case.
GEOELECTRICAL SURVEYS OF DIPPING STRUCTURES1
Authors: BERNABINI M. , CARDARELLI E.
Published: April 2006

Abstract

Among resistivity methods, models containing two dipping discontinuity surfaces with a conductive medium between them have been considered in this study. The theoretical apparent resistivity curves obtained for such models were calculated using Alfano's integral equation for various dip angles of planes at different array distances from the contacts. The results obtained showed that it is possible to achieve the dip values of the discontinuities under particular conditions, but ambiguities cannot be ruled out.
APPLICATION OF THE MULTIFREQUENCY HORIZONTAL‐LOOP EM METHOD IN OVERBURDEN INVESTIGATIONS1
Authors: PALACKY G. J.
Published: April 2006

Abstract

In recent years, geophysical methods (shallow seismic, electromagnetic, resistivity, ground penetrating radar) have been increasingly applied to overburden investigations. Their effectiveness has been found to depend significantly on local geological conditions. Compared with advanced seismic techniques, EM methods are faster and hence more cost‐effective, but they have not been considered sufficiently accurate.

Analysis is carried out of data obtained with the multifrequency horizontal‐loop method (HLEM) in northeastern Ontario, where the overburden consists of Quaternary glacial and glaciolacustrine sediments. Surveying along 1‐6 km long profiles permitted recognition of bedrock inhomogeneities and selection of sites suitable for HLEM data interpretation using the layered model. Phasor diagrams and computer inversion based on the ridge regression technique were used to interpret HLEM soundings obtained at eight frequencies. Interpreted layer resistivities and thicknesses were correlated with the results of Rotasonic drilling at 70 sites. Relatively accurate estimates of overburden thickness (within 10%) could be obtained in about 80% of the cases. Nine examples of HLEM soundings are given and discussed: three each of one‐, two‐ and three‐layer situations. An appropriate interpretation model cannot be selected simply by minimizing the rms error or by analysing the parameter resolution matrix. Frequently, the most effective way of evaluating a solution is to consider whether resistivity values determined by inversion fit any of the ranges determined by statistical analyses of sediment resistivities. A previously published study of electrical properties of Quaternary sediments indicated that resistivities of clay, till and sand are stable within a fairly large area, such as the one under investigation. While the application of HLEM methods to mapping of Quaternary sediments can be considered a success, interpretation of EM data in regions covered by glacial sediments is more difficult than in weathered terrains, where near‐surface layering is more predictable. The problem of equivalence causes non‐uniqueness in interpretation. Thickness equivalence, which results in poor resistivity estimates, was found to affect areas convered by sand and till. Conductance equivalence caused poor resolution of thickness and resistivity for thin clay layers (less than 10 m).
ACOUSTIC MODELLING ON A GRID OF VERTICALLY VARYING SPACING1
Authors: JASTRAM CORD , BEHLE ALFRED
Published: April 2006

The Fourier spectral method and high‐order differencing have both been shown to be very accurate in computing spatial derivatives of the acoustic wave equation, requiring only two and three gridpoints per shortest wavelength respectively. In some cases, however, there is a lack of flexibility as both methods use a uniform grid. If these methods are applied to structures with high vertical velocity contrasts, very often most of the model is oversampled. If a complicated interface has to be covered by a fine grid for exact representation, both methods become less attractive as the homogeneous regions are sampled more finely than necessary.

In order avoid this limitation we present a differencing scheme in which the grid spacings can be extended or reduced by any integer factor at a given depth. This scheme adds more flexibility and efficiency to the acoustic modelling as the grid spacings can be changed according to the material properties and the model geometry. The time integration is carried out by the rapid expansion method. The spatial derivatives are computed using either the Fourier method or a high‐order finite‐difference operator in the x‐direction and a modified high‐order finite‐difference operator in the z‐direction. This combination leads to a very accurate and efficient modelling scheme. The only additional computation required is the interpolation of the pressure in a strip of the computational mesh where the grid spacing changes.
SEISMIC PHASE UNWRAPPING: METHODS, RESULTS, PROBLEMS1
Authors: SHATILO A. P.
Published: April 2006

Abstract

Six known methods of seismic phase unwrapping (or phase restoration) are compared. All the methods tested unwrap the phase satisfactorily if the initial function is a simple theoretical wavelet. None of the methods restore the phase of a synthetic trace exactly.

An initial validity test of the phase‐unwrapping method is that the sum of the restored wavelet phase spectrum and the restored pulse‐trace phase spectrum (assuming the convolutional model for the seismic trace) must be equal to the restored phase spectrum of the synthetic trace. Results show that none of the tested methods satisfy this test. Quantitative estimation of the phase‐unwrapping accuracy by correlation analysis of the phase deconvolution results separated these methods, according to their efficiency, into three groups. The first group consists of methods using a priori wavelet information. These methods make the wavelet phase estimation more effective than the minimum‐phase approach, if the wavelet is non‐minimum‐phase. The second group consists of methods using the phase increment Δø(Δω) between two adjacent frequencies. These methods help to decrease the time shift of the initial synthetic trace relative to the model of the medium. At the same time they degrade the trace correlation with the medium model. The third group consists of methods using an integration of the phase derivative. These methods do not lead to any improvement of the initial seismic trace.

The main problem in the phase unwrapping of a seismic trace is the random character of the pulse trace. For this reason methods based on an analysis of the value of Δø(Δω) only, or using an adaptive approach (i.e. as Δω decreases) are not effective. In addition, methods based on integration of the phase derivative are unreliable, due to errors in numerical integration and differentiation.
SOME FADS AND FALLACIES IN SEISMIC DATA ANALYSIS1
Authors: WALDEN A. T. , WHITE R. E.
Published: April 2006

Abstract

In many branches of science, techniques designed for use in one context are used in other contexts, often with the belief that results which hold in the former will also hold or be relevant in the latter. Practical limitations are frequently overlooked or ignored. Three techniques used in seismic data analysis are often misused or their limitations poorly understood: (1) maximum entropy spectral analysis; (2) the role of goodness‐of‐fit and the real meaning of a wavelet estimate; (3) the use of multiple confidence intervals.

It is demonstrated that in practice maximum entropy spectral estimates depend on a data‐dependent smoothing window with unpleasant properties, which can result in poor spectral estimates for seismic data.

Secondly, it is pointed out that the level of smoothing needed to give least errors in a wavelet estimate will not give rise to the best goodness‐of‐fit between the seismic trace and the wavelet estimate convolved with the broadband synthetic. Even if the smoothing used corresponds to near‐minimum errors in the wavelet, the actual noise realization on the seismic data can cause important perturbations in residual wavelets following wavelet deconvolution.

Finally the computation of multiple confidence intervals (e.g. at several spatial positions) is considered. Suppose a nominal, say 90%, confidence interval is calculated at each location. The confidence attaching to the simultaneous use of the confidence intervals is not then 90%. Methods do exist for working out suitable confidence levels. This is illustrated using porosity maps computed using conditional simulation.
RESOLUTION OF RESISTIVITY TOMOGRAPHY INFERRED FROM NUMERICAL SIMULATION1
Authors: SASAKI YUTAKA
Published: April 2006

Abstract

Some factors affecting the resolution and accuracy of resistivity tomography are examined using numerical simulation. The inversion method used is based on smoothness‐constrained least‐squares and finite‐element methods. An appropriate block discretization is obtained by dividing the target region into square blocks of size equal to half the minimum electrode spacing. While the effect of the damping factor on the resolution is significant, the resolution is not very sensitive to Gaussian noise as long as the damping factor is properly chosen, according to the noise level. The issue of choosing an optimum electrode array should be considered at the planning stage of a survey.

When the instrumental accuracy is high, the dipole‐dipole array is more suitable for resolving complex structures than the pole‐pole array. The pole‐dipole array gives somewhat less resolution than the dipole‐dipole array but yields greater signal strength; thus, the pole‐dipole array may be a good compromise between resolution and signal strength. The effect of an inhomogeneity located outside the target region may be very small if block discretization is done so as to represent the resistivity variations in both the target and outside regions.
APPLICATION OF GEOELECTRIC METHODS USING BURIED ELECTRODES IN EXPLORATION AND MINING1
Authors: DRASKOVITS P. , SIMON A.
Published: April 2006

Abstract

Various geoelectric methods which have been developed and applied in the last 10–20 years in ELGI are discussed. These methods which use buried electrodes are: hole‐to‐surface gradient mapping to detect bauxite deposits in sinkholes below a resistive screening layer; in‐mine gradient profiling to map the basement topography below galleries; and the hole‐to‐surface version of geoelectric layer tracing to find outcrops of mineralized zones penetrated by drillings.

Data processing procedures have been developed on the basis of common concepts and hypotheses to link theoretical models with geological structures. The objects investigated are determined as the difference between the theoretical models and geological structures. The predominant part of the real electric field measured above the geological structures is the theoretical field related to the theoretical model. The effects of the objects (the anomaly) are superposed on the theoretical field but their extent is small compared with the values of the latter. The theoretical field and the anomaly depend strongly on the separation from the sources. For this reason the anomalies are difficult to recognize. Therefore the ratio of the theoretical field to the measured one is computed, since σa, the apparent specific conductivity, is proportional to this ratio.

It is demonstrated that since the changes in the σa curve depending on the location of the observation point are small, the anomalies can easily be recognized on the curve. The σa, curve computed in the above way reflects the objects better than the originally measured electric fields.

Examples illustrate the solution of the above‐mentioned geological problems by the practical application of adequate geoelectric methods using buried electrodes.
AUTOMATED FIRST ARRIVAL PICKING: A NEURAL NETWORK APPROACH1
Authors: MURAT MICHAEL E. , RUDMAN ALBERT J.
Published: April 2006

Abstract

A back‐propagation neural network is successfully applied to pick first arrivals (first breaks) in a background of noise. Network output is a decision whether each half‐cycle on the trace is a first or not. 3D plots of the input attributes allow evaluation of the attributes for use in a neural network. Clustering and separation of first break from non‐break data on the plots indicate that a neural network solution is possible, and therefore the attributes are suitable as network input.

Application of the trained network to actual seismic data (Vibroseis and Poulter sources) demonstrates successful automated first‐break selection for the following four attributes used as neural network input: (1) peak amplitude of a half‐cycle; (2) amplitude difference between the peak value of the half‐cycle and the previous (or following) half‐cycle; (3) rms amplitude ratio for a data window (0.3 s) before and after the half‐cycle; (4) rms amplitude ratio for a data window (0.06 s) on adjacent traces. The contribution of the attributes based on adjacent traces (4) was considered significant and future work will emphasize this aspect.
SEISMIC MODELLING OF SEAM WAVES EXCITED BY ENERGY TRANSMISSION INTO A SEAM1
Authors: GRITTO R. , DRESEN L.
Published: April 2006

Abstract

The traditional method of exciting channel waves in coal deposits underground consists of firing explosive sources in a mid‐seam position generating seam waves of the Rayleigh and Love type. We investigate various source positions and excitation mechanisms within the bedrock structure surrounding the seam to evaluate the effects of source positions adjacent to the seam. The investigation is based on analogue and numerical modelling of half‐ and full‐space cases, for which the excitation and the nature of Rayleigh channel waves are examined.

In the analogue modelling, sources, located from mid‐seam out into the bedrock, along the edge of a 2D plate model, excited channel waves through a conversion of the free surface Rayleigh wave at the edge of the plate. The excited channel wave belongs to the normal mode range. Frequency‐wavenumber analysis shows that the symmetric 2nd mode of the channel wave is excited with frequencies comparable to the forcing frequency of the source signal. The polarization changes from retrograde to prograde, as the wave develops from the front to the rear of the seam, respectively. The amplitude‐depth distribution resembles that of an ordinarily excited seam wave, for the symmetric component. However, the antisymmetric component does not show the characteristic change of sign in amplitudes across the mid‐seam axis.

Numerical modelling with sources located in the bedrock (full‐space case) shows that relocating the source away from the seam lowers the frequency content of the excited channel wave. Based on these investigations, the influence of a lower‐frequency source signal on the excitation of the channel wave is examined in an analogue experiment. Sources are sited in the bedrock adjacent to the seam at three locations. A lower‐frequency wavelet is calculated for each source location from the results obtained in the numerical analysis. For comparison, a higher‐frequency wavelet is also used which is known to be optimal for this model geometry when excited by a mid‐seam source location. It is found that in two cases the use of the lower‐frequency wavelet improves the channel wave excitation, while no amplification is achieved in one case.
DEPTH OF DETECTION OF BURIED CONDUCTIVE TARGETS WITH DIFFERENT ELECTRODE ARRAYS IN RESISTIVITY PROSPECTING1
Authors: APPARAO A. , RAO T. GANGADHARA , SASTRY R. SIVARAMA , SARMA V. SUBRAHMANYA
Published: April 2006

Abstract

Depth of detection of a target can be defined as that depth below which the target cannot be detected with a given electrode array assuming that the minimum detectable anomaly is 10%. Following this definition, physical modelling was carried out to determine depths of detection of conductive targets of limited lateral extent such as a vertical sheet, a horizontal cylinder and a sphere (infinitely conducting).

It is seen that the two‐electrode array has the greatest depth of detection followed by the three‐electrode array, while a Wenner array has the smallest depth of detection, when the array spread is in‐line (i.e. perpendicular to the strike direction). On the other hand, the depth of detection with a Wenner array improves considerably and is almost equal to that of the two‐electrode array when the array spread is broadside (i.e. along the strike direction).

With an increase in the depth extent of the vertical sheet from 10 to 20 times its thickness, there is an increase in the depth of detection with all arrays except for the three‐electrode array when the array spread is in‐line, and with the Wenner array when the array spread is broadside.
MULTIPARAMETER GEOPHYSICAL LOGGING AT THE YAVA LEAD DEPOSIT: A STATISTICAL APPROACH1
Authors: CINQ‐MARS ANNE , MWENIFUMBO C. J. , KILLEEN P. G. , CHOUTEAU M.
Published: April 2006

Abstract

The present study describes multiparameter geophysical logging carried out at the Yava sandstone lead deposit, Nova Scotia, Canada. Statistical analysis of the multiparameter data set shows that the spectral gamma‐gamma ratio log (SGG ratio) is the most useful technique for characterizing the disseminated sulphide mineralization.

Principal component analysis (PCA) indicates that the apparent chargeability (IP parameter) responds to the presence of clay minerals in the sandstone in addition to disseminated sulphides, so that the induced polarization method (IP) does not accurately delineate the disseminated galena content as was originally assumed in the preliminary log interpretation. PCA has also confirmed that the SGG ratio and density are related to lead content and that lithological variations can be delineated with natural radioactivity and resistivity.

The zinc content of the deposit was poorly characterized by geophysical logs. Sphalerite occurrences seem to be localized as narrow bands (< 1 cm) which were not geophysically detectable.
APERTURE COMPENSATION TOMOGRAPHY1
Authors: CARRION P. , VESNAVER A. , BOEHM G. , PETTENATI F.
Published: April 2006

Abstract

Conventional velocity analysis can handle a horizontally stratified medium well. There is no indication, though, that it will be as successful when applied to a more complicated geological structure. In fact, a small angle of incidence may transform to a wide‐angle reflection event for a dipping interface. In this case, conventional velocity analysis may lead to large errors and thus cannot be applied. Seismic tomography is attractive as it is virtually free from any restrictions imposed on the velocity distribution in the model space or on the setup of a seismic experiment. It is important, however, to recall that seismic tomography yields results of inferior quality compared to medical tomography. This paper investigates the reason for this and how to suppress a significant blurring of seismic tomograms. Unlike medical tomography, one cannot provide full angular coverage of the model space in a typical seismic experiment: the sources and the receivers cannot surround an unknown object inside the earth to provide a complete spectrum of view angles. Incomplete angular coverage may lead to the occurrence of large inaccuracies in the computed tomograms especially when the initial model is poorly chosen. We demonstrate a method of suppressing the adverse effects related to an incomplete angular recording. This is ‘compensation tomography’ which can be used efficiently in the case of a limited angular aperture. Numerical experiments illustrate the theory.
POROSITY AND PORE STRUCTURE FROM ACOUSTIC WELL LOGGING DATA1
Authors: TAO G. , KING M.S.
Published: April 2006

Abstract

Wyllie's time‐average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)‐wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)‐wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S‐wave information can be obtained from the sonic log, it may be used with P‐waves to provide a better understanding of pore structure. A new acoustic velocities‐to‐porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional‐and shear‐wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time‐average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self‐consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.
RESIDUAL STATICS ESTIMATION: SCALING TEMPERATURE SCHEDULES USING SIMULATED ANNEALING1
Authors: NØRMARK E. , MOSEGAARD K.
Published: April 2006

Abstract

Linearized residual statics estimation will often fail when large static corrections are needed. Cycle skipping may easily occur and the consequence may be that the solution is trapped in a local maximum of the stack‐power function. In order to find the global solution, Monte Carlo optimization in terms of simulated annealing has been applied in the stack‐power maximization technique. However, a major problem when using simulated annealing is to determine a critical parameter known as the temperature.

An efficient solution to this difficulty was provided by Nulton and Salamon (1988) and Andresen et al. (1988), who used statistical information about the problem, acquired during the optimization itself, to compute near optimal annealing schedules.

Although theoretically solved, the problem of finding the Nulton–Salamon temperature schedule often referred to as the schedule at constant thermodynamic speed, may itself be computationally heavy. Many extra iterations are needed to establish the schedule.

For an important geophysical inverse problem, the residual statics problem of reflection seismology, we suggest a strategy to avoid the many extra iterations. Based on an analysis of a few residual statics problems we compute approximations to Nulton–Salamon schedules for almost arbitrary residual statics problems. The performance of the approximated schedules is evaluated on synthetic and real data.
ON THE COMPLETENESS OF DATA SETS WITH MULTIELECTRODE SYSTEMS FOR ELECTRICAL RESISTIVITY SURVEY
Authors: XU BIWEN , NOEL MARK
Published: April 2006

Abstract

This paper describes how, using a surface linear array of equally spaced electrodes, potential data can be obtained for use in electrical resistivity imaging. The aim is to collect a complete data set which contains all linearly independent measurements of apparent resistivity on such an array using two‐, three‐ or four‐electrode configurations. From this primary data set, it is shown that any other value for apparent resistivity on the array can be synthesized through a process of superposition. Numerical tests show that such transformations are exact within the machine error for calculated data but that their use with real field data may lead to noise amplification.
A gravimetric 3D Global inversion for cavity detection1
Authors: Camacho A.G. , Vieira R. , Montesinos F.G. , Cuéllar V.
Published: April 2006

A gravimetric survey, covering a site 200 m square, was carried out in order to locate karstic cavities. After eliminating the regional trend using a polynomial fit, the residual is modelled by least‐squares prediction. Correlated signals for several wavelengths are detected. The inversion of these anomalies is performed by a global 3D adjustment using spherical bodies as models. The adjustment is repeated in order to obtain a stable configuration. The results show the probable presence of a system of cavities and galleries. Data collected from boreholes and the subsequent appearance of sink‐holes are consistent with the results.
Definitions of apparent resistivity for the presentation of magnetotelluric sounding data1
Authors: Başokur A.T.
Published: April 2006

A new definition of apparent resistivity for the presentation of magnetotelluric sounding data is proposed. The new definition is based on the frequency‐normalized impedance function. Both the existing and proposed definitions of apparent resistivity are analysed theoretically and are compared using model curves computed for a 1D earth model. Apparent resistivity curves computed using the proposed definition are a better approximation to the true resistivity values of the subsurface layers. In addition, the layers are more noticeable on the apparent resistivity curves, which is an advantage, especially for the ascending and descending type of apparent resistivity curve.
A method to estimate the total magnetization direction from a distortion analysis of magnetic anomalies1
Authors: Fedi Maurizio , Florio Giovanni , Rapolla Antonio
Published: April 2006

Knowledge of the declination and inclination of the total and induced magnetization vectors is normally required for the interpretation and analysis of magnetic anomalies. A new method of estimating the direction of the total magnetization vector of magnetized rocks from magnetic anomalies is proposed. The unknown declination and inclination (D*T and I*T) can be found by applying a reduction‐to‐the‐pole operator to the measured anomalies for different couples of total magnetization direction parameters (DT and IT) and by observing the variation of the anomaly minimum as a function of both DT and I*T.and D*T are estimated using the maximum of this function. Comparing our method to previous methods, one advantage is that our estimates are not zero‐level dependent; furthermore, the method allows inclinations to be well estimated, with the same accuracy as declinations; finally declinations are not underestimated. Our method is applied to a real case and meaningful results are obtained; it is shown that the feasibility of the method is improved by removing the low‐frequency components.
An airborne tensor VLF system. From concept to realization1
Authors: Pedersen Laust B. , Qian Wei , Dynesius Lars , Zhang Ping
Published: April 2006

Radio signals from very low frequency (VLF) transmitters distributed world‐wide have been used for several decades to study the lateral variations of the electrical conductivity in the upper few hundred metres of the earth's crust. Traditionally, in airborne applications, the total magnetic fields from one or two transmitters are measured to form the basis for construction of maps that primarily show those conductive structures that are parallel or subparallel to the direction to the transmitters. The tensor VLF technique described in this paper makes use of all signals available in a predefined frequency band to construct transfer functions relating the vertical magnetic field and the two horizontal magnetic field components. These transfer functions are uniquely determined for a particular measuring site and contain information about the lateral conductivity variations in all directions. First experiences with real field data, acquired during a test survey in Sweden, show that maps of the so‐called peaker, the spatial divergence of the transfer functions, give an image of the conducting structures. Most of the structures can be correlated to small valleys filled with conducting sediments or valleys underlain by conductive fracture zones in the crystalline rocks.
Transversely isotropic media equivalent to thin isotropic layers1
Authors: Schoenberg Michael
Published: April 2006

Any set of isotropic layers is equivalent, in the long wavelength limit, to a unique transversely isotropic (TI) layer; to find the elastic moduli of that layer is a solved problem. The converse problem is to find a set of isotropic layers equivalent to a given TI media. Here, explicit necessary and sufficient conditions on the TI stiffness moduli for the existence of an equivalent set of isotropic layers are found by construction of a minimal decomposition consisting of either two or three isotropic constituent layers. When only two constituents are required, their elastic properties are uniquely determined. When three constituents are required, two have the same Poisson's ratio and the same thickness fraction, and even then there is a one‐parameter family of satisfactory minimal decompositions. The linear slip model for fractured rock (aligned fractures in an isotropic background) yields a restricted range of transverse isotropy dependent on only four independent parameters. If the ratio of the normal to tangential fracture compliance is small enough, the medium is equivalent to thin isotropic layering and in general its minimal decomposition consists of three constituents.
Velocity model updating using image gathers1
Authors: Eckhardt Wietze
Published: April 2006

For successful prestack depth migration an accurate velocity model is needed. One method for model updating is based on image gather analysis. In an image gather all reflectors line up horizontally if the correct velocities are used for the depth migration. This is also true for dipping reflectors, as all traces of an image gather belong to the same surface coordinate. The images of the reflector in an image gather curve upwards if the velocity used for the migration is too low, or downwards if the velocity is too high. This deviation can be used for model updating. Curves which depend on depth, offset and a parameter which relates the estimated to the true model are fitted to the image. By calculating the coherence along the deviation curves, this parameter can be estimated and hence an update can be calculated.

Formulae are derived for the deviation curves and the update of the velocity depth model for a multilayered model for both shot and common‐offset migrated data, with and without gradients. The method is tested on synthetic data with satisfactory results.
Numerical tests of 3D true‐amplitude zero‐offset migration1
Authors: Filpo E. , Hubral P.
Published: April 2006

Abstracr

An amplitude‐preserving migration aims at imaging compressional primary (zero‐or) non‐zero‐offset reflections into 3D time or depth‐migrated reflections so that the migrated wavefield amplitudes are a measure of angle‐dependent reflection coeffcients. The principal objective is the removal of the geometrical‐spreading factor of the primary reflections. Various migration/inversion algorithms involving weighted diffraction stacks proposed recently are based on Born or Kirchhoff approximations. Here, a 3D Kirchhoff‐type zero‐offset migration approach, also known as a diffraction‐stack migration, is implemented in the form of a time migration. The primary reflections of the wavefield to be imaged are describeda prioriby the zero‐order ray approximation. The aim of removing the geometrical‐ spreading loss can, in the zero‐offset case, be achieved by not applying weights to the data before stacking them. This case alone has been implemented in this work. Application of the method to 3D synthetic zero‐offset data proves that an amplitude‐preserving migration can be performed in this way. Various numerical aspects of the true‐amplitude zero‐offset migration are discussed.
Determination of a shallow velocity–depth model from seismic refraction data by coherence inversion1
Authors: Landa Evgeny , Keydar Shemer , Kravtcov Alex
Published: April 2006

Seismic refractions have different applications in seismic prospecting. The travel‐ times of refracted waves can be observed as first breaks on shot records and used for field static calculation. A new method for constructing a near‐surface model from refraction events is described. It does not require event picking on prestack records and is not based on any approximation of arrival times. It consists of the maximization of the semblance coherence measure computed using shot gathers in a time window along refraction traveltimes. Time curves are generated by ray tracing through the model. The initial model for the inversion was constructed by the intercept‐time method. Apparent velocities and intercept times were taken from a refraction stacked section. Such a section can be obtained by appling linea moveout corrections to common‐shot records. The technique is tested successfully on synthetic and real data. An important application of the proposed method for solving the statics problem is demonstrated.
Effective filtering of artifacts for implicit finite‐difference paraxial wave equation migration1
Authors: Bunks C.
Published: April 2006

Implicit finite‐difference implementations of the paraxial wave equation are widely used in industrial prestack and post‐stack migration programs for imaging and velocity analysis. This type of implementation gives rise to numerical artifacts which, in general, do not degrade image quality but which do impede effective velocity analysis. This paper reviews the artifacts generated by the paraxial approximation and a post‐extrapolation, spatially varying filtering scheme is described which completely eliminates these artifacts. The method is illustrated with numerous examples.
The effects of source and receiver motion on seismic data1
Authors: Hampson Gary , Jakubowicz Helmut
Published: April 2006

The effects of source and receiver motion on seismic data are considered using extensions of the standard convolutional model. In particular, receiver motion introduces a time‐variant spatial shift into data, while source motion converts the effect of the source signature from a single‐channel convolution in time to a multichannel convolution in time and space. These results are consistent with classical Doppler theory and suggest that Doppler shifting can introduce distortions into seismic data even at relatively slow acquisition speeds. It is shown that, while both source and receiver motion are known to be important for marine vibroseis acquisition, receiver motion alone can produce significant artifacts in marine 3D data. Fortunately, the convolutional nature of the distortions renders them amenable to correction using simple deconvolution techniques. Specifically, the effects of receiver motion can be neutralized by applying an appropriate reverse time‐variant spatial shift, while those due to source motion can be addressed by introducing time‐variant spatial shifts both before and after standard, deterministic, signature deconvolution or correlation.
Impact of processing on the amplitude versus offset response of a marine seismic data set1
Authors: Mazzotti A. , Ravagnan G.
Published: April 2006

The analysis of prestack reflections may have a high diagnostic potential in the evaluation of the petrophysical characteristics of subsurface targets. However, the recovery of reliable seismic responses, especially when examining amplitude versus offset (AVO) variations, is of the utmost importance and is strictly dependent on the acquisition and processing steps.

In order to evaluate the impact of different processing sequences, we examine the AVO responses of three seismic events from a marine data set. Borehole data indicate that these events are related to a lignitic sand, a gas sand and a cineritic bed. The AVO analysis is focused mainly on the reflections from the gas sand. In particular, we compare the results of a standard processing sequence with results from a surface‐consistent approach and with results from a processing sequence tailored to this specific case. A decreasing AVO trend of the gas‐sand reflection results from the analyses of data that have undergone the standard and the surface‐consistent processing sequences. This contrasts with both theory and borehole information, which both predict an energy increase with offset. A detailed study shows that the receiver array attenuation, neglected in previous Studies, plays a major role in attenuating the far‐offset reflections. Other propagation factors, such as offset‐dependent geometrical spreading and Q absorption, produce only minor effects.

Taking into account the above factors, we apply a third processing sequence whose impact on the AVO trend is evaluated step by step and whose results are compared with the previously applied sequences. This new sequence leads to better agreement between the AVOs predicted from borehole data and those measured on surface seismic data.
Shallow karst exploration using MT‐VLF and DC resistivity methods1
Authors: Guerin Roger , Benderitter Yves
Published: April 2006

A geophysical test was carried out over a well‐located and fairly embedded karstic conduit. The MT‐VLF method was selected because of its high resolution and its ability to provide a resistivity parameter sensitive to water and Clay. This method was used together with DC resistivity methods which allow vertical adjustment of the VLF data and show consistency between the investigation and target depths. After correcting the deformations due to the polarization of the primary field, the MT‐VLF data show clearly, in the Central part of the site, that the conduit does not coincide with an anomaly axis but coincides with the boundary between a conductive area and a resistive area. 2D modelling confirms that direct detection of the conduit is not feasible and that the conduit is located close to a conductive zone corresponding to a completely Clay‐filled fractured zone. This situation was observed on the whole site and the conduit seemed systematically to thread its way between the conductive zones to join the outlet. The distribution of the conductive fractured zones and the direction of the hydraulic gradient were two important elements in predicting the location of the conduits. A 3D approach would increase the probability of finding the conduits in such a case.
Phase‐shift migration with a variable‐length spatial transform–an algorithm for moderately varying lateral velocities1
Authors: Benson Alvin K.
Published: April 2006

A migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase‐shift migration by using a variable‐length spatial transform. This process significantly reduces the number of lateral wave‐numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0.
Reflection points and surface points1
Authors: Levin Franklyn K.
Published: April 2006

A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z‐axis perpendicular to the surface and a primed one with a z‐axis perpendicular to the reflector, we have
image

where θ is the dip angle, φ is the profile angle, X is the source‐to‐receiver separation, and D is the depth of the reflector. The reflection point is (x, yp, D) and the surface midpoint is (xc, yc, 0).

Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture.
One‐dimensional non‐linear inversion of magnetotelluric data: the importance of data errorrs1
Authors: Belay R. , Rasmussen T.M.
Published: April 2006

Inversion of noisy magnetotelluric data over a horizontally stratified earth has no unique solution. Instead, the resistivities and thicknesses of the layers can only be specified to lie within certain bounds at a particular confidence level. The significance of having correctly estimated data errors when calculating the parameters and parameter bounds is discussed. Emphasis is put on the very corrunon problem of not being able to obtain models which can be considered acceptable with a reasonable certainty from a statistical point of view. A method is presented to obtain a pragmatic data error description by adjustment of wrongly estimated data errors while keeping the suppression of 1D data features at a minimum. A comparison is made between calculation of the parameter bounds based on approximating the confidence surface by hyperellipsoids and a calculation based on a full non‐linear most‐squares analysis. In general it is found that the approximation works very well when the confidence limit is small. However, significant deviations are found in some cases.
Fourier finite‐difference migration for steeply dipping reflectors with complex overburden1
Authors: Rühl T. , Kopp C. , Ristow D.
Published: April 2006

The improvement in accuracy and efficiency of wave‐equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase‐shift and finite‐difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite‐difference migration’(FFD migration).

In our approach we try to generalize and improve the split‐step Fourier migration method for strong lateral velocity variations using an additional finite‐difference correction term. Like most of the current migration methods in use today, our method is based on the one‐way wave equation. It is solved by first applying the square‐root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square‐root operator and this constant‐velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split‐step Fourier correction term.

Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split‐step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase‐shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher‐order implicit FD schemes. These schemes use two cascaded downward‐continuation steps in order to attain comparable migration performance.
Detection of underground cavities with monofrequency electromagnetic tomography between boreholes in the frequency range 100 MHz to 1 GHz1
Authors: Cĉte Philippe , Degauque Pierre , Lagabrielle Richard , Levent Nathalie
Published: April 2006

In order to detect underground cavities, we have designed a geophysical method based on the interaction of a monochromatic electromagnetic wave in the frequency band 100 MHz to 1 GHz with the ground situated between two boreholes.

Three different approaches are involved in the design of this EM tomographic method.

The application of an ‘exact’ theory is used to calculate artificial data, based on an integral equation method. These data are inverted using a tomographic algorithm whose basic assumptions are rather coarse. The results show that, however, cavities can very well be detected and their position recovered.

Data are obtained with a physical reduced‐scale model in a water tank, in which all parameters are known in advance. The inversion process confirms the validity of the method.

Underground cavities are actually detected.

The above approaches are described and discussed and results are shown. The equipment involved and its operation is quite simple: the surface devices are commercially available and only the transmitter and receiver antennae must be specially built. The method is shown to be quite efficient and its cost should be reasonably low.
An integral equation for the homogeneous Neumann condition1
Authors: Furness Peter
Published: April 2006

Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces.

A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R3 which requires an appropriate interpretation for its implementation.

A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation.