bluuebunny/crossref_metadata_2025 huggingface dataset:
GROUND‐PENETRATING RADAR FOR HIGH‐RESOLUTION MAPPING OF SOIL AND ROCK STRATIGRAPHY1
Authors: DAVIS J. L. , ANNAN A. P.
Published: April 2006

Ground‐penetrating radar is a technique which offers a new way of viewing shallow soil and rock conditions. The need to better understanding overburden conditions for activities such as geochemical sampling, geotechnical investigations, and placer exploration, as well as the factors controlling groundwater flow, has generated an increasing demand for techniques which can image the subsurface with higher resolution than previously possible.

The areas of application for ground‐penetrating radar are diverse. The method has been used successfully to map ice thickness, water depth in lakes, bedrock depth, soil stratigraphy, and water table depth. It is also used to delineate rock fabric, detect voids and identify karst features. The effective application of the radar for the high‐resolution definition of soil stratigraphy and fractures in bedrock is highlighted.

The basic principles and practices involved in acquiring high quality radar data in the field are illustrated by selected case histories. One example demonstrates how radar has been used to map the bedrock and delineate soil horizons to a depth of more than 20 m. Two case histories show how radar has been used to map fractures and changes of rock type to 40 m range from inside a mine. Another case history demonstrates how radar has also been used to detect and map the extent of groundwater contamination. The corroboration of the radar results by borehole investigations demonstrates the power and utility of the high‐resolution radar method as an aid for interpolation and extrapolation of the information obtained with conventional coring programmes. With the advent of new instrumentation and field procedures, the routine application of the radar method is becoming economically viable and the method will see expanded use in the future.
SUGGESTIONS FOR A CONSISTENT TERMINOLOGY FOR SEISMIC ANISOTROPY1
Authors: CRAMPIN STUART
Published: April 2006

Seismic anisotropy is an unfamiliar concept to many geophysicists and the use of misleading and ambiguous terminology has made it more difficult to understand. I suggest here a consistent terminology in which simple expressions have specific meanings similar to their colloquial meanings. It is hoped that use of such language will help to make the increasing number of papers reporting seismic anisotropy more readily comprehensible to the non‐specialist. This not a manual of anisotropy, and it is not intended for theoreticians. It is a list of terms which may make anisotropy a little easier to understand for those more familiar with wave propagation in isotropic solids.
ACHIEVEMENTS IN COPPER SULPHIDE EXPLORATION IN ALBANIA WITH IP AND EM METHODS1
Authors: LANGORE L. , ALIKAJ P. , GJOVREKU D.
Published: April 2006

The copper sulphide exploration programme in Albania involves a number of geophysical methods. The most important ones are the Induced Polarization (IP) and the Turam methods. This paper reports some recent achievements in increasing the depth of investigation and in discriminating sulphide ore textures by the IP, spectral IP and Turam methods.
MODELLING OF SOFT SEDIMENTS AND LIQUID‐SOLID INTERFACES: MODIFIED WAVENUMBER SUMMATION METHOD AND APPLICATION1
Authors: KERNER CLAUDIA
Published: April 2006

Abstract

Alekseev and Mikhailenko have developed a wavenumber‐summation method which combines a finite integral transformation with a finite‐difference calculation and involves no approximations other than numerical ones. However, numerical anisotropy causes velocity errors for shear waves which are unacceptable if Poisson's ratios are larger than 0.4 and unless the number of grid points per wavelength is chosen considerably higher than the value generally regarded as sufficient in finite‐difference computations. To overcome this limitation in the applicability of the otherwise very powerful modelling scheme, the method is applied to the elastodynamic equations for the velocity vector. Thus, instead of solving a second‐order hyperbolic system as in the case of the wave equation, solutions to a first‐order hyperbolic system are computed. The finite‐difference iteration is performed in a staggered grid. In addition to mastering the numerical difficulties in cases where the Poisson's ratio is unusually high, this approach results in a code which can be used for the modelling of liquid layers.

With the new scheme, water reverberations are investigated in terms of normal modes. It is found that for realistic sea‐bottom velocities the critical and supercritical cases exist only for P‐waves. It means that compressional waves are trapped within the water layer but energy leaks into the substratum through converted shear waves. These leaky compressional normal modes attain properties similar to those of shear normal modes or Pseudo‐Love waves. Due to their origin from conversion of dispersed multi‐modal compressional waves the shear waves generated at the sea‐bottom form a long complex wavetrain. They were found to mask the reflections from the target horizon in an offset‐VSP field section.
INVERSE THEORY APPLIED TO MULTI‐SOURCE CROSS‐HOLE TOMOGRAPHY.
Authors: PRATT R. GERHARD
Published: April 2006

Abstract

It is advantageous to consider inversion of multi‐source (wide‐aperture) cross‐hole data using methods that (i) are based on the wave equation rather than its high‐frequency ray approximation, and (ii) use the full information content of the recorded wavefield rather than only first‐arrival times. Wave‐theoretical methods require the ability to forward‐model appropriate wave equations for all source positions in arbitrary reference media. This can be achieved using a frequency‐domain elastic wave propagator that facilitates the modelling of multi‐source data at the cost of temporal bandwidth. The trade‐off is deliberate; the propagator is applied to the cross‐hole imaging problem, in which wide spatial bandwidths are more important than temporal bandwidth.

By using the frequency‐domain propagator, non‐linear inverse techniques are applied to data from a very large number of source positions. The method can be applied in 2D media of arbitrary a priori complexity. In a synthetic example, compressional and shear‐velocity perturbations are successfully resolved with one iteration using only a single frequency component of wide‐aperture elastic wave cross‐hole data.
WEIGHTED STACKING OF SEISMIC DATA USING AMPLITUDE‐DECAY RATES AND NOISE AMPLITUDES1
Authors: ANDERSON RICHARD G. , McMECHAN GEORGE A.
Published: April 2006

Abstract

The signal‐to‐noise (S/N) ratio of seismic reflection data can be significantly enhanced by stacking. However, stacking using the arithmetic mean (straight stacking) does not maximize the S/N ratio of the stack if there are trace‐to‐trace variations in the S/N ratio. In this case, the S/N ratio of the stack is maximized by weighting each trace by its signal amplitude divided by its noise power, provided the noise is stationary. We estimate these optimum weights using two criteria: the amplitude‐decay rate and the measured noise amplitude for each trace. The amplitude‐decay rates are measured relative to the median amplitude‐decay rate as a function of midpoint and offset. The noise amplitudes are measured using the data before the first seismic arrivals or at late record times. The optimum stacking weights are estimated from these two quantities using an empirical equation.

Tests with synthetic data show that, even after noisy‐trace editing, the S/N ratio of the weighted stack can be more than 10 dB greater than the S/N ratio of the straight stack, but only a few decibels more than the S/N ratio of the trace equalized stack. When the S/N ratio is close to 0 dB, a difference of 4 dB is clearly visible to the eye, but a difference of 1 dB or less is not visible. In many cases the S/N ratio of the trace‐equalized stack is only a few decibels less than that of the optimum stack, so there is little to be gained from weighted stacking. However, when noisy‐trace editing is omitted, the S/N ratio of the weighted stack can be more than 10 dB greater than that of the trace‐equalized stack. Tests using field data show that the results from straight stacking, trace‐equalized stacking, and weighted stacking are often indistinguishable, but weighted stacking can yield slight improvements on isolated portions of the data.
Lp‐NORM DECONVOLUTION1
Authors: DEBEYE H. W. J. , VAN RIEL P.
Published: April 2006

Abstract

The purpose of deconvolution is to retrieve the reflectivity from seismic data. To do this requires an estimate of the seismic wavelet, which in some techniques is estimated simultaneously with the reflectivity, and in others is assumed known. The most popular deconvolution technique is inverse filtering. It has the property that the deconvolved reflectivity is band‐limited. Band‐limitation implies that reflectors are not sharply resolved, which can lead to serious interpretation problems in detailed delineation.

To overcome the adverse effects of band‐limitation, various alternatives for inverse filtering have been proposed. One class of alternatives is Lp‐norm deconvolution, L1norm deconvolution being the best‐known of this class.

We show that for an exact convolutional forward model and statistically independent reflectivity and additive noise, the maximum likelihood estimate of the reflectivity can be obtained by Lp‐norm deconvolution for a range of multivariate probability density functions of the reflectivity and the noise. The L∞‐norm corresponds to a uniform distribution, the L2‐norm to a Gaussian distribution, the L1‐norm to an exponential distribution and the L0‐norm to a variable that is sparsely distributed. For instance, if we assume sparse and spiky reflectivity and Gaussian noise with zero mean, the Lp‐norm deconvolution problem is solved best by minimizing the L0‐norm of the reflectivity and the L2‐norm of the noise. However, the L0‐norm is difficult to implement in an algorithm. From a practical point of view, the frequency‐domain mixed‐norm method that minimizes the L1norm of the reflectivity and the L2‐norm of the noise is the best alternative.

Lp‐norm deconvolution can be stated in both time and frequency‐domain. We show that both approaches are only equivalent for the case when the noise is minimized with the L2‐norm.

Finally, some Lp‐norm deconvolution methods are compared on synthetic and field data. For the practical examples, the wide range of possible Lp‐norm deconvolution methods is narrowed down to three methods with p= 1 and/or 2. Given the assumptions of sparsely distributed reflectivity and Gaussian noise, we conclude that the mixed L1norm (reflectivity) L2‐norm (noise) performs best. However, the problems inherent to single‐trace deconvolution techniques, for example the problem of generating spurious events, remain. For practical application, a greater problem is that only the main, well‐separated events are properly resolved.
IMPROVEMENT OF OBSERVATION ACCURACY OF THE LACOSTE‐ROMBERG (MODEL D) GRAVITY METER BY SUPPLEMENTARY INSTALLATION OF ELECTRONIC FEEDBACK1
Authors: CASTEN U. , HAUSSMANN U.
Published: April 2006

Abstract

Recent years have seen an increasing need for high‐precision gravity meters. A widely used and the most accurate one is the LaCoste‐Romberg, model D (LCR‐D) meter, equipped with electronic readout. According to the manual the reading accuracy is 5 μGal. A way of reducing most of the instrumental factors limiting the accuracy is the use of an electronic feedback system.

We have fitted the LCR‐D 34 with a Schnüll‐Röder‐Wenzel, model D (SRW‐D) feedback. After installation the readout voltage was calibrated, the instrumental behaviour tested, and the accuracy of the system determined. By repeat readings in the laboratory without moving the meter, the standard deviation for a single reading is better than 4 μGal in normal mode and better than 1 μGal in feedback mode. The accuracy of gravity differences ‐ this is usually observed in field practice ‐ is the mean value of the repeat errors of several sets of differences observed in a short time to avoid any corrections. This accuracy is better than 9 μGal in normal mode and better than 5 μGal in feedback mode. With this, the accuracy of a single reading becomes more than 6 μGal and more than 3 μGal, respectively.

As the described improvement of accuracy was found to be not as good as expected, additional improvements should centre on the use of electronic levels instead of the standard liquid ones.
ALIGNMENT OF NEAR‐SURFACE INCLUSIONS AND APPROPRIATE CRACK GEOMETRIES FOR GEOTHERMAL HOT‐DRY‐ROCK EXPERIMENTS1
Authors: CRAMPIN STUART
Published: April 2006

Abstract

Ubiquitous splitting of seismic shear‐waves indicates that most rocks in the upper half of the crust are pervaded by stress‐aligned fluid‐filled inclusions, called EDA‐cracks. These inclusions are expected to be aligned perpendicular to the minimum compressional stress by stress relationships similar to those aligning industrial hydraulic fractures. At depths where the overburden stress is sufficiently large (typically below a few hundred metres), this minimum stress is usually horizontal, so that the EDA‐cracks and hydraulic fractures are typically aligned vertically, striking parallel, or subparallel, to the direction of maximum compression. This is confirmed by the polarizations of the split shear‐waves along raypaths at depth in the crust. At the free surface, however, the vertical stress is zero (or approximately zero) and cracks (and hydraulic fractures) at shallow depths in intact rock tend to be horizontal. Thus, the directions of minimum stress, and the orientations of hydraulic fractures, are likely to swing through 90° near the surface of the Earth. Since the behaviour of cracks and stress is often crucial to drilling operations, the rotation of the crack‐ and stress‐geometry near‐surface has important implications, particularly for optimizing hydrocarbon production and geothermal reservoir management. Consequently, evidence gained from experiments, for example in hot‐dry‐rock geothermal heat extraction, in inappropriate crack geometries at shallow depths, may not be valid when applied to other crack‐ and stress‐geometries at depth in hot rock.
EFFECTS OF WELL CASING ON POTENTIAL FIELD MEASUREMENTS USING DOWNHOLE CURRENT SOURCES1
Authors: SCHENKEL C. J. , MORRISON H. F.
Published: April 2006

Abstract

A mathematical formulation for the electric potential from point current‐sources coaxial with a metal casing has been obtained. The excitation caused by the axial point‐sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially‐directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium.

This solution has been used to study the distribution of the potentials in a half‐space for a single current‐source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half‐space of 10‐2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point‐source 100 casing diameters beyond the end of the pipe. It appears that cross‐hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole‐to‐surface surveys are much more affected by the pipe. For a pipe‐source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion.
CONSTRUCTION OF COMPONENT MAPS FROM AEROMAGNETIC TOTAL FIELD ANOMALY MAPS1
Authors: PEDERSEN L. B. , RASMUSSEN T. M. , DYRELIUS D.
Published: April 2006

Abstract

Total field anomalies as defined from normal aeromagnetic surveys give good approximations of the anomalous components along the direction of the main geomagnetic field, which is generally much larger than the anomalous field. Using the relations between vertical and horizontal components of the field, the total field anomaly is related to any vertical or horizontal component and the corresponding horizontal and vertical derivatives. An example from the Siljan impact structure indicates that such directional filters may be applied to extract useful information from magnetic maps.
THE RESOLUTION POSSIBLE IN IMAGING WITH DIFFRACTED SEISMIC WAVES1
Authors: PHADKE SUHAS , KANASEWICH ERNEST R.
Published: April 2006

Abstract

The determination of the vertical and lateral extent of discontinuities is an important aspect of interpreting seismic reflection data. The Common Fault Point (CFP) stacking method appears to be promising in imaging discontinuities in acoustic impedance by making use of diffracted energy from a spatial array of receivers. The problems of vertical and lateral resolution in the method are most important when carrying out an interpretation.

Source signature, subsurface velocities and the depth of the discontinuity are the most important parameters affecting the resolution. We use, for a perfectly coherent source, the first derivative of the Gaussian function which is an antisymmetric band‐limited wavelet. Rayleigh's, Ricker's and Widess' criteria are also applicable to this wavelet. The limits of vertical and lateral resolution are illustrated by using a step fault and a dike model respectively. The vertical resolution of the CFP method is found to be of the order of λ/16 which is half the theoretically predicted value for a single receiver. The lateral resolution is still limited by the size of the Fresnel zone which depends upon the velocity, two‐way time and the dominant frequency of the wavelet. The resolution limits of the CFP method are compared with that of the CDP method, prestack migration and post‐stack migration. Obtaining high resolution with real data is limited by the extent to which it is possible to generate a coherent source or to simulate one during computer processing with before stack seismic data. The CFP method is an artificial intelligence approach to imaging diffracting points as it localizes parts of the structure that scatter acoustic waves.
MODELLING 1D WAVE PROPAGATION IN A SYSTEM OF ABSORBING LAYERS1
Authors: McGEE T. M.
Published: April 2006

Abstract

The purpose of this paper is to derive relationships useful for the analysis of shallow transmission and reflection seismic data. Since the effects of absorption cause such data to be non‐stationary, the derived results do not rely on frequency‐domain representations being independent of the time origin. Rather, results are expressed in the z‐domain and are suitable for implementation in the time domain. In order to give an unambiguous system of notation a classic approach to the problem of 1D wave propagation in a layered system is fully described. Absorption is included in a general but realistic way and the implications of representing it digitally are considered in detail. Computational efficiency is improved by grouping the layers in blocks of similar absorptive effect. The transmissivity and reflectivity of systems composed of such blocks are obtained and a dereverberation filter identified. The filter is described succinctly in terms of a non‐linear recursion relationship. The sequences obtained by convolving the filter with the transmissivity and reflectivity are discussed in detail. The results are illustrated by nominally realistic synthetic examples computed in the time domain.
APPLICATION OF THE PARTIAL KARHUNEN‐LOÈVE TRANSFORM TO SUPPRESS RANDOM NOISE IN SEISMIC SECTIONS1
Authors: AL‐YAHYA KAMAL M.
Published: April 2006

Abstract

The Karhunen‐Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero‐lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K‐L transform.
ELASTIC PARAMETER ESTIMATION BY COHERENCY OPTIMIZATION1
Authors: RESHEF MOSHE , LANDA EVGENY , RAVID TAMAR
Published: April 2006

Abstract

We present a method for estimating P‐ and S‐velocities within defined layers (macromodel), using only kinematic properties (i.e. traveltimes) of the wavefield. The method does not require identification of mixed‐mode events on prestack or post‐stack data. After obtaining a Vp‐depth model by coherency inversion, S‐velocities are determined by coherency optimization along computed traveltime curves for mixed‐mode events on prestack data. Since the method does not involve any dynamic wavefield computations, a simple ray‐tracing algorithm is used to solve the forward problem. The simplicity of the scheme, together with the ability to apply it locally, makes it highly suitable for interactive use. Results of this method may be used to detect Poisson's ratio anomalies within or between layers and may serve as an initial model for more complicated elastic inversion algorithms.
CONVERSION POINTS AND TRAVELTIMES OF CONVERTED WAVES IN PARALLEL DIPPING LAYERS1
Authors: TESSMER GISA , BEHLE ALFRED
Published: April 2006

Abstract

For converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio vp/vs. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration.

The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two‐term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates.
LONG‐OFFSET TRANSIENT EM SOUNDING NORTH OF THE RHINE‐RUHR COAL DISTRICT, GERMANY1
Authors: STEPHAN A. , SCHNIGGENFITTIG H. , STRACK K.‐M.
Published: April 2006

Abstract

During the past two decades electromagnetic methods have been increasingly applied to problems in hydrocarbon exploration. It has been shown that EM methods achieve satisfactory results which can be supplementary to results of the seismic method. We extend the application of the Long‐Offset Transient ElectroMagnetic Sounding (lotem) to exploration problems in the coal mining industry.

A survey was conducted north of the Rhine‐Ruhr coal district using a grounded dipole source and receivers laid out along several profile lines giving areal coverage. The strong noise from cultural as well as natural electromagnetic sources was reduced using prestack data processing techniques resulting in reliable data with a good signal‐to‐noise ratio. The interpretation is self‐consistent and matches the well logs and the geological information of the area quite well. The high station density permitted the mapping of the top of the Carboniferous formation to a depth of between 800 and 1000 m below surface.
STACKING OF P‐SV SEISMIC REFLECTION DATA USING DIP MOVEOUT1
Authors: DEN ROOIJEN HUUB P. G. M.
Published: April 2006

Abstract

The moveout of P‐SV mode‐converted seismic reflection events in a common‐midpoint gather is non‐hyperbolic. This is true even if the medium has constant P‐ and SV‐wave velocities. Furthermore, reflection‐point smear occurs even along horizontal reflectors. These effects reduce the resolution of the zero‐offset stack. In such a medium, the generalization of the dip moveout transformation to P‐SV data can be calculated analytically. The resulting P‐SV dip moveout operators solve the problem of reflection‐point smear, and image any reflector regardless of dip or depth. The viability of this technique is demonstrated on synthetic and field data.
INVERSION OF POST‐STACK SEISMIC DATA USING SIMULATED ANNEALING1
Authors: VESTERGAARD PETER D. , MOSEGAARD KLAUS
Published: April 2006

Abstract

Model‐based inversion of seismic reflection data is a global optimization problem when prior information is sparse. We investigate the use of an efficient, global, stochastic optimization method, that of simulated annealing, for determining the two‐way traveltimes and the reflection coefficients.

We exploit the advantage of an ensemble approach to the inversion of full‐scale target zones on 2D seismic sections.

In our ensemble approach, several copies of the model‐algorithm system are run in parallel. In this way, estimation of true ensemble statistics for the process is made possible, and improved annealing schedules can be produced.

It is shown that the method can produce reliable results efficiently in the 2D case, even when prior information is sparse.
WAVELET ESTIMATION USING THE MULTITAPER METHOD1
Authors: WALDEN A. T.
Published: April 2006

Abstract

An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well‐control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum‐phase assumption.

The construction of the minimum‐phase wavelet is critically dependent on the decay of the spectrum at the low‐frequency end. Traditional methods of cross‐spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side‐lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low‐frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side‐lobe leakage causes poor estimates of the low‐frequency decay, resulting in degraded wavelet estimates.

Thomson's multitaper method of cross‐spectral estimation which suffers little from side‐lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low‐frequency roll‐off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll‐off is only about 36 dB/oct. Thus the multitaper method gives a low‐frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi‐taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.
THE USE OF FORWARD‐ AND BACK‐SCATTERED P‐, S‐ AND CONVERTED WAVES IN CROSS‐BOREHOLE IMAGING1
Authors: BALCH A. H. , CHANG H. , HOFLAND G. S. , RANZINGER K. A. , ERDEMIR C.
Published: April 2006

Abstract

The principles of imaging, for example that of prestack migration, can be applied to cross‐borehole seismic geometry just as they can to surface seismic configurations. However, when using actual cross‐borehole data, a number of difficulties arise that are rarely or never encountered in imaging surface seismic data: discontinuities may reflect or diffract incident seismic waves in any direction. If a discontinuity lies between the lines of sources and receivers, forward‐scattered, or interwell, events may be recorded. If a discontinuity lies outside the interwell region, back‐scattered, or extra‐well, events may be recorded. Many angles of incidence are possible, and all possible reflected modes (P–P, P–S, S–P and S–S) are present, frequently in nearly equal proportions. The planes of the reflectors dip from 0 to ±90°.

In order to deal with these complexities we first separate propagation modes at the receiver borehole using both polarization and velocity. Next we compensate for phase distortion due to dispersion. Finally, and most importantly, we migrate or image the data in cross‐borehole common‐source gathers. To do this, a finite‐difference solution to the 2D scalar wave equation, using reverse time, for an arbitrary distribution of velocities, is used to project the separated, reflected‐diffracted wavefield back into the medium.

There are four reflection modes (P–P, P–S, S–P and S–S), so we can apply four different imaging conditions. The zones outside the boreholes as well as inside the boreholes can be imaged with these conditions.

These operations are repeated for each common‐source gather: each common‐source gather generates four partial images in each image space. This multiplicity of partial images can be stacked in various combinations to yield a final image of the subsurface.

Our experiments using solid (not fluid) physical models indicate that when these procedures are correctly applied, high quality cross‐borehole images can be obtained. These images appear with great clarity even though some of the weak diffractions causing diffraction images may be almost totally obscured by other high‐amplitude events on the raw data.
PSEUDOREFLECTION PROFILING METHOD: AN EFFICIENT COMPLEMENT TO CDP METHOD1
Authors: TSUTSUI TOMOKI
Published: April 2006

Abstract

A method for pseudoreflection profiling (PRP) is presented. By using transmission seismograms, this method produces time sections similar to those obtained using the common depth point (CDP) method.

Pseudoreflection profiles are obtained using the following procedure. Equivalent transmission responses at sites on soft deposits are derived by Wiener filter estimation using seismograms acquired on the sites and on the basement rock. These responses are substituted into the Claerbout‐Kunetz equation to obtain the pseudoreflection profiles.

A 3D subsurface model is produced when the PRP method is applied to explosion seismograms. The time sections thus obtained are consistent with those obtained using the CDP method in a neighbouring area. The maximum station interval for obtaining coherent profiles with this method is estimated to be one quarter of the wavelength of the transmitted waves.

This technique should be used in combination with another method such as the CDP method because it has two weak points: the velocity structure cannot be obtained directly and undesirable waves cannot be eliminated through processing.
SEPARATION OF REGIONAL AND RESIDUAL ANOMALIES BY LEAST‐SQUARES ORTHOGONAL POLYNOMIAL AND RELAXATION TECHNIQUES: A PERFORMANCE EVALUATION1
Authors: AGARWAL B. N. P. , SIVAJI CH.
Published: April 2006

Abstract

The performances of least‐squares orthogonal polynomial and relaxation techniques in the separation of regional and residual anomalies have been evaluated with a view to minimizing personal biasing. The advantage of orthogonal over nonorthogonal polynomials is their ability to estimate an optimum order of polynomial to represent the predominant regional trend in the data using an approximate 2D difference table, the Z‐matrix. The correlation coefficients between residuals of two consecutive orders also give the same result. In the relaxation technique, a linear trend is assumed within each cell of the mesh of a square grid. A set of such linear segments can approximate any complicated regional trend. The performances of these two techniques have been evaluated using simulated gravity anomalies produced by 2D and 3D complex regional structures superimposed on residual fields due to cylinders and prismatic bodies, as well as three field examples taken from the published literature. The analyses have revealed that the relaxation technique produces excellent results when an optimum polynomial order rather than an arbitrary fixed one is used for computing the boundary conditions along the periphery of the map. Analyses have revealed that such boundary conditions provide minimum distortion near the two ends of the profile.
THE COLLOCATION APPROACH TO THE INVERSION OF GRAVITY DATA1
Authors: BARZAGHI A. , GANDINO A. , SANSO F. , ZENUCCHINI C.
Published: April 2006

Abstract

Gravity data inversion can provide valuable information on the structure of the underlying distribution of mass.

The solution of the inversion of gravity data is an ill‐posed problem, and many methods have been proposed for solving it using various systematic techniques.

The method proposed here is a new approach based on the collocation principle, derived from the Wiener filtering and prediction theory.

The natural multiplicity of the solution of the inverse gravimetric problem can be overcome only by assuming a substantially simplified model, in this case a two‐layer model, i.e. with one separation surface and one density contrast only. The presence of gravity disturbance and/or outliers in the upper layer is also taken into account.

The basic idea of the method is to propagate the covariance structure of the depth function of the separation surface to the covariance structure of the gravity field measured on a reference plane.

This can be done since the gravity field produced by the layers is a functional (linearized) of the depth.

Furthermore, in this approach, it is possible to obtain the variance of the estimation error which indicates the precision of the computed solution.

The method has proved to be effective on simulated data, fulfilling the a priori hypotheses.

In real cases which display the required statistical homogeneity, good preliminary solutions, useful for a further quantitative interpretation, have also been derived.

A case study is discussed.
THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A POLARIZABLE SPHERE IN A CONDUCTING HALF SPACE1
Authors: LEE TERRY , THOMAS LINDSAY
Published: April 2006

Abstract

A polarizable sphere embedded in a conducting half‐space can give rise to negative voltage transients in a coincident‐loop time‐domain electromagnetic system. Such transients have been observed in field situations. Our results are obtained from a model in which the contributions of the host rock, the currents in the sphere, and the interaction between the sphere and the host rock are separated and superposed. This model uses approximations to the integral equation solutions rather than finite‐element or finite‐difference approximations, and so allows very rapid computation.

The theoretical demonstration suggests that interpretation of the negative voltage transients as a polarization response is valid, but more detailed interpretation of polarization properties may not be possible, because the superposition of the polarization response on the normal response depends strongly on the position of the target.
INTEGRATED INTERPRETATION OF MARINE ENGINEERING GEOLOGICAL AND GEOPHYSICAL DATA ON THE PRINCIPLES OF EXPERT SYSTEM TECHNOLOGY1
Authors: KOVALEVSKY E. V. , KHARCHENKO V. I.
Published: April 2006

Abstract

We describe an approach to the construction of an engineering geological expert system for identification of sub‐bottom soils in accordance with some predefined nomenclature. The following principles of integrated interpretation of engineering geophysical and geotechnical data are presented: Firstly, the transformation of physical data (compressional‐ and shear‐wave velocities, compressional‐wave attenuation coefficients, electrical conductivity, etc.) for each of the medium points into subjective probabilities for the soil belonging to each type listed in the nomenclature, and secondly, the extrapolation of local geotechnical data (primarily drilling data) to the surrounding space by means of diffusion of the initial membership function distribution, resulting in the same set of probabilities for soil types at each point in the medium under consideration. Aggregation of the fuzzy information obtained, sufficient for reaching a conclusion for most points in the medium, is carried out by means of Bayesian summation. An example is given of integrated interpretation of real data obtained from four different sources (compressional‐ and shear‐wave velocity sections Vp(x, z) and Vs(x, z), and two boreholes) related to the same profile.
A SEMBLANCE‐GUIDED MEDIAN FILTER1
Authors: REITER E. C. , TOKSOZ M. N. , PURDY G. M.
Published: April 2006

Abstract

Reiter, E.C., Toksoz, M.N. and Purdy, G.M. 1992. A semblance‐guided median filter. Geophysical Prospecting41, 15–41.

A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user‐specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well‐known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance.

This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal‐to‐noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal.

We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large‐offset ocean bottom hydrophone data to enhance weak refracted and post‐critically reflected energy.
SEISMIC RAY TRACING USING LINEAR TRAVELTIME INTERPOLATION1
Authors: ASAKAWA EIICHI , KAWANAKA TAKU
Published: April 2006

Abstract

A new ray‐tracing method called linear traveltime interpolation (LTI) is proposed. This method computes traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods.

The LTI method is formulated for a 2D cell model, and calculations of traveltimes and raypaths are carried out only on cell boundaries. Therefore a raypath is considered to be always straight in a cell with uniform velocity. This approach is suitable to tomography analysis.

The algorithm of LTI consists of two separate steps: step 1 calculates traveltimes on all cell boundaries; step 2 traces raypaths for all pairs of receivers and the shot.

A traveltime at an arbitrary point on a cell boundary is assumed to be linearly interpolated between traveltimes at the adjacent discrete points at which we calculate traveltimes. Fermat's principle is used as the criterion for choosing the correct traveltimes and raypaths from several candidates routinely.

The LTI method has been compared numerically with the shooting method and the finite‐difference method (FDM) of the eikonal equation. The results show that the LTI method has great advantages of high speed and high accuracy in the calculation of both traveltimes and raypaths. The LTI method can be regarded as an advanced version of the conventional FDM of the eikonal equation because the formulae of FDM are independently derived from LTI. In the process of derivation, it is shown theoretically that LTI is more accurate than FDM. Moreover in the LTI method, we can avoid the numerical instability that occurs in Vidale's method where the velocity changes abruptly.
A PHYSICAL MODEL STUDY OF SCATTERING OF WAVES BY ALIGNED CRACKS: COMPARISON BETWEEN EXPERIMENT AND THEORY1
Authors: ASS'AD J. M. , TATHAM R. H. , MCDONALD J. A. , KUSKY T. M. , JECH J.
Published: April 2006

Abstract

An approximation to plane‐wave propagation through a composite material is examined using a physical model with oriented but randomly distributed penny‐shaped rubber inclusions within an isotropic epoxy resin matrix. A pulse transmission method is used to determine velocities of shear and compressional waves as a function of angle of incidence and crack density. The experimental and theoretical results of Hudson were compared and limitations within the crack parameters used in this study have been determined. Results from both polarized shear waves (S1, S2) compare favourably with the theory for a composite with up to 7% crack density, but theory and experiment diverge at higher crack densities. On the other hand, compressional‐wave velocities at low crack densities (1% and 3%) compare favourably with the theory. It is also shown that the velocity ratio Vp/Vs for two extreme cases, i.e. propagation normal and parallel to the cracks, as a function of crack density and porosity, has a strong directional dependence.
ANISOTROPIC TRAVELTIME TOMOGRAPHY
Authors: MICHELENA R. J. , MUIR F. , HARRIS J. M.
Published: April 2006

Abstract

Velocity estimation technique using seismic data is often based on time/distance equations which are independent of direction, and even though we now know that many rocks are quite anisotropic, useful results have been obtained over the years from these isotropic estimates. Nevertheless, if velocities are significantly direction‐dependent, then the isotropic assumption may lead to serious structural interpretation errors. Additionally, information on angle‐dependence may lead to a better understanding of the lithology of the rocks under measurement. VSP and cross‐well data may each lack the necessary aperture to estimate more than two velocity parameters for each wave type, and if the data straddle a symmetry axis, then these may be usefully chosen to be the direct velocities (from time‐and‐distance measurements along the axis) and NMO velocities (from differential time‐offset measurements). These sets of two parameters define ellipses, and provide intermediate models for the variation of velocity with angle which can later be assembled and translated into estimates of the elastic moduli of the rocks under scrutiny.

If the aperture of the measurements is large enough e.g. we have access to both VSP and cross‐well data, we divide the procedure into two independent steps, first fitting best ellipses around one symmetry axis and then fitting another set around the orthogonal axis. These sets of four elliptical parameters are then combined into a new, double elliptical approximation. This approximation keeps the useful properties of elliptical anisotropy, in particular the simple relation between group and phase velocities which simplifies the route from the traveltimes measurements to the elastic constants of the medium.

The inversion proposed in this paper is a simple extension of well‐known isotropic schemes and it is conceptually identical for all wave types. Examples are shown to illustrate the application of the technique to cross‐well synthetic and field P‐wave data. The examples demonstrate three important points: (a) When velocity anisotropy is estimated by iterative techniques such as conjugate gradients, early termination of the iterations may produce artificial anisotropy. (b) Different components of the velocity are subject to different type of artifacts because of differences in ray coverage, (c) Even though most rocks do not have elliptical dispersion relations, our elliptical schemes represent a useful intermediate step in the full characterization of the elastic properties.
STUDY OF TRAVELTIME AND AMPLITUDE TIME‐LAPSE TOMOGRAPHY USING PHYSICAL MODEL DATA1
Authors: LEGGETT M. , GOULTY N. R. , KRAGH J. E.
Published: April 2006

Abstract

In seismic tomography the observed traveltimes or amplitudes of direct waves are inverted to obtain an estimate of seismic velocity or absorption of the section surveyed. There has been much recent interest in using cross‐well traveltime tomography to observe the progress of fluids injected into the reservoir rocks during enhanced oil recovery (EOR) processes. If repeated surveys are carried out, then EOR processes may be monitored over a period of time.

This paper describes the results of a simulated time‐lapse tomography experiment to image the flood zone in an EOR process. Two physical models were made out of epoxy resins to simulate an essentially plane‐layered sedimentary sequence containing a reservoir layer and simple geological structure. The models differed only in the reservoir layer, which was uniform in the ‘pre‐flood’ model and contained a flood zone of known geometry in the ‘post‐flood’ model. Data sets were acquired from each model using a cross‐well survey geometry. Traveltime and amplitude tomographic imaging techniques have been applied to these data in an attempt to locate the extent of the flood zone.

Traveltime tomography locates the flood zone quite accurately. Amplitude tomography shows the flood zone as a region of higher absorption, but does not image its boundaries as precisely. This is primarily because of multipathing and diffraction effects, which are not accounted for by the ray‐based techniques for inverting seismic amplitudes. Nevertheless, absorption tomograms could complement velocity tomograms in real, heterogeneous reservoirs because absorption and velocity respond differently to changes in liquid/gas saturations for reservoir rocks.