bluuebunny/crossref_metadata_2025 huggingface dataset:
τ‐p SEISMIC DATA FOR VISCOELASTIC MEDIA ‐ PART 2: LINEARIZED INVERSION1
Authors: MARTINEZ RUBEN D. , McMECHAN GEORGE A.
Published: April 2006

Abstract

An approach to extraction of viscoelastic parameters from seismic data is implemented and succesfully tested. Viscoelastic inversion is performed using adaptive damping factors to control the sensitivity of the viscoelastic parameters in relation to the τ‐p seismic data. A priori information is incorporated through the damping factors as standard deviations of the data and of the viscoelastic model parameters. The stability of the inversion process is controlled by the variation of the damping factors as a function of the residual errors and parameter updates at each iteration.

Tests on synthetic and real data show that P‐ and S‐wave quality factors, Qp and Qs, in addition to P‐ and S‐wave velocities and density Cp, Cs and p, can be extracted from τ‐p seismic information. Singular value decomposition analysis demonstrates that estimated Qp and Qs values are more affected by the presence of data inaccuracies and noise than are those of Cp and p. Cs and Qs are not uniquely recovered due to the limited contribution of P‐S converted waves.

Knowledge of the viscoelastic parameters is of particular importance in accurately describing petrophysical properties of rocks and pore fluids existing in the subsurface; this is demonstrated with real data from the Gulf of Mexico.
COMPARISON OF SIGNAL PROCESSING TECHNIQUES FOR ESTIMATING THE EFFECTS OF ANISOTROPY1
Authors: MACBETH COLIN , CRAMPIN STUART
Published: April 2006

Abstract

Three‐component recordings of shear‐waves in exploration surveys provide an opportunity to measure crustal anisotropy, which may be important in estimating the geometrical and physical parameters of reservoir rocks. VSPs are particularly important for this purpose as they are less subject to the complex interactions of the shear wavefield with the free surface. The first stage in characterizing the subsurface anisotropy requires that the distinctive phenomenon of shear‐wave splitting must be examined for every arrival at each geo‐phone. This effect may be defined by two parameters: the polarization of the leading shear‐wave and the time‐delay between corresponding split shear‐waves. A variety of techniques have been designed to estimate these parameters of shear‐wave splitting. Here, we classify the published techniques into four main categories and review their properties. Representative procedures from each group are applied to a common synthetic data set contaminated with signal‐generated noise. The results allow some general statements to be made about the utility of these methods for processing shear‐waves in VSP data.
JOINT INVERSION OF SEISMIC AND GEOELECTRIC DATA RECORDED IN AN UNDERGROUND COAL MINE1
Authors: DOBRÓKA M. , GYULAI Á. , ORMOS T. , CSÓKÁS J. , DRESEN L.
Published: April 2006

Abstract

Until the present time the ‘ rock‐coal‐rock’ layer sequence and offsets in coal‐seams in underground coal mines have been detected with the aid of seismic waves and geoelectric measurements. In order to determine the geometrical and petrophysical parameters of the coal‐seam situation, the data recorded using seismic and geoelectric methods have been inverted independently. In consequence, the inversion of partially inaccurate data resulted in a certain degree of ambiguity. This paper presents the first results of a joint inversion scheme to process underground vertical seismic profiling data, geolectric resistivity and resistance data.

The joint inversion algorithm makes use of the damped least‐squares method and its weighted version to solve the linearized set of equations for the seismic and geolectric unknowns. In order to estimate the accuracy and reliability of the derived geometrical and petrophysical layer parameters, both a model covariance matrix and a correlation matrix are calculated. The weighted least‐squares algorithm is based on the method of most frequent values (MFV). The weight factors depend on the difference between measured data and those calculated by an iteration process.

The joint inversion algorithm is tested by means of synthetic data. Compared to the damped least‐squares algorithm, the MFV inversion leads to smaller estimation errors as well as lower sensitivities due to the choice of the initial model. It is shown that, compared to an independent inversion, the correlation between the model parameters is definitely reduced, while the accuracy of the parameter estimation is appreciably increased by the joint inversion process. Thus the ambiguity is significantly reduced.

Finally, the joint inversion algorithm using the MFV method is applied to underground field data. The model parameters can be derived with a sufficient degree of accuracy, even in the case of noisy data.
A FILTER, DELAY AND SPREAD TECHNIQUE FOR 3D DMO1
Authors: FERBER R.‐G.
Published: April 2006

Abstract

The calculation of dip moveout involves spreading the amplitudes of each input trace along the source‐receiver axis followed by stacking the results into a 3D zero‐offset data cube. The offset‐traveltime (x–t) domain integral implementation of the DMO operator is very efficient in terms of computation time but suffers from operator aliasing. The log‐stretch approach, using a logarithmic transformation of the time axis to force the DMO operator to be time invariant, can avoid operator aliasing by direct implementation in the frequency‐wavenumber (f–k) domain.

An alternative technique for log‐stretch DMO corrections using the anti‐aliasing filters of the f–k approach in the x‐log t domain will be presented. Conventionally, the 2D filter representing the DMO operator is designed and applied in the f–k domain. The new technique uses a 2D convolution filter acting in single input/multiple output trace mode. Each single input trace is passed through several 1D filters to create the overall DMO response of that trace.

The resulting traces can be stacked directly in the 3D data cube. The single trace filters are the result of a filter design technique reducing the 2D problem to several ID problems. These filters can be decomposed into a pure time‐delay and a low‐pass filter, representing the kinematic and dynamic behaviour of the DMO operator. The low‐pass filters avoid any incidental operator aliasing. Different types of low‐pass filters can be used to achieve different amplitude‐versus‐offset characteristics of the DMO operator.
DAMPED LEAST‐SQUARES INVERSION OF TIME‐DOMAIN AIRBORNE EM DATA BASED ON SINGULAR VALUE DECOMPOSITION1
Authors: HUANG H. , PALACKY G. J.
Published: April 2006

Abstract

Airborne electromagnetic (AEM) methods are increasingly being used as tools of geological mapping, groundwater exploration and prospecting for coal and lignite. In such applications, quantitative interpretation is commonly based on the layered‐earth model. A new approach, a damped least‐squares inversion with singular value decomposition, is proposed for interpretation of time‐domain, towed‐bird AEM data. Studies using theoretical and field AEM data indicate that inversion techniques are dependable and provide fast converging solutions. An analysis has been made of the accuracy of model parameter determination, which depends on resistivity and thickness distribution. In the common case of conductive overburden, upper‐layer resistivity and thickness are usually well determined, although situations exist where their separation becomes difficult. In the case of a resistive layer overlying a conductive basement, the layer thickness is the best‐determined parameter. In both cases, estimates of basement resistivity are the least reliable. Field data obtained with the Chinese‐made M‐l AEM system in Dongling, Anhui Province, China, were processed using the described inversion algorithm. The survey area comprised fluvial Cenozoic clays and weathered Mesozoic sediments. Inversion of AEM data resulted in accurate depth‐to‐bedrock sections and realistic estimates of the resistivities of overburden and bedrock which agree with the results of drilling and resistivity sounding.
MAKING AVO SECTIONS MORE ROBUST1
Authors: WALDEN A. T.
Published: April 2006

Abstract

When large quantities of seismic data are involved it is impossible to examine all gathers by eye for AVO anomalies. The standard approach is to compute, for each amplitude profile (at a specific time) on each gather, the intercept and gradient of a straight‐line fit to seismic amplitudes. These intercepts and gradients are each plotted as a sort of seismic section ‐ an intercept section, and a gradient section.

Estimation of the intercept and gradient for a straight‐line fit to each amplitude profile proceeds traditionally via least‐squares. Two undesirable features can be hidden from the user by the fitting procedure, namely (i) the effect of outlying or uncharacteristic amplitudes on the intercept and gradient estimates, and (ii) complete breakdown of the straight‐line model for the amplitudes, thus rendering meaningless the intercept and gradient estimates. It should be remembered that least‐squares can always fit any sequence of numbers to any other sequence of numbers; checks are needed to show that the result is meaningful.

It is shown that statistically robust estimation methods can greatly limit the damage done by outlying amplitudes, and that a simple test on the model, the runs‐statistic, is capable of detecting breakdown of the straight‐line assumption. It is demonstrated using two seismic data sets that these two techniques, used in tandem, facilitate much better quality control of AVO intercept and gradient calculations.
THE RESOLUTION OF NARROW LOW‐VELOCITY ZONES WITH THE GENERALIZED RECIPROCAL METHOD1
Authors: PALMER DERECKE
Published: April 2006

Abstract

The depth to the surface of a refractor and the seismic velocity within the refractor are very often intimately related. In the shallow environment, increased thicknesses of weathering occur in areas of jointing, shearing or lithological variations, and these zones of deeper weathering can have lower subweathering refractor velocities. This association is important in geotechnical investigations and in the measurement of weathering thicknesses and sub‐weathering velocities for statics corrections for reflection seismic surveys.

Algorithms, which employ forward and reverse traveltime data and which explicitly accommodate the offset distance through the process known as refraction migration, are necessary if detailed structure on a refractor and rapid lateral variations of the seismic velocity within it are to be resolved. These requirements are satisfied with wavefront construction techniques, Hales’ method and the generalized reciprocal method (GRM).

However, these methods employ refraction migration in fundamentally different manners. Most methods compute an offset distance with an often imprecise knowledge of the seismic velocities of the overlying layers. In contrast, the GRM uses a range of offset distances from less than to greater than the optimum value, with the optimum value being selected with a minimum‐variance criterion.

The approach of the GRM is essential where there are undetected layers and where there are rapid variations in the depth to a refractor and the seismic velocity within it. In the latter situations the offset distance necessary to define the seismic velocities can differ considerably from the value required to define depths.

The efficacy of the GRM in resolving structure and seismic velocity is demonstrated with three model studies and two field examples.
VLF RESISTIVITY MAPPING AND VERTICALIZATION OF THE ELECTRIC FIELD1
Authors: TABBAGH ALAIN , BENDERITTER YVES , ANDRIEUX PIERRE , DECRIAUD JEAN PAUL , GUERIN ROGER
Published: April 2006

Abstract

For over 20 years, powerful VLF transmitters have been used as electromagnetic sources for subsurface investigations in mining exploration. Measurements initially concerned the vertical component of the magnetic field or the inclination of the field and were later extended to measurement of the horizontal electric field in the direction of the transmitter, to determine the resistivity of the terrain. Measurement of the electric field is usually performed with electric lines, grounded or not, with lengths of at least 5 m.

This paper presents the concept of a VLF resistivity meter with a very short electric sensor (1 m) and the results obtained with it. This technique improves the measurement of the electric field, which is in principle a point value. It also permits a higher spatial sampling rate and, by closely linking the electric sensor with the magnetic sensor on a lightweight mount, makes it possible for the instrument to be used by a single operator.

In addition, transformation of the electric field data, analogous to reduction to the pole in magnetism, is proposed to correct the horizontal deformation of the anomalies created by polarization of the primary field. Comparison with direct current electrical measurements shows highly satisfactory correlations. This transformation, validated for VLF, can be extended to any electrical or electromagnetic method using a uniform primary field, i.e. gradient array in direct current or low‐frequency magnetotellurics. We call this verticalization of the electric field.

Resistivity measurements and mapping using the VLF frequency range can be applied not only to mining but also to a wide range of shallow geophysical studies (hydrology, civil engineering, etc.) and are not limited to problems concerning the location of conductive targets
SEISMIC REFLECTION AMPLITUDES1
Authors: URSIN BJØRN , DAHL TERJE
Published: April 2006

Abstract

Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset.

Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel‐time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P‐wave, S‐wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter.

For primary reflected P‐waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant.

The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth‐order polynomial in offset, the traveltime by the normal square‐root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.
ENHANCED SERVOVALVE TECHNOLOGY FOR SEISMIC VIBRATORS1
Authors: REUST DENNIS K.
Published: April 2006

Abstract

The Pelton DRTM Servovalve Enhancement causes the natural output of a vibrator to resemble the desired output more closely. This simplifies the control problem and reduces harmonic distortion.

The traditional type of servovalve used on seismic vibrators is a flow‐control servovalve. Flow is proportional to a vibrator's baseplate velocity, with respect to its reaction mass.

The new servovalve control parameter is pressure rather than flow. The differential pressure applied to a vibrator's actuator piston, multiplied by the area of the piston, equals the force applied to the vibrator's baseplate structure. This may be defined as actuator force. There is a simpler and more linear relationship between actuator force and ground force than between actuator velocity and ground force. Thus, it is better for the servovalve to control pressure into the actuator rather than flow.

A flow‐control servovalve can be made to control pressure by sensing the differential pressure across a vibrator's actuator piston and applying it as a negative feedback around the servovalve main stage. This has been carried out and tested. The result is more accurate vibrator control and reduced harmonic distortion.
A STUDY OF MAGNETOTELLURIC STATIC DISTORTION IN THE CONTEXT OF INTRUSIVE VOLCANISM1
Authors: BEAMISH D. , TRAVASSOS J. M.
Published: April 2006

Abstract

MT data from a detailed 84‐site grid array (28 × 12 km) in the Paraná Basin (Brazil) reveal a high degree of frequency‐independent and parallel amplitude distortion. The Palaeozoic sediments across the survey area are covered by 1.2 km of flood basalts. A deep well‐log provides some control regarding the emplacement of thin diabase sills but information regarding vertical feeder dikes is non‐existent. The degree of parallel behaviour is identified using anisotropy ratios which quantify the extent and bandwidth of the distortion characteristics.

A 2D modelling study is carried out using the concept of a horizontally layered (1D) basin with superimposed, small‐scale inhomogeneities. Two likely geological distortion structures are considered. The first represents at‐ or near‐surface (0 to 100 m) inhomogeneities. The second represents thin but vertically elongate dikes. The two distortion effects are found to produce different and characteristic behaviour in the H‐polarization (TM) mode model data. The modelled E‐polarization (TE) mode data are undistorted and provide control. The model developed to represent vertical dikes gives rise to a characteristic frequency dependence which is distinct from that of the undistorted response. This model also generates subparallel distortion effects which give rise to a form of variance in the response estimates as a function of location. The behaviour occurs, importantly, in both the amplitude and phase of the distorted data. A comparison of the normalized amplitude data, observed and modelled, indicates a high degree of correspondence down to a low frequency limit (< 0.1 Hz) where additional and deep contributions to the observed response become apparent. The modelling results and data characteristics indicate that the survey area is underlain by a series of closely parallel, thin intrusive dikes (a dike swarm).
MODELLING GUIDED WAVES IN CROSS‐HOLE SURVEYS IN UNCRACKED AND CRACKED ROCK1
Authors: LOU MIN , CRAMPIN STUART
Published: April 2006

Abstract

The theoretical behaviour of guided waves in cross‐hole seismic surveys is examined with dispersion curves and synthetic seismograms. The modelling suggests, and field observations confirm, that the dominant energy in many cross‐hole seismic surveys propagates as guided waves, as well as body waves, with the energy tied to an interface, or combination of interfaces, whenever there are interfaces with significant velocity contrasts continuous between the wells. The dispersion and waveforms of such modal solutions carry detailed information about the internal structure, particularly the stress‐aligned structure of fluid‐filled inclusions in the immediate neighbourhood of the waveguide. Since the information content can be controlled to some extent by the choice of frequency and source type and the level of source and receiver in the two wells, such guided waves in cross‐hole surveys may be important for monitoring changes in nearly horizontal reservoirs during hydrocarbon production processes. Initially, we investigate the basic properties of propagation in isotropic strata, and then examine the behaviour of guided waves in the stress‐aligned fluid‐filled inclusions.
SIMULATION OF REALISTIC SYNTHETIC REFLECTION SEQUENCES1
Authors: WALDEN A. T.
Published: April 2006

Abstract

It is useful to be able to calculate synthetic primary reflection sequences from which to generate synthetic seismic sections which can be used for testing new processing algorithms. However, these synthetic reflection sequences should closely match real properties found in recent studies. Using the ARMA(1,1) model resulting from such studies to describe the correlation (or spectral) structure of the sequences, and by matching moments up to fourth order (since the sequences are non‐Gaussian in practice), realistic sequences can be generated. A simple scheme is provided which also eliminates the necessity of throwing away large numbers of simulated values at start‐up. The procedure is illustrated on three real sequences and is seen to reproduce all the important features.
ESTIMATION OF ELASTIC PARAMETERS FROM AVO EFFECTS IN THE TAU‐P DOMAIN1
Authors: HELGESEN J. , LANDRØ M.
Published: April 2006

Abstract

A quantitative AVO algorithm suitable for media with slow lateral parameter variations is developed. The method is based on a target‐oriented inversion scheme for estimation of elastic parameters in a locally horizontally stratified medium. The algorithm uses band‐limited PP reflection coefficients in the τ‐p domain to estimate P‐ and S‐wave velocities, densities and layer thicknesses. To obtain these reflection coefficients, a pre‐processing involving the Radon transform and multiple attenuation is necessary. Furthermore, a macromodel for the velocities above the target zone must be found prior to the inversion.

Various inversion tests involving synthetic data with white Gaussian noise and modelling errors that are likely to occur in conjunction with real data have been performed. In general, the inversion algorithm is fairly robust, since it is able to reproduce the main features of the reference model: main interface locations and relative contrasts in the three unknown layer parameters are recovered.

From a test combining the effect of source directivity, one thin layer and 20% white Gaussian noise, it was found that neglect of the source directivity in the inversion caused the largest errors in the estimates. This indicates that it is very important either to eliminate the source directivity in a preprocessing step, or to take the directivity into account in the present algorithm. Despite these problems it was concluded that the inversion algorithm was able to reproduce the main features of the reference model.
ACCURATE FINITE‐DIFFERENCE OPERATORS FOR MODELLING THE ELASTIC WAVE EQUATION1
Authors: JASTRAM CORD , BEHLE ALFRED
Published: April 2006

Abstract

A method is presented for computing the coefficients of finite‐difference operators for the elastic wave equation. As opposed to other algorithms, in this case the amplitude spectrum of the source function is taken into account. Test calculations show that this approach gives more accurate results than operators based on a Taylor expansion or on minimizing the maximum error of the group velocity in a spatial frequency interval.
PARABOLIC AND HYPERBOLIC PARAXIAL TWO‐POINT TRAVELTIMES IN 3D MEDIA1
Authors: SCHLEICHER J. , TYGEL M. , HUBRAL P.
Published: April 2006

Abstract

The 4 × 4 T‐propagator matrix of a 3D central ray determines, among other important seismic quantities, second‐order (parabolic or hyperbolic) two‐point traveltime approximations of certain paraxial rays in the vicinity of the known central ray through a 3D medium consisting of inhomogeneous isotropic velocity layers. These rays result from perturbing the start and endpoints of the central ray on smoothly curved anterior and posterior surfaces. The perturbation of each ray endpoint is described only by a two‐component vector. Here, we provide parabolic and hyperbolic paraxial two‐point traveltime approximations using the T‐propagator to feature a number of useful 3D seismic models, putting particular emphasis on expressing the traveltimes for paraxial primary reflected rays in terms of hyperbolic approximations. These are of use in solving several forward and inverse seismic problems. Our results simplify those in which the perturbation of the ray endpoints upon a curved interface is described by a three‐component vector. In order to emphasize the importance of the hyperbolic expression, we show that the hyperbolic paraxial‐ray traveltime (in terms of four independent variables) is exact for the case of a primary ray reflected from a planar dipping interface below a homogeneous velocity medium.
VISCOELASTIC SEISMIC RESPONSES OF 2D RESERVOIR MODELS1
Authors: KANG I. B. , McMECHAN GEORGE A.
Published: April 2006

Abstract

The use of relaxation mechanisms has recently made it possible to simulate viscoelastic (Q) effects accurately in time‐domain numerical computations of seismic responses. As a result, seismograms may now be synthesized for models with arbitrary spatial variations in compressional‐ and shear‐wave quality factors (Q9, and Qs, as well as in density (ρ) and compressional‐ and shear‐wave velocities (Vp, and Vs).

Reflections produced by Q contrasts alone may have amplitudes as large as those produced by velocity contrasts. Q effects, including their interaction with Vp, Vs and p, contribute significantly to the seismic response of reservoirs. For band‐limited data at typical seismic frequencies, the effects of Q on reflectivity and attenuation are more visible than those on dispersion.

Synthetic examples include practical applications to reservoir exploration, evaluation and monitoring. Q effects are clearly visible in both surface and offset vertical seismic profile data. Thus, AVO analyses that neglect Q may produce erroneous conclusions.
A COMPARISON OF LABORATORY AND FIELD MEASUREMENTS OF P‐WAVE ANISOTROPY1
Authors: SAMS M. S. , WORTHINGTON M. H. , KING M. S. , KHANSHIR M. SHAMS
Published: April 2006

Abstract

P‐wave velocity anisotropy determined from a cross‐hole survey at the Imperial College borehole test site compares favourably with that measured in the laboratory on core from the holes. The holes penetrate a layered sequence of sandstones, shales and carbonates of the Namurian Upper Limestone Group. The Laboratory measurements of the vertical and horizontal velocities of core samples indicate that the shales exhibit P‐wave anisotropies of over 20% but that the sandstones and limestones are only slightly anisotropic. These discrete measurements have been used in combination with wireline data to produce a log of P‐wave anisotropy. Including the anisotropic information vastly improves the match between observed and synthetic traveltimes from the cross‐hole data set. This implies that there is little frequency dependence of intrinsic P‐wave anisotropy.

Inversion of the cross‐hole traveltimes highlights the need for good angular coverage in order to resolve the anisotropy parameters. The observed P‐wave anisotropy of the field data is due to the combined effect of sedimentary layering and the intrinsic anisotropy of the rocks. The intrinsic anisotropy is found to be the dominant factor.
3D KINEMATIC INVERSION FROM A SET OF LINE PROFILES1
Authors: SORIN VALERY , KEYDAR SHEMER , LANDA EVGENY
Published: April 2006

Abstract

In the case of 3D multilayered structures the 2D interval velocity analysis may be inaccurate. This fact is illustrated by synthetic examples.

The method proposed solves the 3D inverse problem within the scope of the ray approach. The solution, i.e. the interval velocities and the reflection interface position, is obtained using data from conventional 2D line profiles arbitrarily located and from normal incidence time maps. Although the input information is essentially limited, the method presented reveals only minor biased velocity estimates.

In order to implement the proposed 3D inversion method, we developed a processing procedure. The procedure performs the evaluation of reflection time and ray parameters along line profiles, 3D interval velocity estimation, and time‐to‐depth map migration. Tools to stabilize the 3D inversion are investigated.

The application of the 3D inversion technique to synthetic and real data is compared with results of the 2D inversion.
MODEL‐BASED STACK: A METHOD FOR CONSTRUCTING AN ACCURATE ZERO‐OFFSET SECTION FOR COMPLEX OVERBURDENS1
Authors: LANDA E. , THORE P. , RESHEF M.
Published: April 2006

Abstract

The interpretation of stacked time sections can produce a correct geological image of the earth in cases when the stack represents a true zero‐offset section. This assumption is not valid in the presence of conflicting dips or strong lateral velocity variations. We present a method for constructing a relatively accurate zero‐offset section. We refer to this method as model‐based stack (MBS), and it is based on the idea of stacking traces within CMP gathers along actual traveltime curves, and not along hyperbolic trajectories as it is done in a conventional stacking process. These theoretical curves are calculated for each CMP gather by tracing rays through a velocity‐depth model. The last can be obtained using one of the methods for macromodel estimation. In this study we use the coherence inversion method for the estimation of the macromodel since it has the advantage of not requiring prestack traveltime picking. The MBS represents an accurate zero‐offset section in cases where the estimated macromodel is correct. Using the velocity–depth macromodel, the structural inversion can be completed by post‐stack depth migration of the MBS.
TEMPERATURE EFFECTS ON AIRGUN SIGNATURES1
Authors: LANGHAMMER JAN , LANDRØ MARTIN
Published: April 2006

Abstract

Experiments in an 850 litre water tank were performed in order to study temperature effects on airgun signatures, and to achieve a better understanding of the physical processes that influence an airgun signature. The source was a bolt airgun with a chamber volume of 1.6 cu.in. The pressure used was 100 bar and the gun depth was 0.5 m. The water temperature in the tank was varied between 5°C and 45°C. Near‐field signatures were recorded at different water temperatures. Typical signature characteristics such as the primary‐to‐bubble ratio and the bubble time period increased with increasing water temperature. For comparison and in order to check whether this is valid for larger guns, computer modelling of airguns with chamber volumes of 1.6 and 40 cu.in. was performed. In the modelling the same behaviour of the signatures with increasing water temperature can be observed. The increase in the primary‐to‐bubble ratio and the bubble time period with increasing water temperature can be explained by an increased mass transfer across the bubble wall.
ON THE COMPUTATION OF THE MAGNETIC FIELD DUE TO A D.C. POINT ELECTRODE AT THE VERTICAL BOUNDARY BETWEEN TWO QUARTER‐SPACES1
Authors: HVOŽDARA M.
Published: April 2006

Abstract

New formulae are presented for the calculation of the horizontal magnetic field due to a point electrode situated at the vertical boundary between two quarter‐spaces of different electrical conductivities. Previously the solution was obtained using a double Fourier transform of the expression for the vertical component of the magnetic field. The new formulae are given in the form of single integrals.
BOREHOLE EFFECTS ON DOWNHOLE SEISMIC MEASUREMENTS1
Authors: PENG CHENGBIN , CHENG C. H. , TOKSÖZ M. N.
Published: April 2006

Abstract

An exact formulation for borehole coupling, which is valid for all frequencies and all azimuthally symmetric and non‐symmetric components, is presented. The borehole effects on downhole seismic measurements are studied in detail as functions of frequency, angle of incidence and polarization of an incident wave as well as geophone orientation. We found that correction for the borehole effect on downhole measurements should be made for frequencies above 500 Hz in a hard formation. In a soft formation, if the angle of incidence is well away from the resonance angle for SV incidence, no borehole correction is needed for frequencies below 300 Hz, while for frequencies above 300 Hz, the borehole can cause severe problems in downhole measurements. The borehole can also significantly alter the particle motion direction which implies that horizontal component rotation from data itself is unreliable for experiments with frequencies above 1 kHz in the hard formation and around 500 Hz in the soft formation.
Using the pseudospectral technique on curved grids for 2D acoustic forward modelling1
Authors: Nielsen Per , If Flemming , Berg Per , Skovgaard Ove
Published: April 2006

The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non‐physical diffractions by using curved grids that generally follow the interfaces.

A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled.

One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so‐called multiblock strategy).

The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space.

The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.
Elastic modelling on a grid with vertically varying spacing1
Authors: Jastram Cord , Tessmer Ekkehart
Published: April 2006

We present a discrete modelling scheme which solves the elastic wave equation on a grid with vertically varying grid spacings. Spatial derivatives are computed by finite‐difference operators on a staggered grid. The time integration is performed by the rapid expansion method. The use of variable grid spacings adds flexibility and improves the efficiency since different spatial sampling intervals can be used in regions with different material properties. In the case of large velocity contrasts, the use of a non‐uniform grid avoids spatial oversampling in regions with high velocities. The modelling scheme allows accurate modelling up to a spatial sampling rate of approximately 2.5 gridpoints per shortest wavelength. However, due to the staggering of the material parameters, a smoothing of the material parameters has to be applied at internal interfaces aligned with the numerical grid to avoid amplitude errors and timing inaccuracies. The best results are obtained by smoothing based on slowness averaging. To reduce errors in the implementation of the free‐surface boundary condition introduced by the staggering of the stress components, we reduce the grid spacing in the vertical direction in the vicinity of the free surface to approximately 10 gridpoints per shortest wavelength. Using this technique we obtain accurate results for surface waves in transversely isotropic media.
Cased borehole effects on downhole seismic measurements1
Authors: Peng Chengbin , Cheng Chuen Hon , Toksöz M. Nafi
Published: April 2006

Both approximate and exact formulations for the interaction of an incident elastic wave with a cased borehole are presented. In the approximate method, simple and explicit formulae are derived for the pressure in fluid at low frequencies. In the exact method, elastic potentials in each annulus are represented as a superposition of fundamental solutions to the Helmholtz equations. Continuity of displacements and stresses across layer boundaries are used to determine unknown coefficients. A global matrix algorithm is employed to compute simultaneously these coefficients in individual layers. Calculations show that, in cased boreholes, the borehole effects on downhole seismic measurements are more significant than in open boreholes. A strong resonance occurs in the fluid for SV‐wave incidence from a soft formation. This resonance is prominent even at very high frequencies because the tube‐wave velocity is raised well above the formation shear velocity by the steel pipe. At a particular angle of incidence of a plane P‐wave, the pressure in the fluid is near zero at low frequencies (the cased borehole screening phenomenon). For hard formations and frequencies above 1 kHz, the cased borehole influence on a downhole geophone measurement is significant, especially at grazing incidence. For soft formations, both the pressure in the fluid and the solid displacement on the borehole wall show strong dependence on frequency and angle of incidence, even at low frequencies.
Gravity interpretation of sedimentary basins with hyperbolic density contrast1
Authors: Rao C. Visweswara , Pramanik A.G. , Kumar G.V.R.K. , Raju M.L.
Published: April 2006

The variation in the density of sediments with depth in a sedimentary basin can be represented by a hyperbolic function. Gravity anomaly expressions for a 2D vertical prism and an asymmetric trapezium with a hyperbolic density distribution are derived in a closed form. These are used in inverting the gravity anomaly of a sedimentary basin with variable density. Firstly, the basin is viewed as a series of prisms juxtaposed with each other. The initial thickness of each prism is obtained from the gravity anomaly at its centre, based on the gravity anomaly of an infinite slab with a hyperbolic density contrast. These thicknesses are improved, based on the differences between the observed and the calculated anomalies. For an improved rate of convergence of the solution, these thicknesses may alternatively be refined using the well‐known ridge regression technique. Secondly, the basin is approximated by an asymmetric trapezium and its anomalies are inverted for the parameters of the trapezium using the ridge regression. Since this approximation serves to oversimplify the floor of the basin, it must be used only when the sediment‐basement interface has minor undulations. The results of a hypothetical case and two field cases (the San Jacinto Graben, California and the Godavari Graben, southern India) are presented. In both field cases, the interpreted depths are comparable with the real ones, proving the validity of the assumption of a hyperbolic density distribution of the sediments in the two basins considered.
A sample of controlled experiments in diff radion tomography1
Authors: Gelius L.‐J.
Published: April 2006

Various applications of a new geophysical reconstruction method, generalized acoustical diffraction tomography (GADT), which is based on transmission data as input are considered. Conventional diffraction tomography methods normally require linearization with respect to a uniform reference medium and regular sampling along a straight line. Thus, these methods will not work well when the background is strongly non‐uniform and/or the acquisition geometry is arbitrary. However, GADT can, in principle, handle both irregularly spaced data, curved acquisition lines, and non‐uniform background models.

A number of controlled model tank and field experiments, where the model and the test object(s) are known a priori, have been carried out. After acquiring the tomographic data in each experiment, these are used to compute a reconstruction of the model, which can then be compared with the actual, known model. The method's ability to yield high‐quality images of the different targets is demonstrated.
2D modelling of resistivity and magnetotelluric data from the Belvedere Spinello salt mine, Italy1
Authors: Iliceto V. , Santarato G. , Zerilli A.
Published: April 2006

The Belvedere Spinello salt mine is located in the Catanzaro Province of Calabria in Southern Italy. An extensive mining program has caused the development of Underground cavities filled with brine and the migration of this brine has been of great environmental concern to the mine owners. This paper presents the results of a multidimensional interpretation of a two‐phase resistivity and magnetotelluric (MT) survey that was performed in an attempt to determine the complex conductivity structure of the mine area and to gain information on brine development and migration pathways. Key resistivity soundings were interpreted using a 2.5D algorithm based on the Polozhii decomposition method. The MT data were interpreted using a 2D finite‐element code. A conductivity model was developed, integrating available geological and drill‐hole information. The interpretation of the MT data, collected five years after the acquisition of the resistivity data, shows a conductive feature of depth that is not resolved in the resistivity interpretation. This feature has been interpreted as a thick brine zone that has developed as a result of mining during the interval between the resistivity and the MT measurements.
Tracking the amplitude versus offset (AVO) by using orthogonal polynomials1
Authors: Johansen T.A. , Bruland L. , Lutro J.
Published: April 2006

Inversion for S‐wave velocities from the amplitude variation with offset of P‐wave data is far from being a standard routine in the seismic processing sequence. However, the need for tracking the amplitude versus offset (AVO) occurs in several situations, for example in order to estimate the zero‐offset amplitude, to reveal areas with particular AVO characteristics, or to compress the AVO so that it is more easily obtainable at a later stage of the seismic processing. Furthermore, weak reflections can occasionally, due to the effect of the angle‐dependent reflectivity, have a polarity‐shift with offset, resulting in a very poor, or even vanishing, stack response. In such cases, the reflection event has to be represented by some other property than its mean amplitude or stack value.

We outline how the AVO of seismic data may be extracted and classified by the use of orthogonal polynomials. The main advantage of this method compared to a general polynomial fit is that the AVO may be classified by a unique Spectrum of polynomial coefficients. This is in analogy to Fourier coefficients where the orthogonal basis is harmonic functions. The set of orthogonal polynomials is constructed entirely from the set of offset coordinates, and these polyno‐mials are defined only on the offset window considered. Compared to a Fourier transform, this is a major advantage since there is no effect of a limited spatial bandwidth.

The AVO of normal‐moveout corrected data may be represented by a data gather where the orthogonal polynomial coefficients are given as time traces with each trace revealing a certain AVO characteristic. For instance, the stack is proportional to the zeroth‐order coefficient, the mean gradient is given by the firstorder coefficient, while the second‐order coefficient indicates whether the AVO increases and then decreases, or vice versa.
Phase inversion deconvolution for long and short period multiples attenuationl1
Authors: Lichrnan Eugene , Northwood E. John
Published: April 2006

Abctract

A new approach to deconvolution has been developed to improve the attenuation of multiple energy. This approach to deconvolution is unique in that it not only eliminates the usual assumptions of a minimum phase lag wavelet and a random distribution of impulses, but also overcomes the noise limitation of the homomorphic deconvolution and its inherent instability to phase computation.

We attempt to analyse the continuous alteration of the acoustic waveform during the propagation through a linear system. Based on the results of this analysis, the surface‐related measurements are described as a convolution of the impulse response of the system with the non‐stationary forward wavelet which includes all multiple terms generated within the system.

The amplitude spectrum of the forward wavelet is recovered from the amplitude spectrum of the recorded signal, using the difference between the rate of decay of the source wavelet and the duration of the measurement.

The phase spectrum of the forward wavelet is estimated using the Hilbert transform and the fact that the mixed phase lag wavelet can be presented as a convolution of the minimum and maximum phase lag wavelets.

The multiples are discriminated from primaries by comparison of the phase spectrum of the seismic signal and the inverse of the forward wavelet. Therefore, the technique is called phase inversion deconvolution (PID). This approach requires no velocity information in order to recognize and attenuate multiple energy. Therefore, primary energy is recovered in the near‐offset region where the velocity differential between primary and multiple energies is very small.
Quantitative evaluation of crosshole seismic reflection images using physical model data1
Authors: Rowbotharn Peter S. , Goulty Neil R.
Published: April 2006

Physical models give us a known geometry with which to compare our processed reflection images and therefore our imaging techniques. We show how this comparison may be quantified in order to evaluate processed images properly. A crosshole data set was acquired through a model interrogated at ultrasonic frequencies using Durham University's physical modelling system. Various reflectivity images were obtained using processing sequences which include deconvolution, wavefield separation and migration. An error‐energy scheme was used to assess the quality of these images, by comparing them against a best‐fit depth model. A synthetic data set was also used to evaluate the imaging capability of the crosshole geometry and the effectiveness of the different processing schemes.
Error estimation and optimization of gravity surveys1
Authors: Keating Pierre
Published: April 2006

Gravity data are often acquired over long periods of time using different instruments and various survey techniques, resulting in data sets of non‐uniform accuracy. As station locations are inhomogeneously distributed, gravity values are interpolated on to a regular grid to allow further processing, such as computing horizontal or vertical gradients. Some interpolation techniques can estimate the interpolation error. Although estimation of the error due to interpolation is of importance, it is more useful to estimate the maximum gravity anomaly that may have gone undetected by a survey. This is equivalent to the determination of the maximum mass whose gravity anomaly will be undetected at any station location, given the data accuracy at each station. Assuming that the maximum density contrast present in the survey area is known or can be reasonably assumed from a knowledge of the geology, the proposed procedure is as follows: at every grid node, the maximum mass whose gravity anomaly does not disturb any of the surrounding observed gravity values by more than their accuracies is determined. A finite vertical cylinder is used as the mass model in the computations. The resulting map gives the maximum detection error and, as such, it is a worst‐case scenario. Moreover, the map can be used to optimize future gravity surveys: new stations should be located at, or near, map maxima. The technique is applied to a set of gravity observations obtained from different surveys made over a period of more than 40 years in the Abitibi Greenstone Belt in eastern Canada.