bluuebunny/crossref_metadata_2025 huggingface dataset:
THE GRAVITY AND MAGNETIC FIELDS FROM ELLIPSOIDAL BODIES IN THE WAVENUMBER DOMAIN*
Authors: PEDERSEN L. B.
Published: April 2006

Wavenumber domain expressions for bodies with elliptical cross‐section and of ellipsoidal shape have been developed both for homogeneous bodies and for certain bodies of density/magnetization varying linearly with depth or, more generally, according to a polynomial with depth. The simple expressions thus obtained lend themselves to an easy analysis, especially for long and short wavelengths. At the long‐wavelength end of the spectra their decay is governed by an exponential with a decay “depth” equal to the depth to the center of mass. At the short‐wavelength end this depth is replaced by the depth to the upper focus of the ellipsoid (or the elliptic cross‐section). For vertically inhomogeneous ellipsoids the decay rate is also dependent on the product of the vertical gradient of density/magnetization and their semi‐axes.
SEISMIC MODELING IN THE IMPLICIT MODE*
Authors: MUFTI I. R.
Published: April 2006

Abstract

Finite‐difference seismic models are often saddled with huge memory requirements for data manipulation, a prohibitive amount of CPU time and even approximate results. At least part of these costs may be due to the fact that most of the work reported on this subject is devoted to the development of explicit models which suffer from severe limitations of stability and necessitate extremely fine time sampling of the wavefield.

A new method of seismic modeling which works in the implicit mode and is unconditionally stable is put forward. It is based on the self‐adjoint version of the acoustic wave equation. The evaluation of the wavefield is done by using a highly efficient splitting algorithm which does not require transposing the field data at the various time steps. Moreover, it can accommodate anisotropic media as well as three‐dimensional structures. Computational efficiency is achieved by introducing an unconventional procedure which yields the sum of the values of the wavefield corresponding to a new time step and a previous time step. The new value can be obtained from this sum by a simple subtraction.

A number of numerical examples, some obtained by using time steps about five times larger than the largest permissible time step in the corresponding explicit model, are presented. The effect of topographic changes on the growth of the wavefield due to a source located near the surface of the ground is investigated.
DATA QUALITY ASSESSMENT OF TIME‐DOMAIN IP DECAY CURVES*
Authors: BUSBY J. P.
Published: April 2006

Abstract

Data quality assessments have been made on time‐domain induced polarization decay curves taken over sulphide ore bodies of Cyprus. The data were taken with the dipole‐dipole, pole‐dipole and symmetrical quadripole arrays. The results indicate that at larger array separations decay curves taken with the dipole‐dipole and pole‐dipole arrays are often seriously affected by noise, but that curves taken with the symmetrical quadripole array are not so affected. Optimum pseudo‐sections designed to minimize the noise show that the noise results in spurious highs and lows.

This work was carried out as part of a NERC research studentship at the University of Leicester.
A NUMERICAL STUDY OF LAMB'S PROBLEM*
Authors: KUHN M. J.
Published: April 2006

Abstract

This paper considers propagation of elastodynamic waves in an imperfectly elastic half‐space. Two different excitation modes are investigated: a buried source of compressional waves and a vertically directed areal load applied to the surface. Numerical integration of the analytical solution of the wave equation allows study of the vertical and horizontal components of displacement and/or particle velocity anywhere in the half‐space. One case of particular interest concerns the examination of particle displacement and velocity at the surface in a circular area above the source. In another application seismograms generated by an explosive buried source are contrasted with seismograms generated by the transient application of a vertically directed load to the free surface. Still another application of considerable practical interest concerns the study of the nongeometrical pS—wave, in particular its characteristics as functions of range and depth. Finally, in the last application the behavior of a rarely observed wave (denoted here by the letter U) is studied in both elastic and visco‐elastic half‐spaces.
THE APPLICATION OF VHF MEASUREMENTS TO EARTHQUAKE PREDICTION*
Authors: SINGH R. P. , RANKIN D.
Published: April 2006

Abstract

The use of Very High Frequency measurements applied to the detection of the variation in dielectric constant as a precursor to earthquakes is examined. It is concluded that such a technique is feasible and that the installation of source and sensor in separate deep boreholes provides a suitable environment for this type of study. The boreholes could also be used for a considerable range of other types of instrumentation.
TRANSIENT FINITE INTEGRAL POINT SOURCE RESPONSE FROM A PLANAR ACOUSTIC INTERFACE: THE CAUSALITY APPROACH*
Authors: HUBRAL P. , TYGEL M.
Published: April 2006

Point source reflection/transmission responses from planar interfaces based on the Sommerfeld‐Weyl integral are causal and are given in the form of a solution integral with an infinite integration limit. They can be simply transformed to integrals with a finite limit by an approach that takes into account causality as well as time‐symmetry aspects. To introduce the fundamental principles involved, the transformation is applied to the simple case of a point‐source response from a planar acoustic interface. For a point source above a planar interface separating an upper and lower acoustic half‐space of velocity c1and c2 the inhomogeneous plane waves in the Sommerfeld‐Weyl source representation do not contribute to the final result if c1≤c2 and only a limited spectrum of inhomogeneous plane waves comes into play if c1c2.
WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS.
Authors: WAPENAAR C. P. A. , BERKHOUT A. J.
Published: April 2006

Abstract

Wave field extrapolation including critical angle events in modeling, migration and inversion can be handled with algorithms based on both the one‐way wave equations and the two‐way wave equation. It is shown that for 1‐D inhomogeneous media, critical angle events as well as multiple reflections may elegantly be included in pre‐stack modeling, pre‐stack migration and velocity inversion. For 2‐D and 3‐D inhomogeneous media a powerful pre‐stack migration scheme can be developed which includes critical angle events as well as multiple reflections. Finally, suggestions for practical applications are given.
QUANTITATIVE INTERPRETATION OF PULSE EM MEASUREMENTS OVER A WEATHERED KIMBERLITE DIATREME*
Authors: RAI S. S. , BHATTACHARYA B. B.
Published: April 2006

Abstract

The application of pulse EM and MAXMIN II systems in search of a kimberlite diatremes under conducting cover has been demonstrated through a field example. The effectiveness of the PEM system in the search for conductive zones of economic importance and in discrimination against geologic noise such as overburden has been investigated. The transient observation has been transformed to equivalent half‐space resistivities at various times. The feasibility of mapping thin conducting overburden using the PEM system has been studied by inverting the transient measurement to the thin infinite horizontal sheet conductance. The PEM measurement is shown to be an economic and effective tool for shallow geoelectric mapping.
TESTING THE TRANSIEL METHOD IN MINERAL AND GEOTHERMAL EXPLORATION*
Authors: DUPRAT A. , ROUDOT M. , SPITZ S.
Published: April 2006

Transiel is the name given to a qualitative, time domain induced polarization (IP) method. The aim of the method is twofold: to locate and to distinguish between deep and shallow polarizable media. This discrimination is based on the data analysis, which distinguishes Transiel from the conventional IP methods.

Two case histories are presented: one related to mineral prospecting and the other to geothermal exploration. The information supplied by Transiel on the deep polarizable layers is checked at each test site by an independent inversion of the recorded transients.

At the mineral test site, the method correctly predicts the target location. In this particular survey, the maximum penetration depth of the method is 700 m. At the geothermal test site, a fair correlation is found between IP anomalies and the productive wells. Since the method's penetration depth does not exceed 500 m, we believe that the observed IP anomalies are related to reduction phenomena occurring in the overburden and leading to pyrite formation. We suppose that these phenomena are caused by thermochemical exchanges between the reservoir and the overburden above zones of high reservoir permeability.
SAMPLING AND MINIMUM PHASE FROM BOTH A CONTINUOUS AND DISCRETE POINT OF VIEW*
Authors: MITCHELL A.R. , STOKES W.D.
Published: April 2006

Examples show that the sampling operation–i.e., the change from the continuous time domain to the discrete time domain–does not necessarily preserve the minimum‐phase property. Further examples can be constructed to show that the resampling operation on the discrete time domain does not necessarily preserve the minimum‐phase property. Finally it can be shown that the minimum‐phase property can be either created or destroyed by sampling or resampling.
SOLUTION OF THE VSP ONE‐DIMENSIONAL INVERSE PROBLEM*
Authors: MACE D. , LAILLY P.
Published: April 2006

The acoustical impedance distribution of the substratum, or equivalently, the reflection coefficient sequence, is determined from VSP data. This nonlinear inverse problem is solved by a least‐squares method.

As the wavelet is unknown, the impedance distribution and the Neumann boundary condition (which characterizes the excitation of the medium) are simultaneously identified.

The inversion method is applied to synthetic and field VSP's; the result is satisfactory, even when strong noise corrupts the data, provided that a suitable constraint on the impedance distribution is introduced in order to ensure the stability of the inverse problem.

The reliability of the inversion result in the case of field VSP, is confirmed. Some ways in which this result may be used are illustrated (calibration of the seismic surface data, multiple identification, prediction ahead of the bit).
STATISTICAL MULTIVARIATE ANALYSIS OF AIRBORNE GEOPHYSICAL DATA ON THE SE BORDER OF THE CENTRAL LAPLAND GREENSTONE COMPLEX*
Authors: LANNE E.
Published: April 2006

Statistical multivariate methods for the integrated processing of airborne geophysical data were tested. The data consisted of magnetic, electromagnetic and gamma radiation measurements, to which cluster analysis, principal components analysis and discriminant analysis were applied. Also, auxiliary variables were derived from the original ones and their value was tested. Although the frequency distributions of the data do not favour statistical analysis, the practical results are acceptable. Principal component analyses show geological and technical aspects that are difficult to obtain from the original observations. In cluster analyses, the sources of measured fields control the grouping of variables. Discriminant analysis was applied to the automatic identification of rocks by geophysical data. The rocks investigated are metasediments and metavolcanics, some magnetic and others conductive. When all available geophysical data were included, correct identifications were made in more than 60% of cases. In particular, gamma ray observations were found to improve the discrimination of non‐magnetic and non‐conductive rocks. The geophysical similarity of rocks studied by cluster analysis depends on electrical and magnetic properties as well as on their origin; the content of radioactive elements in turn is related to the origin.
NONLINEAR COMPLEX RESISTIVITY OF SOME NICKEL SULPHIDES FROM WESTERN AUSTRALIA*
Authors: HALL S.H. , OLHOEFT G.R.
Published: April 2006

The electrochemical transfer characteristics of nickel sulphides from six West Australian localities are examined by the nonlinear complex resistivity (nlcr) method. Ores are classified on the basis of their state of oxidation (supergene, transition zone and primary ores) in an equivalent mine water electrolyte; evidence is found for a systematic change of electrical response with oxidation that is symptomatic of electrochemical reactions varying from diffusion to charge‐transfer controlled processes. The analysis is based on the assumption that the Randies’ circuit is an effective model of a rock's electrical response in its natural electrolyte. Both complex impedance plane graphs and computer inversion are used to study the model. Harmonic distortion is a useful aid in this interpretation.
SIGNAL‐TO‐NOISE RATIO ENHANCEMENT IN MULTICHANNEL SEISMIC DATA VIA THE KARHUNEN‐LOÉVE TRANSFORM*
Authors: JONES I.F. , LEVY S.
Published: April 2006

The Karhunen‐Loéve transform, which optimally extracts coherent information from multichannel input data in a least‐squares sense, is used for two specific problems in seismic data processing.

The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal‐to‐noise ratio by removing from the data that information which is incoherent trace‐to‐trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen‐Loéve transform is useful for data compression for the transmission and storage of stacked seismic data.

The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen‐Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.
TOPOGRAPHIC REDUCTION OF GRAVITY MEASUREMENTS BY NUMERICAL INTEGRATION OF BOUNDARY INTEGRALS*
Authors: GRANSER H.
Published: April 2006

A numerical method for calculating the topographic reduction of gravity measurements is developed which follows the approximation of the topography by a single valued function. The method involves the conversion of the volume integral for the gravity effect into a two‐dimensional definite integral. The definite integral is partly solved by explicit, and partly by numerical, integration, using the Gauss‐Legendre quadrature formula. This method is well suited to calculating the topographic reduction of 50 to approximately 1000 m from the station–especially for microgravimetric surveys in areas of steeply sloping terrain. To test the method in practice it was applied in an area of rough relief in Keban (East Turkey).
PHASE ERRORS OF FINITE‐DIFFERENCE MIGRATION*
Authors: BEAUMONT C. M. , BOYCE J. F. , SILVA R.
Published: April 2006

A quantitative analysis of the various approximations to the scalar wave equation used in seismic migration can be obtained by a study of the resulting phase errors. In the space‐time domain the effects of different modes of parameter optimization are displayed. In the space‐frequency domain the spatial derivatives may be expanded as a linear filter operator whose coefficients are determined by requiring that the resulting phase shifts agree with those that arise from planar wave solutions of the exact wave equation over a range of angles and frequencies.
TRACE INTERPOLATION IN SEISMIC DATA PROCESSING *
Authors: BARDAN V.
Published: April 2006

Abstract

Trace interpolation of spatially aliased seismic data is used to improve the quality of multi‐trace processing, especially that of migration. We consider non‐rectangular sampling lattices. After stating the real sampling requirements for (two‐dimensional or 3‐D) digitized signals, the paper explains geometrically the effect of migration and of the 2‐D dip filtering upon the aliased events, as well as our ability to interpolate traces from undersampled seismic data.
JOINT INTERPRETATION OF GRAVITY AND MAGNETIC DATA OVER AXIAL SYMMETRIC BODIES WITH APPLICATION TO THE DARNLEY BAY ANOMALY, NWT CANADA*
Authors: CHAVEZ R.E. , BAILEY R.C. , GARLAND G.D.
Published: April 2006

A method is presented for determining bounds of the properties of axial symmetric bodies from a finite number of gravity and magnetic observations based on Parker's theory of ideal bodies. Bounds on the density contrast and the intensity of magnetization are calculated as a function of depth to the top of the anomalous source, restricting the range of smallest possible solutions to fit the data.

The model studied is approximated by an array of vertical annuli cylinders, each of uniform density and magnetization. Linear programming algorithms based on the ideal body theory were used to calculate the distribution of these parameters within the body.

Simultaneous inversion of gravity and magnetic data is performed assuming a constant ratio between the density contrast and the intensity of magnetization and that a common body is responsible for both observed fields. The parameter k(|J|/δp) provides information about the rock type of the structure.

Interpretation of gravity and aeromagnetic data from Darnley Bay, NWT, Canada, indicated the presence of a shallow ultrabasic intrusion.
INTERPRETATION OF TRANSIENT EM COMMON‐LOOP ANOMALIES BY RESPONSE CHARACTERISTICS*
Authors: OGILVY R.D.
Published: April 2006

Theoretically exact type curves for a semi‐infinite thin conductor are presented for various dip, angles, depth of burial and conductance. The study shows that the common‐loop response shape is sensitive to small changes in conductor dip, but is affected more subtly by comparable strike variations. For large sheet conductors a decrease in the strike angle results in a broadening but unlike that for a finite plate there is no reduction in peak amplitude. For dipping conductors, response asymmetry and the direction and magnitude of peak amplitude displacement can be used to assess the disposition and quality of the conductor. A generalized interpretation scheme is proposed, based on dimensionless response characteristics and normalized decay curves, to facilitate the rapid in‐field determination of conductor dip, conductance and depth of burial, for any time regime.
VERTICAL HETEROGENEITY AND MOVEOUT IN THE ONE‐DIMENSIONAL MEDIUM*
Authors: VETTER W.J.
Published: April 2006

Since the important contributions of Dürbaum and Dix, 30 years ago, velocity profile estimation procedures on horizontally layered and vertically heterogeneous media from seismic probing data have been based largely on hyperbolic moveout models and RMS and stacking velocity concepts. Re‐examination of the fundamentals reveals that quantitative velocity heterogeneity and canonical valocity profiles have been implicit factors for moveout modelling and for profile inversion in the use of the Dix procedure. Heterogeneity h is the ratio (and vRMS the geometric or harmonic mean) of the path‐average and time‐average velocities for a raypath or, in a more restricted sense, for the normal ray belonging to a velocity profile. The canonical profile for a given velocity profile or profile segment is a moveout‐equivalent monotonically increasing ramp‐like profile.

The ramp or constant gradient in depth is the simplest velocity profile approximator which can explicitly accommodate velocity heterogeneity. A ramp model structure is detailed which facilitates moveout simulation and model parameter estimation, and the parametric effects are explored. The horizontal offset range is quantified for which this model can give good moveout approximations.
STUDIES OF ROADWAY MODES IN A COAL SEAM BY DISPERSION AND POLARIZATION ANALYSIS: A CASE HISTORY*
Authors: KRAJEWSKI P. , DRESEN L. , SCHOTT W. , RÜTER H.
Published: April 2006

Abstract

Field data from two‐component in‐seam seismic measurements are used to study roadway modes and their interaction with reflected seam waves. Using the multiple‐filter technique to investigate the dispersion behaviour of the different waves, it can be shown that the roadway modes disperse very similarly to the related transmitted seam waves. However, because of the free surface of the coal face, the dispersion curves of the roadway modes show a velocity reduction and a slight shift to lower frequencies compared to those of the related transmitted seam waves. Polarization analysis using hodograms, rectilinearity and polarization angle confirms these results. The parameters found by polarization analysis can be used to design polarization filters which help to separate roadway modes and reflected events in the traveltime range of superposition in the presented field case.
HYBRID SEISMIC MODELLING: A TECHNIQUE TO COMBINE PHYSICAL AND COMPUTER METHODS FOR VERTICAL WAVE INCIDENCE*
Authors: MEISTER J. , DRESEN L.
Published: April 2006

Abstract

A hybrid seismic modelling technique has been developed to investigate complex geological phenomena. Those parts of a geological structure which are too complicated to be treated theoretically are studied by two‐dimensional physical models; other sections of the structure which can be treated theoretically, i.e., inhomogeneities in the vertical direction, are modelled by computer methods. A feedback process is used to combine the results of both physical and computer modelling.

Horizontally layered coal‐seam models are presented to test the hybrid modelling technique for normal incidence. A comparison of the hybrid seismograms with pure synthetic seismograms shows an acceptable conformity for normal incidence. A hybrid zero‐offset section is shown to investigate a complex geological structure in the Ruhr coalfield in Germany.
MOVING SOURCE PROFILING (MSP)1
Authors: BRAUNER W. , DÜRSCHNER H. , KOOPMANN B. , MARSCHALL R. , PETERS K.
Published: April 2006

Moving source profiling is a modification of walk‐away vertical seismic profiling in which the source is moved along a line across a well while the signal is recorded in the well at a certain depth. The method was designed to better predict the target horizon below the drill bit and away from the well location. The method has several advantages in areas of complicated overburden.

In overthrust regions, the receiver is placed below much of the complicated structure to minimize distortion of the reflected signal. The final seismic image is a depth presentation of the subsurface structure and stratigraphy based on wavefront calculations. This depth estimation is obtained without extensive processing of the recorded data. The final result is available within a few days and can help interpreters to decide if and where to sidetrack the well. The method is demonstrated using an example from the overthrust zone of the Lower Saxonian Basin and the Pompeckj's well in Northern Germany.
SEISMIC VIBRATOR MODELLING1
Authors: BAETEN G. J. M. , FOKKEMA J. T. , ZIOLKOWSKI A. M.
Published: April 2006

The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half‐space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far‐field of the medium are derived and it is shown that the far‐field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium.

The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load.

The theory is applied to the Vibroseis configuration, using a P‐wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field.

The accuracy of three different phase‐feedback signals is compared using synthetic data. Baseplate velocity phase‐feedback leads to huge deviations in the determination of the far‐field wavelet; reaction mass acceleration phase‐feedback looks stable but neglects the differentiating earth filter; and phase‐feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate.

The model can be extended to a lossy layered earth.
MULTIFREQUENCY INVERSION OF INDUCTION LOGS1
Authors: KUTH CH. , NEUBAUER F. M.
Published: April 2006

The concept of multifrequency induction logging simulations in the frequency range of 10 kHz to 1 MHz, applied to two‐dimensional, axial symmetric model geometries, is presented. The scalar Helmholtz equation has been solved by a finite‐element procedure. The model domain has been discretisized under the condition that the discontinuities in conductivity are represented by the nodes of the adjacent triangular elements. The modification of the signal distribution by the skin effect is illustrated for several models. Several sets of induction logs have been calculated with particular consideration of the frequency‐dependent conductivities and permittivities.

The improvement of a multifrequency inversion technique, based on standard least‐squares methods, is shown for a two‐layer model including borehole and invasion zones. Using this improved inversion technique we can state, as an additional inversion parameter, the frequency dependence of each inverted rock conductivity.
PRINCIPLES AND APPLICATION OF MAXIMUM KURTOSIS PHASE ESTIMATION1
Authors: LONGBOTTOM J. , WALDEN A. T. , WHITE R. E.
Published: April 2006

Methods of minimum entropy deconvolution (MED) try to take advantage of the non‐Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band‐pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band‐limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters.

The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal‐dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data.

Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full‐band, noise‐free data.
ON THE ABSORPTION‐DISPERSION CHARACTERISTICS OF CHANNEL WAVES PROPAGATING IN COAL SEAMS OF VARYING THICKNESS1
Authors: DOBRÓKA M.
Published: April 2006

The WKB‐method is used for the derivation of both the complex dispersion relation and displacement functions for Love channel‐waves that propagate in a coal seam of varying thickness. The constant Q‐model is used to describe the anelastic friction. With numerical solutions of the absorption‐dispersion relation, the influence of thickness changes on the phase velocity and absorption coefficient of Love seam‐waves is analysed at various frequencies. It is shown that the changes in the seam thickness can be optimally detected around the average Airy‐phase frequency. An equivalence is pointed out between the wave guide structures: homogeneous with varying seam thickness and horizontally inhomogeneous with constant seam thickness.
THE NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS CAN BE PERFORMED EITHER BY TIME EXTRAPOLATION OR BY DEPTH EXTRAPOLATION1
Authors: TARANTOLA A. , JOBERT G. , TREZEGUET D. , DENELLE E.
Published: April 2006

The classical aim of non‐linear inversion of seismograms is to obtain the earth model which, for null initial conditions and given sources, best predicts the observed seismograms. This problem is currently solved by an iterative method: each iteration involves the resolution of the wave equation with the actual sources in the current medium, the resolution of the wave equation, backwards in time, with the current residuals as sources; and the correlation, at each point of space, of the two wavefields thus obtained.

Our view of inversion is more general: we want to obtain a whole set of earth model, initial conditions, source functions, and predicted seismograms, which are the closest to some a priori values, and which are related through the wave equation. It allows us to justify the previous method, but it also allows us to set the same inverse problem in a different way: what is now searched for is the best fit between calculated and a priori initial conditions, for given sources and observed surface displacements. This leads to a completely different iterative method, in which each iteration involves the downward extrapolation of given surface displacements and tractions, down to a given depth (the‘bottom’), the upward extrapolation of null displacements and tractions at the bottom, using as sources the initial time conditions of the previous field, and a correlation, at each point of the space, of the two wavefields thus obtained. Besides the theoretical interest of the result, it opens the way to alternative numerical methods of resolution of the inverse problem. If the non‐linear inversion using forward‐backward time propagations now works, this non‐linear inversion using downward‐upward extrapolations will give the same results but more economically, because of some tricks which may be used in depth extrapolation (calculation frequency by frequency, inversion of the top layers before the bottom layers, etc.).
COMMON REFLECTION POINT DATA‐STACKING TECHNIQUE FOR CONVERTED WAVES1
Authors: TESSMER G. , BEHLE A.
Published: April 2006

For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PS‐ and SP‐type in a stack of horizontal layers.

The coordinates of the conversion points for waves of PS‐ or SP‐type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio vp/vs. Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of vp/vs is required to obtain the CCP for a given reflector depth.

A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix‐type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.
SEISMIC MODELLING: HIGH‐FREQUENCY RANGE1
Authors: ALMOSSAWI H. I. H.
Published: April 2006

An increase in the grain/pore size can cause the received echo signal to be distorted due to the preferential attenuation of the high‐frequency components of the transmitted acoustic signal. Therefore, a rock acts as a low‐pass filter and the property of the filter has a linear relation to the grain/pore size. The results have shown that P‐ and S‐wave attenuations can be used to characterize selected internal characteristics of a rock. For example, an increase in the differential stress can cause an increase in the attenuation, due to the sensitivity of the S‐wave to microcracks.
THE DETECTION OF BURIED PLACER DEPOSITS BY GROUND MAGNETIC SURVEY1
Authors: SCHWARZ E. J. , WRIGHT N.
Published: April 2006

A method is proposed to detect buried magnetite concentrations within river sediments. Model studies show that relatively small (thickness 1 m, width 10 m) plate‐shaped volumes with magnetite contents of 0.5% within a non‐magnetic matrix can be detected by a detailed ground magnetic survey using a sensitive (0.1 nT) magnetometer. Tests along lines perpendicular to the river but at a different angle to the bedrock trend (or the aeromagnetic anomaly trend) reveal that essentially all total field and vertical’gradient’anomalies detected in the profiles are elongated in the river and/or valley direction. This shows that the anomaly sources are (buried) volumes of higher magnetite content within the river sediments. Further evidence for this is (1) that higher intensity total field and vertical’gradient’anomalies occur in an area where the river cuts through strongly magnetic serpentinites, (2) the absence of high frequency anomalies over unsorted glacial till, and (3) some features on power spectra. Relatively large volumes of high magnetite concentrations within the river sediments may well contain the highest concentration of heavy economic minerals such as gold. Consequently, the areas of greatest interest in the exploitation of buried placers may be selected from maps obtained by detailed magnetic surveys either on the ground or at low altitude by helicopter.
A GYRO‐ORIENTED 3‐COMPONENT BOREHOLE MAGNETOMETER FOR MINERAL PROSPECTING, WITH EXAMPLES OF ITS APPLICATION1
Authors: BOSUM W. , EBERLE D. , REHLI H.‐J.
Published: April 2006

A triple axis borehole magnetometer is described that consists of a Förster‐probe (fluxgate) triplet (sensitivity 1 n T), a Förster‐probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16‐bit AD converter). The sensitive fluxgate‐magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3‐component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically‐determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3‐component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.
SEISMIC INVERSION BY A RMS BORN APPROXIMATION IN THE SPACE‐TIME DOMAIN1
Authors: FOKKEMA JAKOB T. , VAN DEN BERG PETER M.
Published: April 2006

Abstract

A new approximate method to calculate the space‐time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half‐spaces where the source and the receiver are located in the upper half‐space. A distorted‐wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root‐mean‐square acoustic wave speed. A closed‐form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.
RECENT DEVELOPMENTS IN UNDERGROUND GRAVITY SURVEYS1
Authors: CASTEN U. , GRAM CHR.
Published: April 2006

Abstract

Underground gravity observations in deep coal mines using the conventional gravity meters Worden (type Master) and LaCoste‐Romberg (model D), both of which have been adapted to the fire damp regulations, can be accurate to ± 10 and ± 3 μgal, respectively. For underground determination of the vertical gradient of gravity the LaCoste‐Romberg meter is used together with a specially designed measuring tower. Using this euipment an accuracy in tower gradient observations of ± 30 E was obtained.

To apply the equipment to precision gravity observations in underground situations an additional correction, i.e. a gallery correction, is needed. High accuracy in correction is achieved by a new method of three‐dimensional modelling. The gravity effect is computed for bodies with a surface approximated by triangular elements, which are generated from corner points of the body. The combination of gallery correction with tower gradient data leads to a new method for in situ density determination. It offers the possibility of horizontal instead of vertical density profiling.

To demonstrate the effectiveness of the developments in underground observations the localization of a pump room is presented. Microgravity and tower gradient observations were carried out to detect the cavity. The horizontal gradient was also calculated to give a more reliable location.
3D ACOUSTIC REVERSE‐TIME MIGRATION1
Authors: CHANG WEN‐FONG , McMECHAN GEORGE A.
Published: April 2006

Acoustic reverse‐time finite‐difference migration for zero‐offset data is extended from two‐ to three‐dimensional media. The formulation is based on the full three‐dimensional acoustic wave equation and so has no dip restrictions and it involves extrapolation in a velocity distribution variable in three dimensions. The algorithm is demonstrated by successful migration of synthetic data sets for three models: a point diffractor, an oblique pinch‐out, and a dome overlying a planar reflector.
DIRECT CURRENT ELECTRIC POTENTIAL FIELD ASSOCIATED WITH TWO SPHERICAL CONDUCTORS IN A WHOLE‐SPACE1
Authors: ALDRIDGE D. F. , OLDENBURG D. W.
Published: April 2006

Bispherical coordinates are used to derive an exact mathematical solution for the potential field generated by direct current electric conduction in an earth model consisting of two spherical inclusions in a uniform whole‐space. The solution takes the form of a spherical harmonic expansion in bispherical coordinates; coefficients in the expansion are obtained by solving sets of linear equations. Rapid forward modelling of numerous interesting situations in d.c. resistivity prospecting is facilitated by the generality and computational efficiency inherent to this new solution. For example, the accuracy of image (or superposition) methods for calculating potential solutions can be quantified. Similarly, the ability of d.c. conduction methods to resolve two distinct bounded bodies in three‐dimensional space can be examined by repeatedly calculating the secondary potential or apparent resistivity response of an earth model as a selected parameter is varied. Synthetic mise à la masse, crosshole, or areal potential data sets can be generated for subsequent use in inversion studies. Improvements in solution technique derived here also apply to a simpler model consisting of a single sphere buried in a half‐space.
VELOCITY‐STACK PROCESSING1
Authors: YILMAZ ÖZDOǦAN
Published: April 2006

Abstract

A conventional velocity‐stack gather consists of constant‐velocity CMP‐stacked traces. It emphasizes the energy associated with the events that follow hyperbolic traveltime trajectories in the CMP gather. Amplitudes along a hyperbola on a CMP gather ideally map onto a point on a velocity‐stack gather. Because a CMP gather only includes a cable‐length portion of a hyperbolic traveltime trajectory, this mapping is not exact. The finite cable length, discrete sampling along the offset axis and the closeness of hyperbolic summation paths at near‐offsets cause smearing of the stacked amplitudes along the velocity axis. Unless this smearing is removed, inverse mapping from velocity space (the plane of stacking velocity versus two‐way zero‐offset time) back to offset space (the plane of offset versus two‐way traveltime) does not reproduce the amplitudes in the original CMP gather. The gather resulting from the inverse mapping can be considered as the model CMP gather that contains only the hyperbolic events from the actual CMP gather. A least‐squares minimization of the energy contained in the difference between the actual CMP gather and the model CMP gather removes smearing of amplitudes on the velocity‐stack gather and increases velocity resolution. A practical application of this procedure is in separation of multiples from primaries.

A method is described to obtain proper velocity‐stack gathers with reduced amplitude smearing. The method involves a t2‐stretching in the offset space. This stretching maps reflection amplitudes along hyperbolic moveout curves to those along parabolic moveout curves. The CMP gather is Fourier transformed along the stretched axis. Each Fourier component is then used in the least‐squares minimization to compute the corresponding Fourier component of the proper velocity‐stack gather. Finally, inverse transforming and undoing the stretching yield the proper velocity‐stack gather, which can then be inverse mapped back to the offset space. During this inverse mapping, multiples, primaries or all of the hyperbolic events can be modelled. An application of velocity‐stack processing to multiple suppression is demonstrated with a field data example.
SOME EFFECTS OF MULTIPLE LATERAL IN HOMOGENEITIES IN MAGNETOTELLURICS1
Authors: GROOM R. W. , BAILEY R. C.
Published: April 2006

The analytical solution, for the H‐polarization magnetotelluric impedance, of a series of multiple, vertical, conducting slabs (dikes) embedded in a host medium is extended to an infinite array in order to model an anisotropic layer. The solution is used to study the effects of such strongly anisotropic media on the surface impedance. At low frequencies such vertically laminated structures behave as a bulk material. It is shown that the effective bulk parameters are those expected from d.c. theory. However, practical electrode separations may not be long enough or adequately positioned to correctly obtain these bulk parameters from the measured impedance. Thus, such structures can masquerade as quite different one‐dimensional structures. A haphazard use of long electrode spacings will not necessarily produce correct results.
ITERATIVE TOMOGRAPHIC METHODS TO LOCATE SEISMIC LOW‐VELOCITY ANOMALIES: A MODEL STUDY1
Authors: KRAJEWSKI CHRISTINA , DRESEN LOTHAR , GELBKE CHRISTOPH , RÜTER HORST
Published: April 2006

The possibilities for reconstructing seismic velocity distributions containing low‐velocity anomalies by iterative tomographic methods are examined studying numerical and analogue 2D model data. The geometrical conditions of the model series were designed to generalize the geometrical characteristics of a typical cross‐hole tomographic field case. Models with high (30%) and low (8%) velocity contrasts were realized. Traveltimes of 2D ultrasonic P‐waves, determined for a dense net of raypaths across each model, form the analogue data set. The numerical data consists of traveltimes calculated along straight raypaths. Additionally, a set of curved‐ray traveltimes was calculated for a smoothed version of the high‐contrast model.

The Simultaneous Iterative Reconstruction Technique (SIRT) was chosen from the various tomographic inversion methods. The abilities of this standard procedure are studied using the low‐contrast model data. The investigations concentrate on the resolving power concerning geometry and velocity, and on the effects caused by erroneous data due to noise or a finite time precision. The grid spacing and the source and receiver patterns are modified. Smoothing and slowness constraints were tested. The inversion of high‐contrast analogue model data shows that curved raypaths have to be considered. Hence, a ray‐tracing algorithm using velocity gradients was developed, based on the grid structure of the tomographic inversion. This algorithm is included in the SIRT‐process and the improvements concerning anomaly localization, resolution and velocity reconstruction are demonstrated. Since curved‐ray tomography is time‐consuming compared with straight‐ray SIRT, it is necessary to consider the effects of grid spacing, ray density, slowness constraints and the
ON THE ROLE OF PARTIAL RAY EXPANSION IN THE COMPUTATION OF RAY SYNTHETIC SEISMOGRAMS FOR LAYERED STRUCTURES1
Authors: COVEY J. D. , HRON F. , PEACOCK K. L.
Published: April 2006

This paper presents results of testing an efficient ray generation scheme needed whenever ray synthetic seismograms are to be computed for layered models with more than 10‘ thick’layers. Our ray generation algorithm is based on the concept of kinematically equivalent waves (the kinematic analogs) having identical traveltimes along different ray‐paths between the source and the receiver, both located on the surface of the model. These waves, existing in any medium composed of laterally homogeneous parallel layers, interfere at any location along the recording surface, thereby producing a composite wavelet whose amplitude and shape depend directly on the number of kinematic analogs (the multiplicity factor). Hence, explicit knowledge of the multiplicity factor is crucial for any analysis based on the amplitude and shape of individual wavelets, such as wavelet shaping, Q estimation, or linearized wavelet inversion.

For unconverted waves, such as those discussed in this paper, the multiplicity factor can be computed analytically using formulae given in the Appendix; for converted waves, the multiplicity factor should be computed numerically, using the algorithm employed for the computation of the seismograms presented in a previous paper by one of the authors.