bluuebunny/crossref_metadata_2025 huggingface dataset:
ATTENUATION OF RANDOM NOISE BY 2‐D AND 3‐D CDP STACKING AND KIRCHHOFF MIGRATION*
Authors: KREY TH.C.
Published: April 2006

Three‐dimensional seismic surveys, in general, do not need the same high degree of CDP coverage as 2‐D surveys to achieve a certain signal‐to‐noise ratio after migration.

This can be shown theoretically for Kirchhoff migration and laterally uncorrelated noise. More precisely, there exists a formal relationship between the multiplicity of CDP coverage of a 3‐D survey and that of a 2‐D survey with the same signal‐to‐uncorrelated‐noise ratio. Frequency and aperture are parameters in the corresponding expression. Heuristically the relationship can be obtained by applying the concept of the Fresnel zone.

Though the mathematics in this paper refer to laterally uncorrelated noise, the underlying concepts can probably also be used for weakly correlated noise, e.g., for multiple reflections and for the low‐frequency remnants of surface waves.
IN SITU MEASUREMENTS OF SHEAR‐WAVE VELOCITY IN SEDIMENTS WITH HIGHER‐MODE RAYLEIGH WAVES*
Authors: GABRIELS P. , SNIEDER R. , NOLET G.
Published: April 2006

A seismic survey was carried out on a tidal flat in the SW‐Netherlands in order to determine shear‐wave velocities in sediments by means of higher‐mode Rayleigh waves. The dispersion properties of these Rayleigh waves were measured in the 2‐D amplitude spectrum–or f, k‐spectrum–and resulted in phase velocities for six different modes as a function of frequency (5–30 Hz). These observed phase velocities were inverted for a nine‐layer model for the shear‐wave velocity to a depth of 50 m.
THREE‐DIMENSIONAL KINEMATIC MIGRATION IN VARIABLE VELOCITY MEDIA*
Authors: WEN JING , McMECHAN G.A.
Published: April 2006

A three‐dimensional (3‐D) kinematic migration algorithm for media in which migration velocity varies linearly with depth is developed, implemented and tested. The algorithm is based on the concept that a single reflection or diffraction in a (zero‐ or finite‐offset) trace may have originated at any point on a constant traveltime surface within the Earth defined by the observed two‐way traveltime. The envelope of all such constant time surfaces, for all observed reflections and diffractions produced by one reflector, is the desired migrated 3‐D image. The optimal envelope position in depth is determined, beneath each point on a regular grid, by a statistical imaging condition; an incremental function of depth containing the number of constant time surfaces passing through that depth increment is cross‐correlated with a Gaussian function whose width is chosen to correspond to the vertical scale of the features of interest.

The numerical procedures are based on the observation that, in a medium in which velocity varies linearly with depth, ray segments are circular so traveltimes can be computed analytically. Also, traveltimes are independent of azimuth so the 3‐D problem can be collapsed into an equivalent 2‐D problem.

The algorithm is illustrated and tested by application to synthetic data and to scale‐model data from the Seismic Acoustics Laboratory at the University of Houston.
TRANSFORMATION OF DIPOLAR, WENNER AND TWO‐ELECTRODE CURVES TO SCHLUMBERGER APPARENT RESISTIVITY SOUNDING CURVES*
Authors: BANERJEE BUDDHADEB , SENGUPTA B. J.
Published: April 2006

A simple mathematical technique based on regressional analysis allows the transformation of dipolar, Wenner and two‐electrode apparent resistivity sounding curves to Schlumberger ones. The algorithm is suitable for a programmable pocket calculator and the accuracy is very high. This has been demonstrated by comparing Schlumberger master curves with transformations of master curves for the other configurations for the same model.
A SIMPLE METHOD OF INTERPRETATION OF RESISTIVITY SOUNDING DATA USING EXPONENTIAL APPROXIMATION OF THE KERNEL FUNCTION*
Authors: NIWAS SRI , ISRAIL M.
Published: April 2006

A simple unified equation of apparent resistivity for a general four‐electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge‐regression estimation method is used in the identification of layer parameters from the kernel function.
GEOPHYSICAL DETECTION OF MINERAL CONDUCTORS IN TROPICAL TERRAINS WITH TARGET CONDUCTORS PARTLY EMBEDDED IN THE CONDUCTIVE OVERBURDEN*
Authors: BARONGO J.O.
Published: April 2006

Ground geophysical methods were used in the greenstone belt of Western Kenya as follow‐up of an Input airborne electromagnetic survey. Observation and drilling results showed that the graphite and pyrite bodies, which constitute the main target conductors in the area, either outcrop or reach near to the ground surface. The drilling results further showed that the weathered layer is between 20 m and 60 m thick. Therefore the target conductors are partly embedded in this fairly conductive weathered layer and may be in galvanic contact with it. The geophysical methods were able to delineate the conductors. However, by virtue of the galvanic contact between the conductors and the conductive overburden, the profiles from the horizontal loop EM measurements are highly enhanced. This effect makes interpretation of the profiles possible at low frequencies but difficult at high frequencies. The interpreted EM results show that the target conductors appear shallow and less conductive at higher frequencies. Thus one must choose geophysical instruments and operating frequencies carefully to ensure good results in tropical terrains.
RESISTIVITY INVERSION WITH A PRIORI INFORMATION*
Authors: POUS J. , MARCUELLO A. , QUERALT P.
Published: April 2006

An inversion algorithm for interpreting electrical soundings based on a probabilistic treatment of the a priori information not only includes all the previous ones, but allows consideration of the constraints between the parameters. By introducing the a priori information, a unique solution among all the equivalent ones is obtained which is coherent with the geological background. Several examples dealing with the usual problems in the automatic interpretation of the electrical soundings illustrate the advantages of this algorithm. Good results are obtained with this method.
EXAMPLES OF ELECTROMAGNETIC PROSPECTING FOR KARST AND FAULT SYSTEMS*
Authors: VOGELSANG D.
Published: April 2006

Electromagnetic (EM) surveys using the horizontal coplanar loop (‘Slingram’) geometry have been successful in the location of karst aquifer systems in limestone areas of Germany and the Mediterranean. In spite of the rapid changes in shape and resistivity of karst pipes, correlations of significant EM minima can be made by reference to the main structural directions. The EM results have often been verified by drilling. EM prospecting need not be confined to limestone areas. It can be used on all hard rocks where faulting has created vertical zones with a resistivity contrast to the undisturbed rock.

EM siting of wells has proved successful in water‐supply schemes for several places. This method is now being applied as a routine, fast and low‐cost procedure to tap ground‐water resources in hard‐rock areas.
DECOMPOSITION AND INVERSION OF SEISMIC DATA–AN INSTANTANEOUS SLOWNESS APPROACH*
Authors: MILKEREIT B.
Published: April 2006

Interpretation techniques are presented that aim at the estimation of seismic velocities. The application of localized slant stacks, weighted by coherency, produces a decomposition of multichannel seismic data into single trace instantaneous slowness p(x, t) components. Colour displays support the interpretation of seismic data relevant to the near surface velocity structure. Since p(x, t) is directly related to stacking velocities and the depth of reflection, or bottoming points, in the subsurface, this data transformation provides a powerful tool for the inversion of reflection and refraction data.
THE INTERPRETATION OF TRAVELTIME FIELDS IN REFRACTION SEISMOLOGY*
Authors: BRÜCKL E.
Published: April 2006

We consider multiply covered traveltimes of first or later arrivals which are gathered along a refraction seismic profile. The two‐dimensional distribution of these traveltimes above a coordinate frame generated by the shotpoint axis and the geophone axis or by the common midpoint axis and the offset axis is named a traveltime field.

The application of the principle of reciprocity to the traveltime field implies that for each traveltime value with a negative offset there is a corresponding equal value with positive offset. In appendix A procedures are demonstrated which minimize the observational errors of traveltimes inherent in particular traveltime branches or complete common shotpoint sections.

The application of the principle of parallelism to an area of the traveltime field associated with a particular refractor can be formulated as a partial differential equation corresponding to the type of the vibrating string. The solution of this equation signifies that the two‐dimensional distribution of these traveltimes may be generated by the sum of two one‐dimensional functions which depend on the shotpoint coordinate and the geophone coordinate. Physically, these two functions may be interpreted as the mean traveltime branches of the reverse and the normal shot. In appendix B procedures are described which compute these two functions from real traveltime observations by a least‐squares fit.

The application of these regressed traveltime field data to known time‐to‐depth conversion methods is straightforward and more accurate and flexible than the use of individual traveltime branches. The wavefront method, the plus‐minus method, the generalized reciprocal method and a ray tracing method are considered in detail. A field example demonstrates the adjustment of regressed traveltime fields to observed traveltime data. A time‐to‐depth conversion is also demonstrated applying a ray tracing method.
WEIGHTED STACKING FOR ROCK PROPERTY ESTIMATION AND DETECTION OF GAS*
Authors: SMITH G.C. , GIDLOW P.M.
Published: April 2006

Amplitude versus offset concepts can be used to generate weighted stacking schemes (here called geo‐stack) which can be used in an otherwise standard seismic data processing sequence to display information about rock properties.

The Zoeppritz equations can be simplified and several different approximations appear in the literature. They describe the variation of P‐wave reflection coefficients with the angle of incidence of a P‐wave as a function of the P‐wave velocities, the S‐wave velocities and the densities above and below an interface.

Using a smooth, representative interval velocity model (from boreholes or velocity analyses) and assuming no dip, the angle of incidence can be found as a function of time and offset by iterative ray tracing. In particular, the angle of incidence can be computed for each sample in a normal moveout corrected CMP gather. The approximated Zoeppritz equation can then be fitted to the amplitudes of all the traces at each time sample of the gather, and certain rock properties can be estimated. The estimation of the rock properties is achieved by the application of time‐ and offset‐variant weights to the data samples before stacking. The properties which can be displayed by geo‐stack are: P‐wave reflectivity (or true zero‐offset reflectivity), S‐wave reflectivity, and the reflectivity of P‐wave velocity divided by S‐wave velocity (or ‘pseudo‐Poisson's ratio reflectivity’). If assumptions are made about the relation between P‐wave velocity and S‐wave velocity for water‐bearing clastic silicate rocks, then it is possible to create a display which highlights the presence of gas.
ENGINEERING GEOPHYSICAL STUDIES OF THE LOVIISA NUCLEAR POWER PLANT SITE, FINLAND*
Authors: ROUHIAINEN P.J.
Published: April 2006

Field studies have been performed in the power plant area of Loviisa in southern Finland to evaluate the suitability of the local bedrock for disposal of low‐level and intermediate‐level reactor wastes. The aim of the borehole geophysical studies was to evaluate the geometry and properties of fracture zones in relatively homogeneous granite.

Of the single‐hole methods, the dipmeter method was used to determine the orientation of individual fractures. The sonic log was used to evaluate the openness (width or thickness) of fractures. Cross‐hole methods such as the seismic and the mise‐à‐la‐masse method were used to determine the geometry and continuity of fractured zones between boreholes.

It was, in general, impossible to evaluate the continuity of single fractures. However, fracture sets can be identified based on the dipmeter data. The continuity of fracture zones can be evaluated with the combined results of single‐ and cross‐hole methods.
FORWARD MODELLING FOR FREQUENCY DOMAIN MARINE ELECTROMAGNETIC SYSTEMS*
Authors: GOLDMAN M.
Published: April 2006

An algorithm for the accurate evaluation of rapidly oscillating integrals is described. The method is based on deformation of the integration path into the complex plane of the integration variable. Numerical integration is then carried out along appropriate cuts where the oscillating factor is transformed to the decaying factor. Contrary to standard methods, the proposed technique permits accurate evaluation of numerically divergent integrals.

The algorithm is especially useful in forward modelling for high‐frequency electromagnetic methods and, in particular, for the new marine electromagnetic system based on measuring signals on the sea bottom at high induction numbers.

Results of calculations using both the proposed and standard methods are compared with available analytical solutions.
SIGNAL ADJUSTMENT OF VIBROSEIS AND IMPULSIVE SOURCE DATA*
Authors: BRÖTZ R. , MARSCHALL R. , KNECHT M.
Published: April 2006

Abstract

In certain areas continuous Vibroseis profiling is not possible due to varying terrain conditions. Impulsive sources can be used to maintain continuous coverage. While this technique keeps the coverage at the desired level, for the processing of the actual data there is the problem of using different sources resulting in different source wavelets. In addition, the effect of the free surface is different for these two energy sources.

The approach to these problems consists of a minimum‐phase transformation of the two‐sided Vibroseis data by removal of the anticipation component of the autocorrelation of the filtered sweep and a minimum‐phase transformation of the impulsive source data by replacement of the recording filter operator with its minimum‐phase correspondent. Therefore, after this transformation, both datasets show causal wavelets and a conventional deconvolution (spike or predictive) may be used. After stacking, a zero‐phase transformation can be performed resulting in traces well suited for computing pseudo‐acoustic impedance logs or for application of complex seismic trace analysis. The solution is also applicable to pure Vibroseis data, thereby eliminating the need for a special Vibroseis deconvolution.

The processing steps described above are demonstrated on synthetic and actual data. The transformation operators used are two‐sided recursive (TSR) shaping filters.

After application of the above adjustment procedure, remaining signal distortions can be removed by modifying only the phase spectrum or both the amplitude and phase spectra. It can be shown that an arbitrary distortion defined in the frequency domain, i.e., a distortion of the amplitude and phase spectrum, is noticeable in the time section as a two‐sided signal.
THE SPECTRAL FUNCTION OF A VERTICALLY INHOMOGENEOUS MEDIUM1
Authors: URSIN B.
Published: April 2006

Elastic, acoustic and electromagnetic waves in media consisting of vertically inhomogeneous layers are considered in a common formulation. The spectral function of a vertically inhomogeneous medium is the downward energy flux due to an impulsive source at the top of the first layer. A propagation‐invariant form is used to derive several identities for the reflection and transmission matrices. When the top layer is bounded by a free surface, one of the expressions reduces to a formula derived by Kunetz for the one‐dimensional wave equation.

A source radiating upwards and downwards gives a discontinuity in the propagation‐invariant form which is equal to the source energy. A new formula is derived for when the source is located just beneath the top interface of the layers.
A NEW APPROACH FOR DERIVING PSEUDOVELOCITY LOGS FROM RESISTIVITY LOGS1
Authors: DOS SANTOS W. L. BRITO , ULRYCH T. J. , DE LIMA O. A. L.
Published: April 2006

This paper describes a method of generating pseudovelocity logs using measurements of electrical resistivity. A theoretical relation between electrical resistivity and transit time, which is applicable to a wide range of lithologies, has been developed. The application of this relation using a method which defines lithoresistivity zones as lithological intervals related to the same formation and showing small resistivity variations, has been tested in the Recôncavo sedimentary basin in Bahia, Brazil. A comparison of derived pseudovelocity logs with actual sonic logs for five wells whows the validity of the present approach.
CRUSTAL REFLECTIVITY PATTERN AND ITS RELATION TO GEOLOGICAL PROVINCES1
Authors: TRAPPE H. , WEVER TH. , MEISSNER R.
Published: April 2006

The statistical treatment of deep seismic reflections from several different geological units has resulted in different reflectivity histograms. Reflectivity in old and cold shields differs significantly from that in younger, warmer areas. In the shields reflectivity is generally poor and concentrated in the upper crust whilst Caledonian and Variscan areas show strong reflecting lamellae in their lower crust. Also the length of the reflecting elements varies with age and heat flow. The lower crust in young areas is a zone of a strong viscosity minimum as derived from model studies with a temperature dependent rheology. The subhorizontal reflecting lamellae in the lower crust are considered to have been created in a large‐scale high‐temperature, low‐viscosity ordering process whose remnants are still preserved today. Local‐scale differences of reflectivity histograms define certain subprovinces which can be distinguished by their specific patterns.
ENERGY‐INTERACTION: THE LONG‐RANGE INTERACTION OF SEISMIC SOURCES1
Authors: LAWS R. , PARKES G. , HATTON L.
Published: April 2006

The quantity of energy that is radiated as sound by marine seismic sources is examined. When more than one source is used, the total radiated acoustic energy depends on the separation of the sources and is not constant, even when the separation is sufficiently large that the individual signatures are substantially unaffected. We believe that this long‐range interaction has not been described before in the literature and have called it energy‐interaction.

The existence of energy‐interaction is demonstrated experimentally for airguns. In. the experiment presented, the acoustic output is more than doubled because of energy‐interaction.

Two methods are described for computing the energy of the wavefield of an array of sources. One method is simple and direct; the energy that is radiated into the far field is calculated by integrating the directivity pattern over all directions. The other method finds the energy that is radiated into the near field. Because the medium is assumed lossless, these two energies are the same. Although the near‐field method is conceptually more difficult, it is faster, more accurate and provides a more detailed description of the energy budget.
SEISMIC AND ELECTRICAL PROPERTIES OF UNCONSOLIDATED PERMAFROST1
Authors: KING M. S. , ZIMMERMAN R. W. , CORWIN R. F.
Published: April 2006

A model has been developed to relate the velocities of acoustic waves Vp and Vs in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave‐scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts Vp and Vs to be decreasing functions of both the porosity and the water‐to‐ice ratio. The theory has been applied to laboratory measurements of Vp and Vs in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples.

Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.
THE MAXIMUM ENTROPY APPROACH TO THE INVERSION OF ONE‐DIMENSIONAL SEISMOGRAMS1
Authors: RIETSCH E.
Published: April 2006

Determination of impedance or velocity from a stacked seismic trace generally suffers from noise and the fact that seismic data are bandlimited. These deficiencies can frequently be alleviated by ancillary information which is often expressed more naturally in terms of probabilities than in the form of equations or inequalities.

In such a situation information theory can be used to include ‘soft’information in the inversion process. The vehicle used for this purpose is the Maximum Entropy (ME) principle. The basic idea is that a prior probability distribution (pd) of the unknown parameter(s) or function(s) is converted into a posterior pd which has a larger entropy than any other pd which also accounts for the information. Since providing new information generally lowers the entropy, this means that the ME pd is as non‐committal as possible with regard to information which is not (yet) available. If the information used is correct, then the ME pd cannot be contradicted by new, also correct, data and thus represents a conservative solution to the inverse problem.

In the actual implementation, the final result is, generally, not the pd itself (which may be quite broad) but rather the expectation values of the desired parameter(s) or function(s).

A general problem of the ME approach is the need for a prior pd for the parameter(s) to be estimated. The approach used here for the velocity is based on an invariance criterion, which ensures that the result is the same whether velocity or slowness is estimated. Unfortunately, this criterion does not provide a unique prior pd but rather a class of functions from which a suitable one must be selected with the help of other considerations.
DESIGN OF MODELS FOR ELECTROMAGNETIC SCALE MODELLING1
Authors: CHAKRIDI R. , CHOUTEAU M.
Published: April 2006

Electromagnetic scale modelling for most conductors encountered in prospecting requires models of conductivity in the range 10‐1000 S/m. A polyester composite filled with aluminium fillers is used to design the required materials. The fillers are chosen with a high aspect ratio to achieve the desired conductivities without altering mechanical properties. The design process, consisting of a chemical reaction, is simple, repeatable and easy to realize in a geophysical laboratory.

The conductivity of the designed material is estimated by an inductive method based upon the variation of the quality factor of a coil in which the samples are inserted. This method is much less influenced by the distribution and orientation of fillers in the resin matrix than a galvanic method.

The conductivities obtained fill the major part of the interval 10‐1000 S/m without requiring unreasonable mixing ratios. The homogeneity of the material was tested and the anisotropy was low at high conductivities. The electrical properties do not vary with time in free air or when immersed in salt water.

We propose standard curves giving conductivities of composites filled with aluminium fibres and flakes. A large cylindrical model of fixed resin‐to‐filler ratio was made to show the capability of the technique to produce models of useful size. Its measured conductivity agrees well with the expected conductivity from the established standard curves. A scale modelling experiment with the horizontal loop technique was carried out over a horizontal thin sheet made of the material, and again the conductivity obtained from the results agrees reasonably well with the expected value.

The noted difference between the inductively and galvanically measured conductivities of the proposed material presently restricts the use of the technique to EM scale experiments for which the host rock is considered very resistive.
PHYSICAL PROPERTIES OF SYNTHETIC SANDSTONE ROCKS1
Authors: ALMOSSAWI H. I. H.
Published: April 2006

A novel process is used to coat glass spheres with a polymerizing thermo‐setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin‐coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.
THE TIME‐DOMAIN ELECTROMAGNETIC RESPONSE OF POLARIZABLE BODIES: AN APPROXIMATE CONVOLUTION ALGORITHM1
Authors: SMITH R. S. , WALKER P. W. , POLZER B. D. , WEST G. F.
Published: April 2006

It is now believed that the negative transients observed in coincident‐loop transient electromagnetic (TEM) measurements are caused by polarizable bodies (bodies whose conductivity increases as a function of frequency). Ordinarily the TEM response of polarizable bodies is obtained by calculating the frequency‐domain response at many frequencies and transforming it to the time domain via Fourier, Laplace or Hankel transforms. This is normally a computationally laborious task. However, for some simple non‐polarizable bodies the time‐domain response is analytical and can be computed easily. When these simple bodies are weakly polarizable an approximate response can be obtained by convolving the easily‐calculated, non‐polarizable response with the impulse response of the polarization. The approximate response is found to be very similar to the exact response for the polarizabilities normally seen in geological materials.
APPLICATION OF PETROPHYSICAL MEASUREMENTS TO THE PREDICTION OF SEISMIC RESPONSES OF DIFFERING LITHOLOGYOR PORE FLUIDS1
Authors: RAFISON B. J.
Published: April 2006

Determination of petrography and pore fluid content is an ultimate goal of an integrated seismic‐petrophysical study. For lack of a general inversion technique, forward modelling is useful in studying the relations between lithology, stratigraphy, pore fluid content and the seismic response. This report describes a study of two clastic sequences in Utah, from which 32 rock samples were analysed. A detailed petrographic study was done. Laboratory measurements were made of ultrasonic compressional‐ and shear‐wave velocity as a function of pressure. We computed the velocities at seismic frequencies for the samples when dry, over‐pressured, brine saturated, and oil saturated. The velocities were sensitive to the porosity, carbonate cementation and the depositional facies. We generated velocity profiles for hypothetical reservoirs for a range of saturation states. The velocity profiles were used to generate synthetic seismic shot gathers to study the seismic response of these clastic reservoirs. The fluid‐saturation strongly affects the seismic respone, as does the presence of a coal seam. An amplitude change with offset is often observed. However, stratigraphy appears to have a stronger effect on the seismic response.
TWO‐PASS 3D MIGRATION AND LINEARIZED INVERSION IN THE (x, t)‐DOMAIN1
Authors: JAKUBOWICZ H. , MILLER D.
Published: April 2006

Abstract

3D Kirchhoff migration and acoustic Born inversion of zero‐offset seismic data in a constant‐velocity medium can be uniformly factored as a cascade of two 2D diffraction integrals. The formal argument is based on a straightforward implementation of the original time‐domain approach of Gibson, Larner and Levin. The factorization differs from the factorization described by Jakubowicz and Levin in omitting all time‐dependent filters from the 2D operators in favour of ID filtrations performed as a preprocess and a postprocess.
SEISMIC MIGRATION IN ELLIPTICALLY ANISOTROPIC MEDIA1
Authors: VERWEST BRUCE J.
Published: April 2006

Abstract

The study of wave propagation in media with elliptical velocity anisotropy shows that seismic energy is focused according to the horizontal component of the velocity field while the vertical component controls the time‐to‐depth relation. This implies that the vertical component cannot be determined from surface seismic velocity analysis but must be obtained using borehole or regional geological information. Both components of the velocity field are required to produce a correctly focused depth image. A paraxial wave equation is developed for elliptical anisotropic wave propagation which can be used for modelling or migration. This equation is then transformed by a change of variable to a second paraxial equation which only depends on one effective velocity field. A complete anisotropic depth migration using this transformed equation involves an imaging step followed by a depth stretching operation. This allows an approximate separation or splitting of the focusing and depth conversion steps of depth migration allowing a different velocity model to be used for each step. This split anisotropic depth migration produces a more accurate result than that obtained by a time migration using the horizontal velocity field followed by an image‐ray depth conversion using the vertical velocity field. The results are also more accurate than isotropic depth migration and yield accurate imaging in depth as long as the lateral variations in the anisotropy are slow.
Q‐LOG DETERMINATION ON DOWNGOING WAVELETS AND TUBE WAVE ANALYSIS IN VERTICAL SEISMIC PROFILES1
Authors: MARI J. L.
Published: April 2006

Seismic attenuation introduces modifications in the wavelet shape in vertical seismic profiles. These modifications can be quantified by measuring particular signal attributes such as rise‐time, period and shape index. Use of signal attributes leads to estimations of a seismic‐attenuation log (Q‐log).

To obtain accurate signal attributes it is important to minimize noise influence and eliminate local interference between upgoing and downgoing waves at each probe location. When tube waves are present it is necessary to eliminate them before performing separation of upgoing and downgoing events. We used a trace‐by‐trace Wiener filter to minimize the influence of tube waves. The separation of upgoing and downgoing waves was then performed in the frequency domain using a trace‐pair filter.

We used three possible methods based on signal attribute measurements to obtain g‐log from the extracted downgoing wavefield. The first one uses a minimum phasing filter and the arrival time of the first extremum. The two other methods determine the Q‐factor from simple relations between the amplitudes of the first extrema and the pseudo‐periods of the down‐going wavelet.

The relations determined between a signal attribute and traveltime over quality factor were then calibrated using field source signature and constant‐Q models computed by Ganley's method.

Q‐logs thus obtained from real data are discussed and compared with geological information, specifically at reservoir level.

Analysis of the tube wave arrivals at the level of the reservoir showed a tube wave attenuation that could not be explained by simple transmission effects. There was also a loss of signal coherence. This could be interpreted as tube wave diffusion in the porous reservoir, followed by dispersion. If this interpretation can be verified, tube wave analysis could lead to further characterization of porous permeable zones.
DETECTION OF LATERAL VARIATIONS IN GEOLOGICAL STRUCTURES USING ELECTRICAL RESISTIVITY GRADIENT PROFILING1
Authors: SHETTIGARA V. K. , ADAMS W. M.
Published: April 2006

Hydrogeological problems which involve the determination of lateral variations in structures or physical properties may be solved with electrical resistivity gradient profiling if there are significant variations in electrical resistivity, spatially or temporally. The method is explained, evaluated for sensitivity, compared with other methods, and applied to the location of volcanic dike zones that are impounding an anomalous water body near Schofield, Oahu, Hawaii. From the electrical soundings and other independent data, the lateral positions of the boundaries have been refined and their nature estimated.
3D ELECTROMAGNETIC INVERSION USING INTEGRAL EQUATIONS1
Authors: EATON PERRY A.
Published: April 2006

Utilizing electromagnetic data in geophysical exploration work is difficult when measured responses are complicated by the effects of 3D structures. 1D and 2D models may not be capable of accurately simulating the physical processes that contribute to a measured response. 3D conductive‐host modelling is difficult, costly and time‐consuming. Using a 3D inverse procedure it is possible to automate the interpretation of controlled‐source electromagnetic data. This procedure uses an inverse formulation based on frequency‐domain, volume integral equations and a pulse‐basis representation for the internal electrical field and anomalous conductivity. Beginning with an initial model composed of a 3D inhomogeneous region residing in a laterally homogeneous (layered‐earth) geoelectrical section, iterative least‐squares algorithms are used to refine the geometry and the conductivity of the inhomogeneity. This novel approach for 3D electromagnetic interpretation yields a reliable and stable inverse solution provided constraints on how much the variable can change at each iteration are incorporated. Integral‐equation‐based inverse formulations that do not correctly address the non‐linearity of this inverse problem may have poor convergence properties, particularly when dealing with the high conductivity contrasts that are typical of many exploration problems.

While problems associated with contamination of the data by random noise and non‐uniqueness of solutions do not usually influence the inverse solution in an adverse manner, problems associated with model inadequacy and errors in an assumed background conductivity structure can produce undesirable effects.
SPONTANEOUS POTENTIALS AND RESISTIVITY SURVEYS APPLIED TO HYDROGEOLOGY IN A VOLCANIC AREA: CASE HISTORY OF THE CHAÎNE DES PUYS (PUY‐DE‐DÔME, FRANCE)1
Authors: FOURNIER CLAUDE
Published: April 2006

Two geophysical methods [resistivity soundings and spontaneous potentials (SP)] are used to investigate aquifers in the Quaternary volcanic formations of the Chaîne des Puys (France). The interpretation of the resistivity soundings required a specific work of determination of the resistivity of the formations concerned. The basement topography, characterized by axial horst and graben structures and perpendicular palaeovalleys, was revealed. SP was developed experimentally in the field and theoretically. It is shown that the SP anomalies can be considered as double‐layer potentials, with their source on the aquifers' interfaces. The most significant of them is the water table, which creates an SP anomaly of similar but inverted form. SP anomalies due to flows in unconfined aquifers, in palaeovalleys, and in volcanic ranges are computed and compared with the observed ones. These two methods have determined the extent and the boundary conditions of the different hydrogeological basins and have determined the major drainage axes and the groundwater flow pattern.
INVERSION OF MAGNETOTELLURIC DATA: A NON‐LINEAR LEAST‐SQUARES APPROACH1
Authors: PEDERSEN L. B. , RASMUSSEN T. M.
Published: April 2006

Abstract

The inverse problem of magnetotellurics over a horizontally stratified earth is described, with emphasis on practical application. The inversion is divided into basically two steps. The construction of some best solution, and the analysis of that solution with regard to uncertainty and complexity. For the construction of best solutions a robust non‐linear solver was developed, and for the estimation of parameter errors a modified eigenvalue‐eigenvector analysis is performed to better describe non‐linear effects. The choice of the number of layers is shown to be intimately connected with the structure of data errors and the misfit between model and data. An example from the Siljan impact structure in Sweden illustrates the power of the technique.
MODEL‐BASED TRANSFORMATIONS OF COMMON MIDPOINT GATHERS1
Authors: NÆSS O. E.
Published: April 2006

A method for transforming Normal Moveout corrected CMP‐gathers is proposed. The method is based upon the availability of a model of the CMP‐gather. However, the transformation can be performed with any degree of accuracy in the model. Ideally the employed model should be a synthesis of all available a priori information about the particular data set.

Mathematically the transformation is performed as follows. The CMP‐gather is considered to be a matrix. This matrix is first decomposed into a set of submatrices of the same dimensions. Each submatrix consists of non‐zero elements or samples with the same relative amount of noise. By reducing each of these submatrices to a vector (a trace) we get a new set of traces. This set then represents the transformed CMP‐gather.

The purpose of the transformation is to organize the CMP data in a form which makes it easier both to analyse the noise distribution and to take the necessary steps to improve the signal‐to‐noise ratio at the stacking stage. In principle the method incorporates the exploitation of multichannel recordings with the use of models. Several examples of transformed gathers and their applications to the improvement of real seismic data are shown.
A SIMPLE EFFICIENT METHOD OF DIP‐MOVEOUT CORRECTION1
Authors: JAKUBOWICZ H.
Published: April 2006

Abstract

Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis‐stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non‐zero‐offset seismic data after NMO to true zero‐offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post‐stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack.

In this paper we consider the frequency‐wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip‐dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.
INVERSE THEORY APPLIED TO MULTI‐SOURCE CROSS‐HOLE TOMOGRAPHY.
Authors: PRATT R. GERHARD , WORTHINGTON M. H.
Published: April 2006

Abstract

Frequency‐domain methods are well suited to the imaging of wide‐aperture cross‐hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source‐receiver geometries, are overcome by applying inverse techniques that operate in the frequency‐space domain.

In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency‐domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite‐difference equations to be factored in‐place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions.

Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non‐linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non‐linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time‐lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.
THE OPTIMUM GATE LENGTH FOR THE TIME‐VARYING DECONVOLUTION OPERATOR1
Authors: DIMRI VIJAY P. , SRIVASTAVA KIRTI
Published: April 2006

Abstract

The time‐varying deconvolution operator designed by dividing time‐varying sequence has been extended to include an optimal division of the input data. A numerical example illustrates that the error energy is less in the case of optimally divided input in comparison with arbitrary division.
3D AND 2½ D MODELLING OF GRAVITY ANOMALIES WITH VARIABLE DENSITY CONTRAST1
Authors: RAO D. BHASKARA , PRAKASH M. J. , BABU N. RAMESH
Published: April 2006

Abstract

The decrease of density contrast in sedimentary basins may be approximated by a quadratic function. A sedimentary basin may be viewed as a number of prisms placed in juxtaposition. Equations in closed form for the gravity anomalies of 3D and 2½ D prismatic models are derived. Approximate equations for these models are also derived for rapid calculations. Efficient methods are developed for anomaly calculation by an appropriate use of the exact and approximate equations, and hence, for 3D and 2½ D modelling. The depths to the basement are adjusted iteratively by comparing the calculated anomalies with the observed anomalies. These methods are applied for analysis of the residual anomaly map of the Los Angeles Basin, California.
METHODS FOR CALCULATING FRÉCHET DERIVATIVES AND SENSITIVITIES FOR THE NON‐LINEAR INVERSE PROBLEM: A COMPARATIVE STUDY1
Authors: McGILLIVRAY P. R. , OLDENBURG D. W.
Published: April 2006

Abstract

A fundamental step in the solution of most non‐linear inverse problems is to establish a relationship between changes in a proposed model and resulting changes in the forward modelled data. Once this relationship has been established, it becomes possible to refine an initial model to obtain an improved fit to the observed data. In a linearized analysis, the Fréchet derivative is the connecting link between changes in the model and changes in the data. In some simple cases an analytic expression for the Fréchet derivative may be derived. In this paper we present three techniques to accomplish this and illustrate them by computing the Fréchet derivative for the ID resistivity problem. For more complicated problems, where it is not possible to obtain an expression for the Fréchet derivative, it is necessary to parameterize the model and solve numerically for the sensitivities ‐ partial derivatives of the data with respect to model parameters. The standard perturbation method for computing first‐order sensitivities is discussed and compared to the more efficient sensitivity‐equation and adjoint‐equation methods. Extensions to allow for the calculation of higher order, directional and objective function sensitivities are also presented. Finally, the application of these various techniques is illustrated for both the 1D and 2D resistivity problems.
A FAST ALGORITHM FOR THE COMPUTATION OF RADON TRANSFORMS1
Authors: HANEVELD C. J. , HERMAN G. C.
Published: April 2006

Abstract

A fast algorithm is presented for numerical evaluation of forward and inverse Radon transforms. The algorithm does not perform exact one‐to‐one mapping as the discrete Fourier transform but, due to the use of band‐limited basis functions, it is robust and sufficiently accurate for seismic applications. By rewriting the transform as a convolution, a computational speed is obtained similar to the speed of the 2D fast Fourier transform.
ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES1
Authors: TSINGAS C. , VAFIDIS A. , KANASEWICH E. R.
Published: April 2006

Abstract

When treating the forward full waveform case, a fast and accurate algorithm for modelling seismic wave propagation in anisotropic inhomogeneous media is of considerable value in current exploration seismology. Synthetic seismograms were computed for P‐SV wave propagation in transversely isotropic media. Among the various techniques available for seismic modelling, the finite‐difference method possesses both the power and flexibility to model wave propagation accurately in anisotropic inhomogeneous media bounded by irregular interfaces. We have developed a fast high‐order vectorized finite‐difference algorithm adapted for the vector supercomputer. The algorithm is based on the fourth‐order accurate MacCormack‐type splitting scheme. Solving the equivalent first‐order hyperbolic system of equations, instead of the second‐order wave equation, avoids computation of the spatial derivatives of the medium's anisotropic elastic parameters. Examples indicate that anisotropy plays an important role in modelling the kinematic and the dynamic properties of the wave propagation and should be taken into account when necessary.
SEISMIC CHARACTER MAPPING OVER RESERVOIR INTERVALS1
Authors: LENDZIONOWSKI V. , WALDEN A. T. , WHITE R. E.
Published: April 2006

Abstract

This paper presents some results from an investigation into the utility of pattern recognition methods in seismic interpretation. The seismic instantaneous attributes of amplitude, phase and frequency provide a way of quantifying the character of a simple reflection. Measures of character can be developed from cross‐plots and cluster analysis of these attributes. It is demonstrated that such seismic character can produce better‐defined maps than a single attribute. These procedures can be extended to attributes derived from seismic trace segments, such as trace energy and centre frequency, and to multitrace attributes, but more effort is then needed to analyse the attributes and search out useful ones.

An introduction is given to projection pursuit which has proved a useful exploratory tool for the anlysis of attribute relationships.

It is important to stress that pattern recognition techniques simply help bring relationships and patterns in the data to the attention of the interpreter and the most persistent problem in applying these techniques is the evaluation of potentially interesting patterns. The decision on what use can be made of them is highly interpretive and their calibration is difficult. Well control is vital but it normally allows only very limited supervision of a seismic classifier. An example is presented to illustrate these problems.