bluuebunny/crossref_metadata_2025 huggingface dataset:
The usefulness of multicomponent, time‐domain airborne electromagnetic measurements
Authors: Smith Richard S. , Keating Pierre B.
Published: April 2003

Time‐domain airborne electromagnetic (AEM) systems historically measure the inline horizontal (x) component. New versions of the electromagnetic systems are designed to collect two additional components [the vertical (z) component and the lateral horizontal (y) component] to provide greater diagnostic information. In areas where the geology is near horizontal, the z‐component response provides greater signal‐to‐noise, particularly at late delay times. This allows the conductivity to be determined to greater depth. In a layered environment, the symmetry implies that the y component will be zero; hence a nonzero y component will indicate a lateral inhomogeneity. The three components can be combined to give the “energy envelope” of the response. Over a vertical plate, the response profile of this envelope has a single positive peak and no side lobes. The shape of the energy envelope is dependent on the flight direction, but less so than the shape of the x‐component response profile. In the interpretation of discrete conductors, the z‐component data can be used to ascertain the dip and depth to the conductor using simple rules of thumb. When the profile line is perpendicular to the strike direction and over the center of the conductor, the y component will be zero; otherwise it appears to be a combination of the x and z components. The extent of contamination of the y component by the x and z components can be used to ascertain the strike direction and the lateral offset of the target, respectively. Having the z and y component data increases the total response when the profile line has not traversed the target. This increases the possibility of detecting a target located between adjacent flight lines or beyond a survey boundary.
Resistive‐limit, time‐domain AEM apparent conductivity
Authors: Annan A. Peter , Smith Richard S. , Lemieux Jean , O’Connell Michael D. , Pedersen Rolf N.
Published: April 2003

On‐time measurements, which can be obtained with existing airborne transient electromagnetic (AEM) systems, are used to map the apparent conductivity of the ground. Such measurements can extend the conductivity aperture of these systems substantially at the low end of the conductivity range. A theoretical analysis is given that provides a simple, approximate, resistive‐limit solution for any transient EM waveform. The approximate result is compared to the full‐numerical result for the specific case of the GEOTEM system over a conductive half‐space. Examples of GEOTEM data reduced to apparent conductivity using the approximate analytical solution are presented from surveys for kimberlites and massive sulfide deposits.
A semianalytical solution for the propagation of electromagnetic waves in 3‐D lossy orthotropic media
Authors: Carcione José M. , Cavallini Fabio
Published: April 2003

We derive an analytical solution for electromagnetic waves propagating in a 3‐D lossy orthotropic medium for which the electric permittivity tensor is proportional to the magnetic permeability tensor. The solution is obtained through a change of coordinates that transforms the spatial differential operator into a pure Laplace operator and the differential equations for the electric and magnetic field components into pure Helmholtz equations. A plane‐wave analysis gives the expression of the slowness and attenuation surfaces as a function of frequency and propagation direction. The transverse electric and transverse magnetic surfaces degenerate to one repeated sheet so that, in any direction, the two differently polarized plane waves have the same slowness. A computer experiment with realistic geophysical parameters has shown that the anisotropic propagation and dissipation properties emerging from plane‐wave analysis agree with the different time histories of the magnetic field computed at a number of representative receiver locations.
Cross‐equalization data processing for time‐lapse seismic reservoir monitoring: A case study from the Gulf of Mexico
Authors: Rickett J. E. , Lumley D. E.
Published: April 2003

Nonrepeatable noise, caused by differences in vintages of seismic acquisition and processing, can often make comparison and interpretation of time‐lapse 3‐D seismic data sets for reservoir monitoring misleading or futile. In this Gulf of Mexico case study, the major causes of nonrepeatable noise in the data sets are the result of differences in survey acquisition geometry and binning, temporal and spatial amplitude gain, wavelet bandwidth and phase, differential static time shifts, and relative mispositioning of imaged reflection events. We attenuate these acquisition and processing differences by developing and applying a cross‐equalization data processing flow for time‐lapse seismic data. The cross‐equalization flow consists of regridding the two data sets to a common grid; applying a space and time‐variant amplitude envelope balance; applying a first pass of matched filter corrections for global amplitude, bandwidth, phase and static shift corrections, followed by a dynamic warp to align mispositioned events; and, finally, running a second pass of constrained space‐variant matched filter operators. Difference sections obtained by subtracting the two data sets after each step of the cross‐equalization processing flow show a progressive reduction of nonrepeatable noise and a simultaneous improvement in time‐lapse reservoir signal.
3‐D characterization of a clastic reservoir analog: From 3‐D GPR data to a 3‐D fluid permeability model
Authors: Szerbiak R. B. , McMechan G. A. , Corbeanu R. , Forster C. , Snelgrove S. H.
Published: April 2003

A three‐dimensional (3‐D) 100 MHz ground‐penetrating radar (GPR) data volume is the basis of in‐situ characterization of a fluvial reservoir analog in the Ferron Sandstone of east‐central Utah. We use the GPR reflection times to image the bounding surfaces via 3‐D velocity estimation and depth migration, and we use the 3‐D amplitude distribution to generate a geostatistical model of the dimensions, orientations, and geometries of the internal structures from the surface down to ∼12 m depth. Each sedimentological element is assigned a realistic fluid permeability distribution by kriging with the 3‐D correlation structures derived from the GPR data and which are constrained by the permeabilities measured in cores and in plugs extracted from the adjacent cliff face. The 3‐D GPR image shows that GPR facies changes can be interpreted to locate sedimentological bounding surfaces, even when the surfaces do not correspond to strong GPR reflections. The site contains two main sedimentary regimes. The upper ∼5 m contain trough cross‐bedded sandstone with average permeability of ∼40 md and maximum correlation lengths [Formula: see text]. The lower ∼7 m contain scour and fill fluvial deposits with average permeability varying from ∼30 md to ∼15 md as clay content increases, and maximum correlation lengths [Formula: see text]. These representations are suitable for input to fluid flow modeling.
Inductive interaction between closely spaced steeply dipping tabular conductors located in a resistive host
Authors: Duckworth K. , Clement B.
Published: April 2003

Physical scale‐model studies of the responses provided by horizontal coplanar and vertical coincident coil moving‐source electromagnetic systems when operated over closely spaced, steeply dipping, tabular conductors located in a resistive host are presented. For separations of the conductors that permit separate anomalies to be identified, the detected effect of inductive interaction between the conductors depends on the configuration of the exploration device. As conductors are moved closer together, the horizontal coplanar coil system produces responses for each conductor that become progressively weaker than the individual responses when each conductor is isolated. By comparison, vertical coincident coils detect an initial increase of the anomalies from the individual conductors as the conductor separation is reduced until just before the separate anomalies merge. As the anomalies merge, the vertical coincident coil responses decline in magnitude. After the anomalies merge and present the appearance of the response of a single conductor, both coil systems record an expected strong increase of response which exceeds the response when the conductors are in contact. These mutual inductive interactions cause significant variations in the depth estimates provided by horizontal coplanar coils. Depth estimates provided by vertical coincident coils are always smaller than the true target depths. The vertical coincident coil configuration displays an ability to identify separate conductors at significantly smaller conductor separations than can the horizontal coplanar coils.
Examination of the relative influence of current gathering on fixed loop and moving source electromagnetic surveys
Authors: Duckworth K. , Nichols T. D. , Krebes E. S.
Published: April 2003

A physical model study was conducted of the responses provided by moving‐source and fixed‐loop frequency‐domain electromagnetic prospecting systems when operated over the same target conductor located in a conductive host environment. The results indicate that the fixed‐loop responses display enhancement due to the current gathering effect that exceeds that seen in the moving‐source responses by at least an order of magnitude for all the source‐to‐receiver separations tested for the moving‐source system. The results also indicate that as transmitter frequency is increased the current gathering effect displays an abrupt onset in the responses provided by both systems, but that this onset begins at a frequency which is a decade lower for the fixed‐loop system than the corresponding frequency of onset for the moving‐source system. The current gathering enhancement effects show a clear reduction with increase of target depth for the fixed‐loop system but an increase with depth for the moving‐source system. The model parameters employed in these studies are shown to be well related to typical conditions found in full‐scale surveys.
Mapping remanent magnetization using the local phase
Authors: Thurston J. B.
Published: April 2003

For uniformly magnetized 2‐D contacts, thin sheets, horizontal cylinders, and dykes, the apparent inclination of the magnetization vector (i.e., the inclination projected into a plane perpendicular to the strike of a 2‐D anomaly) can be computed from the difference in the anomaly shapes of the total field and the vertical field. The calculation can be performed using gridded data, resulting in a grid containing estimates of apparent inclination. These estimates take into account varying source‐strike direction. This quantity is important for computing source dip wherever the data are likely to be affected by the presence of remanent magnetization. As well, it is useful for input to forward models computed along profiles perpendicular to strike. Further, without knowledge of source dip, the apparent inclination can be used to map the presence of remanent magnetization. This is an aid to geologic mapping, allowing isolated paleomagnetic measurements to be extrapolated over a broad area. Knowing the extent of remanent magnetization can also help indicate how well the reduction to the pole process will work. The method requires both total‐field and vertical‐field component data. Most modern airborne surveys are conducted with optically pumped magnetometers that record only the total field. To apply the method in these cases requires estimation of the vertical component from the total field using a 2‐D Fourier operator, which in turn requires the assumption that the earth’s field direction is constant over the study region and the induced field is small compared to the ambient field. This restricts application to areas of several hundred square kilometers. Apparent inclination is estimated from synthetic data computed over a generalized cross‐section of the center of the Manicouagan impact structure (Canada) and to measured aeromagnetic data over this structure. The results of the synthetic test indicate that for the northern and southern edges of this source, the method can distinguish the present‐day and paleomagnetic fields with the same spatial resolution as the analytic signal has for identifying magnetization boundaries. Application to the airborne data indicates that where the source strikes at high angles to the declination of the present‐day field, the estimated apparent inclination is influenced by both the remanent and inducing fields. For other strikes the field is almost entirely remanent or no distinction between the present‐day and paleomagnetic fields can be made. As well, the source dip, estimated from the local phase and the estimated apparent inclination, is consistent with previously published results.
Inversions of surface and borehole data from large‐loop transient electromagnetic system over a 1‐D earth
Authors: Zhang Z. , Xiao J.
Published: April 2003

Large‐loop electromagnetic (EM) systems that measure transient EM (TEM) data on the surface or in boreholes have shown increased application in exploration geophysics. Accurate interpretation of borehole TEM data is necessary to discover deep hidden targets that cannot be detected with surface systems. However, the inversion of borehole TEM data has not been fully addressed. In this paper, we study the propagation of the TEM field from a large‐loop EM borehole system inside a layered earth and develop a new inversion algorithm to reconstruct layered conductivity structures from large‐loop TEM data measured with both surface and borehole configurations. The magnetic field and sensitivities are first computed in the frequency domain and are then transformed into the time domain where the inversion is performed. The surface data have a higher S/N ratio at early time channels, while the borehole data have a higher S/N ratio at late time channels. Consequently, the surface data can be inverted to better resolve shallow structures, and the borehole data can be used to better detect deep structures. The merits of joint inversions of borehole and surface data are explored. We test our inversion algorithm using numeric examples.
Characterization of geological boundaries using 1‐D wavelet transform on gravity data: Theory and application to the Himalayas
Authors: Martelet G. , Sailhac P. , Moreau F. , Diament M.
Published: April 2003

We investigate the use of the continuous wavelet transform for gravity inversion. The wavelet transform operator has recently been introduced in the domain of potential fields both as a filtering and a source‐analysis tool. Here we develop an inverse scheme in the wavelet domain, designed to recover the geometric characteristics of density heterogeneities described by simple‐shaped sources. The 1‐D analyzing wavelet we use associates the upward continuation operator and linear combinations of derivatives of any order. In the gravity case, we first demonstrate how to localize causative sources using simple geometric constructions. Both the upper part of the source and the whole source can be studied when considering low or high altitudes, respectively. The homogeneity degree of the source is deduced without prior information and allows us to infer its shape. Introducing complex wavelets, we derive analytically the scaling behavior of the wavelet coefficients for the dyke and the step sources. The modulus term is used in an inversion procedure to recover the thickness of the source. The phase term provides its dip. This analysis is performed on gravity data we measured along a profile across the Himalayas in Nepal. Good agreement of our results with well‐documented thrusting structures demonstrates the applicability of the method to real data. Also, deeper, less constrained structures are characterized.
A geometric optics model for high‐frequency electromagnetic scattering from dielectric cylinders
Authors: Baumgartner François , Munk Jens , Daniels Jeffrey
Published: April 2003

The cylinder is a fundamental shape for (2‐D) geophysical modeling, and cylindrical objects (e.g., pipes) are a common target for ground penetrating radar. This paper presents physical and theoretical model responses for a cylinder which provide insight into responses that can be anticipated in field data. We calculate the exact expressions for the scattered field components of an obliquely incident plane wave over an infinitely long homogeneous dielectric cylinder and express them in the time domain. We project the field on a horizontal plane over the dielectric cylinder and interpret them for a large range of permittivity contrasts. The high‐frequency approximation presented in this paper includes the processes of specular reflection and critical refraction, which satisfy Snell’s law. Assuming the velocity of the surface waves is equal to the velocity of the fastest medium, and assuming their travel path is the shortest one possible, we derive a geometric optics model which is valid over a wide range of permittivities. We show that the critically refracted response can be separated and measured from the specular reflections in the received signal. The identification and isolation of these different responses of the bistatic measurements enable a characterization of the target’s properties, such as its size, orientation, and formation. We confirm our theoretical results by comparison with measurements using a physical model.
Scattering, symmetry, and bias analysis of source‐position estimates in Euler deconvolution and its practical implications
Authors: Silva J. B. C. , Barbosa V. C. F. , Medeiros W. E.
Published: April 2003

Despite being widely used, Euler deconvolution has received little attention in its theoretical aspects. We obtain analytical estimators [Formula: see text] and [Formula: see text] for the horizontal [Formula: see text] and the vertical [Formula: see text] source positions, which are the parameters to be estimated when the structural index is assigned a tentative value. By analyzing the estimators’ properties, we show two things. (1) Scattering of the alternative solutions associated with different data window positions has two components: data noise and the use of a wrong tentative value for the structural index, (2) The differences [Formula: see text] and [Formula: see text], as a function of the data window position, exhibit antisymmetric and symmetric behaviors, respectively, about [Formula: see text] when the magnetization and the geomagnetic field inclinations are 90°, 0°, or 45°. For intermediate inclinations there is a moderate departure from the symmetry properties. This analysis shows that the criterion for determining the structural index as the tentative value producing the smallest solution scattering is theoretically sound but occasionally fails in practice because data noise also contributes to solution scattering. In addition, the lower sensitivity of the averages of estimates of the horizontal position (as compared with the vertical position) occurs because [Formula: see text] displays an antisymmetric behavior with respect to the true horizontal position while the estimates of the vertical position display a symmetric behavior with respect to the same point.
Seismic reservoir mapping from 3‐D AVO in a North Sea turbidite system
Authors: Avseth P. , Mukerji T. , Jørstad A. , Mavko G. , Veggeland T.
Published: April 2003

We present a methodology for estimating uncertainties and mapping probabilities of occurrence of different lithofacies and pore fluids from seismic amplitudes, and apply it to a North Sea turbidite system. The methodology combines well log facies analysis, statistical rock physics, and prestack seismic inversion. The probability maps can be used as input data in exploration risk assessment and as constraints in reservoir modeling and performance forecasting. First, we define seismic‐scale sedimentary units which we refer to as seismic lithofacies. These facies represent populations of data (clusters) that have characteristic geologic and seismic properties. In the North Sea field presented in this paper, we find that unconsolidated thick‐bedded clean sands with water, plane laminated thick‐bedded sands with oil, and pure shales have very similar acoustic impedance distributions. However, the [Formula: see text] ratio helps resolve these ambiguities. We establish a statistically representative training database by identifying seismic lithofacies from thin sections, cores, and well log data for a type well. This procedure is guided by diagnostic rock physics modeling. Based on the training data, we perform multivariate classification of data from other wells in the area. From the classification results, we can create cumulative distribution functions of seismic properties for each facies. Pore fluid variations are accounted for by applying the Biot‐Gassmann theory. Next, we conduct amplitude‐variation‐with‐offset (AVO) analysis to predict seismic lithofacies from seismic data. We assess uncertainties in AVO responses related to the inherent natural variability of each seismic lithofacies using a Monte Carlo technique. Based on the Monte Carlo simulation, we generate bivariate probability density functions (pdfs) of zero‐offset reflectivity [R(0)] versus AVO gradient (G) for different facies combinations. By combining R(0) and G values estimated from 2‐D and 3‐D seismic data with the bivariate pdfs estimated from well logs, we use both discriminant analysis and Bayesian classification to predict lithofacies and pore fluids from seismic amplitudes. The final results are spatial maps of the most likely facies and pore fluids, and their occurrence probabilities. These maps show that the studied turbidite system is a point‐sourced submarine fan in which thick‐bedded clean sands are present in the feeder‐channel and in the lobe channels, interbedded sands and shales in marginal areas of the system, and shales outside the margins of the turbidite fan. Oil is most likely present in the central lobe channel and in parts of the feeder channel.
Reservoir characterization using crosswell electromagnetic inversion: A feasibility study for the Snorre field, North Sea
Authors: Hoversten G. M. , Newman G. A. , Morrison H. F. , Gasperikova E. , Berg John‐Inge
Published: April 2003

The spatial resolution of a commercially available crosswell electromagnetic (EM) system is demonstrated using models derived from three time steps from a reservoir simulation of the Snorre field in the North Sea. The numerical simulation of the Snorre field waterflood shows that crosswell EM field measurements provide high sensitivity to changes in the reservoir over time. This sensitivity is achieved by combining the reservoir geometry derived from surface 3‐D seismic interpretation, reservoir conductivities at well locations, and constrained EM inversion of the reservoir’s electrical conductivity. Inversions of 2‐D and 3‐D numerical models show that the changes in electrical conductivity attributable to changes in water saturation can be quantitatively mapped as a function of time. The inversions provide smooth estimates of the spatial variation of reservoir electrical conductivity that can discriminate between the level of water saturation at different stages of the waterflood. Inversions performed on 2‐D data show that for the Snorre example, 3%–5% Gaussian random noise (depending on the model) can be added without a significant degradation in the inverse models. Two‐dimensional inversions of the full 3‐D data in the Snorre example can map the vertical average electrical conductivity within the reservoir in the interwell region almost as well as when the model is two dimensional (constant in strike direction). The effect of 3‐D structure does not seriously degrade 2‐D inversion in the Snorre example‐even between wells that lie in a line parallel to structure. A series of 2‐D inversions where various constraints and starting models are used demonstrates the importance of incorporating a priori information in the form of starting models and restricting the inversion domain to the reservoir zone. These tests show that totally unconstrained, smooth inversions of the interwell volume provide very limited quantitative information. However, when the reservoir geometry is constrained by seismic data and starting models are provided by linear interpolation of conductivities at well locations, the reservoir’s vertical average electrical conductivity can be predicted to within a few percent by 2‐D inversion. The snorre field consists of a full‐scale reservoir with interwell spacings that exceed 1 km where previous work has demonstrated the applicability of crosswell EM in shallow reservoirs with well separations on the order of 100 m. The simulations show that, given current transmitter and receiver technology, the magnetic fields could be measured in the Snorre field in steel‐cased wells separated from the transmitter by up to 725 m.
Vertical hydrophone cable acquisition and imaging on land
Authors: Gulati J. S. , Stewart R. R. , Hoffe B. H.
Published: April 2003

We acquired seismic data using a vertical hydrophone cable in a shallow, fluid‐filled borehole over the Blackfoot oil field in Alberta, Canada. The hydrophone data were recorded simultaneously with a surface seismic survey using dynamite sources. In addition, buried three‐component (3‐C) geophone data were acquired near the vertical cable. We observe that events on the hydrophone records are in phase with corresponding geophone data. Tube waves, which can be a problem on hydrophone data, are suppressed using a predictive deconvolution operator. Imaging, using the hydrophone data, results in a section that correlates well with a surface seismic image from vertical‐component geophone data. An anomaly, interpreted to be associated with the sand reservoir in the area, is evident on the hydrophone image (as well as on the surface seismic sections). The vertical hydrophone cable promises excellent imaging potential for land applications.
Seismic array design by spatial convolution
Authors: Kerekes Albin K.
Published: April 2003

Deriving the response of an array is one thing, designing an array to match a desired response is quite another. The first is easy, the second is not. Given a selected pass and reject requirement in the spatial frequency domain, an array can be obtained that best matches such requirement within the limits of available hardware. Optimum spatial arrays for 2‐D and 3‐D/4‐D seismic surveys can be designed using the technique of spatial convolution. Such a technique relies upon uniform arrays of differing shapes and sizes as building blocks. These building blocks are convolved in space because their selected responses matching notch points against side lobes to achieve a desired end result in the spatial frequency domain. The final array design can be made optimum for a given set of requirements, such as signal preservation within the passband, attenuation within the reject band, and azimuthal distribution for 3‐D/4‐D seismic surveys. For any given design, solely the number and the spacing of the elements limit the optimization. A rule of thumb has been observed which shows that the required number of elements in a 2‐D array for 3‐D/4‐D seismic is equal to the square of the number of elements in a 1‐D equivalent array for 2‐D seismic. It is also observed that for a given number of elements, narrow azimuth designs can offer greater attenuation than wide azimuth designs.
Estimating and interpreting velocity uncertainty in migrated images and AVO attributes
Authors: Grubb H. , Tura A. , Hanitzsch C.
Published: April 2003

Estimating a suitable velocity field for use in prestack depth migration is inherently uncertain because of limitations on the available data and estimation techniques. This uncertainty affects both the migrated depth of structures and their amplitudes in the inverted images. These effects can be estimated by performing multiple migrations with a set of velocity fields and colocating features in the migrated images. This lets us examine the imaging procedure’s sensitivity to changes in the velocity field so we can assess both structural and amplitude uncertainties in migrated images. These two types of uncertainties affect interpretation in different ways. For instance, with structural uncertainty interpretation we consider the change in migrated location of structures when deciding on drilling locations, optimizing well trajectories, or computing uncertainty in volumetric calculations. With amplitude uncertainty or amplitude versus offset (AVO) uncertainty interpretation, we consider (1) uncertainty in crossplots of pairs of AVO attributes at a point of interest or (2) uncertainty of the attribute values along identified structures. For any interpretation informing a decision, the uncertainty can help estimate risk. Our data processing approach is based on amplitude‐preserving prestack depth migration followed by AVO inversion, or AVO migration/inversion. It is valid for estimating AVO attributes in simple to moderately complex structural settings. Our methods of assessing the effect of velocity uncertainty can also be applied when obtaining structural uncertainties for a complex overburden geology or amplitude uncertainties in conventional NMO‐based AVO analysis. They may also be applied straightforwardly to any poststack attribute analysis. Key to the approach is the availability of multiple velocity fields to generate multiple migrated images. In our application, an automatic algorithm samples possible fields, but the set of fields to consider could be generated from another source, such as interpretation.
Inversion of a seismic transmission response
Authors: Robinson Enders A.
Published: April 2003

Traveling waves are used not only in exploration geophysics but also in other disciplines faced with remote detection problems. A physical system may be described in terms of the input (the source), the medium, and the output (the received signal). The received signal can be made up of either transmitted waves or reflected waves. Two types of inverse problems can be considered, namely, the inverse source problem and the inverse medium problem. In the inverse source problem, the objective is to determine the source. In the inverse medium problem, the objective is to determine the medium. Thus, in terms of this general classification, four types of problems can be encountered, namely, an inverse source problem with transmitted waves, an inverse source problem with reflected waves, an inverse medium problem with transmitted waves, and an inverse medium problem with reflected waves. Let us look at nature. Twinkle, twinkle, little star. The transmission of starlight though the atmosphere makes the star twinkle. A better image of the star can be obtained by solving an inverse source problem using the transmitted starlight. In the typical inverse source problem, the source of energy is remote, the medium transmits the source signal, and the received data are the transmitted waves. Examples are classical earthquake seismology, radio transmission, and passive sonar. Shakespeare said; “For the eye sees not by itself, but by reflection.” Thus the miracle of eyesight solves an inverse medium problem that uses reflected waves. In the typical inverse medium problem, the source of energy is local and often man‐made, the medium reflects the source signal, and the received data are the reflected waves. Examples are reflection seismology, radar, and active sonar. Thus, the two principle types of inverse problems encountered in nature are the inverse source problem with transmitted waves and the inverse medium problem with reflected waves.
Prestack Gaussian‐beam depth migration
Authors: Hill N. Ross
Published: April 2003

Kirchhoff migration is the most popular method of three‐dimensional prestack depth migration because of its flexibility and efficiency. Its effectiveness can become limited, however, when complex velocity structure causes multipathing of seismic energy. An alternative is Gaussian beam migration, which is an extension of Kirchhoff migration that overcomes many of the problems caused by multipathing. Unlike first‐arrival and most‐energetic‐arrival methods, which retain only one traveltime, this alternative method retains most arrivals by the superposition of Gaussian beams. This paper presents a prestack Gaussian beam migration method that operates on common‐offset gathers. The method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points. Gaussian beam migration of the two‐dimensional Marmousi test data set demonstrates the method’s effectiveness for structural imaging in a case where there is multipathing of seismic energy.
The Hartley transform in seismic imaging
Authors: Kühl Henning , Sacchi Maurico D. , Fertig Jürgen
Published: April 2003

Phase‐shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast Fourier transform (FFT). Generally, the Hermitian symmetry of the complex‐valued Fourier transform causes computational redundancies in terms of the number of operations and memory requirements. In practice a combination of the FFT with the well‐known real‐to‐complex Fourier transform is often used to avoid such complications. As an alternative means to the Fourier transform, we introduce the inherently real‐valued, non‐symmetric Hartley transform into phase‐shift migration techniques. By this we automatically avoid the Hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real‐to‐complex FFT. We derive the phase‐shift operator in the Hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation, split‐step migration, and split‐step double‐square‐root prestack migration in terms of the Hartley transform as examples. We test the Hartley phase‐shift operator for poststack and prestack migration using the SEG/EAGE salt model and the Marmousi data set, respectively.
The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media
Authors: Zeng Y. Q. , He J. Q. , Liu Q. H.
Published: April 2003

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, a method is developed to extend the perfectly matched layer to simulating seismic wave propagation in poroelastic media. This nonphysical material is used at the computational edge of a finite‐difference algorithm as an ABC to truncate unbounded media. The incorporation of PML in Biot’s equations is different from other PML applications in that an additional term involving convolution between displacement and a loss coefficient in the PML region is required. Numerical results show that the PML ABC attenuates the outgoing waves effectively.
Spectral analysis of a ghost
Authors: Hamarbitan N. S. , Margrave G. F.
Published: April 2003

A seismic line was shot such that the source‐ghost effect from two different dynamite source patterns could be compared. Two 15‐shot seismic datasets were created that were identical in all respects except that one used 4 kg of explosives in a single 18‐m hole, while the other used 2 kg of explosives in each of two 9‐m holes. After identical processing, the final stacked sections of the 18‐m and 9‐m datasets are dramatically different in character and temporal resolution. An f‐x spectral analysis of the stacked sections reveals that the 18‐m data shows a loss in power and phase coherence from 45 to 58 Hz, while the 9‐m data shows a similar effect from 65 to 78 Hz. A spectral notch, centered near 55 Hz, due to a source ghost is suggested as the reason for the lower power in the 18‐m dataset. The 9‐m data is consistent with a spectral notch at a higher central frequency near 72 Hz. Above its spectral notch, 18‐m data shows a reemergence of weak signal that persists to near 80 Hz; the 9 m dataset shows little signal above 65 Hz. Examination of raw shot records shows that these effects are very difficult to observe in field records. Without specialized deghosting, the 9‐m dataset shows greater temporal resolution; however, the 18‐m dataset has a broader signal bandwidth and is potentially superior.
Narrow‐band spectral analysis and thin‐bed tuning
Authors: Marfurt K. J. , Kirlin R. L.
Published: April 2003

Running window seismic spectral decomposition has proven to be a very powerful tool in analyzing difficult‐to‐delineate thin‐bed tuning effects associated with variable‐thickness sand channels, fans, and bars along an interpreted seismic horizon or time slice. Unfortunately, direct application of spectral decomposition to a large 3‐D data set can result in a rather unwieldy 4‐D cube of data. We develop a suite of new seismic attributes that reduces the input 20–60 running window spectral components down to a workable subset that allows us to quickly map thin‐bed tuning effects in three dimensions. We demonstrate the effectiveness of these new attributes by applying them to a large spec survey from the Gulf of Mexico. These two thin‐bed seismic attributes provide a fast, economic tool that, when coupled with other attributes such as seismic coherence and when interpreted within the framework of geomorphology and sequence stratigraphy, can help us quickly evaluate large 3‐D seismic surveys. Ironically, in addition to being more quantitatively linked to bed thickness, the thin‐bed attributes described here allow us to analyze thicker features than the conventional instantaneous and response frequencies, which cannot calculate the spectral interference between two well‐separated reflectors.
Mapping lithofacies and pore‐fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics
Authors: Mukerji T. , Jørstad A. , Avseth P. , Mavko G. , Granli J. R.
Published: April 2003

Reliably predicting lithologic and saturation heterogeneities is one of the key problems in reservoir characterization. In this study, we show how statistical rock physics techniques combined with seismic information can be used to classify reservoir lithologies and pore fluids. One of the innovations was to use a seismic impedance attribute (related to the [Formula: see text] ratio) that incorporates far‐offset data, but at the same time can be practically obtained using normal incidence inversion algorithms. The methods were applied to a North Sea turbidite system. We incorporated well log measurements with calibration from core data to estimate the near‐offset and far‐offset reflectivity and impedance attributes. Multivariate probability distributions were estimated from the data to identify the attribute clusters and their separability for different facies and fluid saturations. A training data was set up using Monte Carlo simulations based on the well log—derived probability distributions. Fluid substitution by Gassmann’s equation was used to extend the training data, thus accounting for pore fluid conditions not encountered in the well. Seismic inversion of near‐offset and far‐offset stacks gave us two 3‐D cubes of impedance attributes in the interwell region. The near‐offset stack approximates a zero‐offset section, giving an estimate of the normal incidence acoustic impedance. The far offset stack gives an estimate of a [Formula: see text]‐related elastic impedance attribute that is equivalent to the acoustic impedance for non‐normal incidence. These impedance attributes obtained from seismic inversion were then used with the training probability distribution functions to predict the probability of occurrence of the different lithofacies in the interwell region. Statistical classification techniques, as well as geostatistical indicator simulations were applied on the 3‐D seismic data cube. A Markov‐Bayes technique was used to update the probabilities obtained from the seismic data by taking into account the spatial correlation as estimated from the facies indicator variograms. The final results are spatial 3‐D maps of not only the most likely facies and pore fluids, but also their occurrence probabilities. A key ingredient in this study was the exploitation of physically based seismic‐to‐reservoir property transforms optimally combined with statistical techniques.
The differential parameter method for multifrequency airborne resistivity mapping
Authors: Huang Haoping , Fraser Douglas C.
Published: April 2003

Helicopter EM resistivity mapping began to be accepted as a means of geologic mapping in the late 1970s. The data were first displayed as plan maps and images. Some 10 years later, sectional resistivity displays became available using the same “pseudolayer” half‐space resistivity algorithm developed by Fraser and the new centroid depth algorithm developed by Sengpiel. Known as Sengpiel resistivity sections, these resistivity/depth images proved to be popular for the display of helicopter electromagnetic (EM) data in conductive environments.

A limitation of the above resistivity and depth algorithms is that the resulting Sengpiel section may imply that the depth of exploration of the EM system is substantially less than is actually the case. For example, a target at depth may be expressed in the raw data, but its appearance on the Sengpiel section may be too shallow (which is a problem with the depth algorithm), or it may not even appear at all (which is a problem with the resistivity algorithm).

An algorithm has been adapted from a ground EM analytic method that yields a parameter called the differential resistivity, which is plotted at the differential depth. The technique yields the true resistivity when the half‐space is homogeneous. It also tracks a dipping target with greater sensitivity and to greater depth than does the Sengpiel display method. The input parameters are the apparent resistivity and apparent depth from the pseudolayer half‐space algorithm and the skin depth for the various frequencies. The output parameters are differential resistivity and differential depth, which are computed from pairs of adjacent frequencies.
Convergence Properties of Perturbed Markov Chains
Authors: Roberts Gareth O. , Rosenthal Jeffrey S. , Schwartz Peter O.
Published: April 2003

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation. We are motivated primarily by interest in Markov chain Monte Carlo algorithms.
Asymptotic Expansions for Array Branching Processes with Applications to Bootstrapping
Authors: Sriram T. N.
Published: April 2003

Asymptotic expansions are obtained for the distribution function of a studentized estimator of the offspring mean sequence in an array branching process with immigration. The expansion result is shown to hold in a test function topology. As an application of this result, it is shown that the bootstrapping distribution of the estimator of the offspring mean in a sub-critical branching process with immigration also admits the same expansion (in probability). From these considerations, it is concluded that the bootstrapping distribution provides a better approximation asymptotically than the normal distribution.
Hoare's Selection Algorithm: A Markov Chain Approach
Authors: Grübel Rudolf
Published: April 2003

We obtain bounds for the distribution of the number of comparisons needed by Hoare's randomized selection algorithm FIND and give a new proof for Grübel and Rösler's (1996) result on the convergence of this distribution. Our approach is based on the construction and analysis of a suitable associated Markov chain. Some numerical results for the quantiles of the limit distributions are included, leading for example to the statement that, for a set S with n elements and n large, FIND will need with probability 0.9 about 4.72 x n comparisons to find the median of S.
Phase Transition and Law of Large Numbers for a Non-Symmetric One-Dimensional Random Walk with Self-Interactions
Authors: Vermet Franck
Published: April 2003

We study a not necessarily symmetric random walk with interactions on ℤ, which is an extension of the one-dimensional discrete version of the sausage Wiener path measure. We prove the existence of a repulsion/attraction phase transition for the critical value λc ≡ −μ of the repulsion coefficient λ, where μ is a drift parameter. In the self-repellent case, we determine the escape speed, as a function of λ and μ, and we prove a law of large numbers for the end-point.
Stationary Time Series Models with Exponential Dispersion Model Margins
Authors: Jørgensen Bent , Xue-Kun Song Peter
Published: April 2003

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.
Multivariate Convex Orderings, Dependence, and Stochastic Equality
Authors: Scarsini Marco
Published: April 2003

We consider the convex ordering for random vectors and some weaker versions of it, like the convex ordering for linear combinations of random variables. First we establish conditions of stochastic equality for random vectors that are ordered by one of the convex orderings. Then we establish necessary and sufficient conditions for the convex ordering to hold in the case of multivariate normal distributions and sufficient conditions for the positive linear convex ordering (without the restriction to multi-normality).
On Reliability Bounds via Conditional Inequalities
Authors: Xie M. , Lai C. D.
Published: April 2003

In this paper we study an approximation of system reliability using one-step conditioning. It is shown that, without greatly increasing the computational complexity, the conditional method may be used instead of the usual minimal cut and minimal path bounds to obtain more accurate approximations and bounds. We also study the conditions under which the approximations are bounds on the reliability. Some further extensions are also presented.
Bias Optimality in Controlled Queueing Systems
Authors: Haviv Moshe , Puterman Martin L.
Published: April 2003

This paper studies an admission control M/M/1 queueing system. It shows that the only gain (average) optimal stationary policies with gain and bias which satisfy the optimality equation are of control limit type, that there are at most two and, if there are two, they occur consecutively. Conditions are provided which ensure the existence of two gain optimal control limit policies and are illustrated with an example. The main result is that bias optimality distinguishes these two gain optimal policies and that the larger of the two control limits is the unique bias optimal stationary policy. Consequently it is also Blackwell optimal. This result is established by appealing to the third optimality equation of the Markov decision process and some observations concerning the structure of solutions of the second optimality equation.