bluuebunny/crossref_metadata_2025 huggingface dataset:
The self‐potential method in the geothermal exploration of Greece
Authors: Apostolopoulos George , Louis Ioannis , Lagios Evangelos
Published: October 2002

Self‐potential (SP) anomalies are generated by flows of fluid, heat, and ions in the earth. SP investigations have been used to locate and delineate sources associated with such flows in three areas of geothermal interest in Greece—Lesvos Island, Loutra Hypatis (central Greece), and Nisyros Island. A combination of geophysical methods, with SP being the primary method, has been applied in these areas. The SP method is adversely influenced by various sources of noise. Field procedures have been suggested to minimize their effects by monitoring electrode polarization and telluric activity. The interpretation of SP contour maps is preferred to using profile data. A procedure was adopted for SP interpretation, and the results were satisfactory. However, this model is based on thermoelectric sources only and is not related directly to hot fluid movement. In all three survey areas, the geothermal zones delimited by the SP interpretation in combination with data acquired by other geophysical methods result in an integrated interpretation of the geothermal system. Since SP and very‐low‐frequency (VLF) anomalies can be generated by the same geological source (i.e., geothermal, highly conductive zone), the corresponding results are compared to provide a strong indication of the presence of geothermal zones. The activity of geothermal zones affects the conductivity of the surrounding medium, which also can be detected by dc resistivity and audio‐magnetotelluric (AMT) methods. In addition, geothermal zones can be related to various interfaces or tectonic features that can be detected by gravity or seismic methods.
On: “3-D seismic imaging and seismic attribute analysis of genetic sequences deposited in low‐ accommodation conditions” (B. A. Hardage, D. L. Carr, D.E. Lancaster, J. L. Simmons Jr., D. S. Hamilton, R. Y. Elphick, K. L. Oliver, and R. A. Johns, GEOPHYSICS, 61, 1351–1362)
Authors: Roksandić Miodrag M.
Published: October 2002

The paper deals with the results of a multidisciplinary study of the Bend Conglomerate (Middle Pennsylvanian fluvio‐deltaic clastics) in a portion of Boonsville gas field in the Fort Worth Basin of North‐Central Texas, especially with those related to the Caddo sequence, at the top of the Bend Conglomerate. The purpose of the study was “to determine how modern geophysical, geological, and engineering techniques could be combined to understand the mechanisms by which fluvio‐deltaic depositional processes create reservoir compartmentalization in a low‐ to moderate‐accommodation basin.” According to Hardage et al. (1996), complexly arranged key chronostratigraphic surfaces are major controls on compartmentalization and architecture of reservoirs. These key chronostratigraphic surfaces are flooding surfaces, maximum flooding surfaces, and erosion surfaces.
Effects of borehole stress concentrations on dipole anisotropy measurements
Authors: Winkler Kenneth W. , Sinha Bikash K. , Plona Thomas J.
Published: October 2002

We show both experimentally and theoretically how stress concentrations affect the velocity field around a borehole, and how the velocity field influences dipole anisotropy measurements. At low frequencies the dipole mode is sensitive to the far‐field stresses primarily, so standard sonic log interpretation correctly yields the direction of maximum stress. At higher frequencies, the dipole mode is sensitive to near‐field stress concentrations such that the fast polarization direction is aligned with the direction of minimum tectonic stress. These effects combine to produce a crossover in the dipole dispersion curves measured in the fast and slow directions. With broad‐band dipole data, the dispersion crossover can be used as an indicator of stress‐induced anisotropy dominating over weak intrinsic anisotropy.
Effect ofP-wave scattering on velocity and attenuation in unconsolidated sand saturated with immiscible liquids
Authors: Seifert Patricia K. , Geller Jil T. , Johnson Lane R.
Published: October 2002

Seismic wave tomography is a potentially powerful tool for detecting and delineating nonaqueous phase liquid (NAPL) contaminants in the shallow subsurface. To develop this application, we are conducting laboratory and numerical studies to understand the mechanisms of P-wave transmission through NAPL-water‐sand systems. P-wave measurements of traveltime and amplitude were taken in the 100–900 kHz frequency range through saturated sand with variable NAPL content. To simulate the stress conditions of the shallow surface, a low confining and axial pressure of 60 and 140 kPa, respectively, was applied. The measurements show a significant change in the traveltime and amplitude of the primary arrival as a function of NAPL saturation. To simulate the laboratory measurements, we performed numerical calculations of P-wave propagation through a 1-D medium. The results show that the main behavior of traveltime and amplitude variation can be explained by P-wave scattering. This represents an alternative explanation to the theories that describe local fluid flow as the dominant mechanism for seismic wave attenuation and velocity dispersion.
Nonlinear viscoelastic behavior of sedimentary rocks, Part II: Hysteresis effects and influence of type of fluid on elastic moduli
Authors: Tutuncu Azra N. , Podio Augusto L. , Sharma Mukul M.
Published: October 2002

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.
Acoustic approximations for processing in transversely isotropic media
Authors: Alkhalifah Tariq
Published: October 2002

When transversely isotropic (VTI) media with vertical symmetry axes are characterized using the zero‐dip normal moveout (NMO) velocity [[Formula: see text]] and the anisotropy parameter ηinstead of Thomsen’s parameters, time‐related processing [moveout correction, dip moveout (DMO), and time migration] become nearly independent of the vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text], respectively). The independence on [Formula: see text] and [Formula: see text] is well within the limits of seismic accuracy, even for relatively strong anisotropy. The dependency on [Formula: see text] and [Formula: see text] reduces even further as the ratio [Formula: see text] decreases. In fact, for [Formula: see text], all time‐related processing depends exactly on only [Formula: see text] and η. This fortunate dependence on two parameters is demonstrated here through analytical derivations of time‐related processing equations in terms of [Formula: see text] and η. The time‐migration dispersion relation, the NMO velocity for dipping events, and the ray‐tracing equations extracted by setting [Formula: see text] (i.e., by considering VTI as acoustic) not only depend solely on [Formula: see text] and η but are much simpler than the counterpart expressions for elastic media. Errors attributed to this use of the acoustic assumption are small and may be neglected. Therefore, as in isotropic media, the acoustic model arising from setting [Formula: see text], although not exactly true for VTI media, can serve as a useful approximation to the elastic model for the kinematics of P-wave data. This approximation can boost the efficiency of imaging and DMO programs for VTI media as well as simplify their description.
Spectral ringing suppression and optimal windowing for attenuation and Q measurements
Authors: Pan Cheh
Published: October 2002

In the first part of this paper, briefly the appearance of the Gibbs phenomenon in a discrete Fourier transform and its removal is discussed. The data‐flipping method is then applied to suppress the ringing effect in the spectral ratios for a more accurate measurement of attenuation and Q from seismic or acoustic waves. Such a measurement is invariant to velocity change. The second part concerns optimal windowing of wave modes. Data flipping makes measurement less sensitive to window length. A floating‐length window designed to pick up first arrivals cycle by cycle improves the result. A pickup of the first arrival up to the trough of the second cycle, instead of only to the zero‐line before the trough of the second cycle, gives much better attenuation and Q estimates.
Fifty years of amplitude control
Authors: Helbig Klaus
Published: October 2002

The amplitudes of seismic waves have always been a foremost concern of the seismologist to which considerable ingenuity was devoted. In the 1920s the problem was to magnify the ground motion sufficiently for detection. This was done at first by simple levers that moved mechanical pens. But at the start of exploration seismology, this had already been superseded by optical levers, photographic recording, and (soon after) electromechanical transduction followed by amplification. From the 1930s to about the early ’60s, devices of increasing complexity were introduced to compress the large amplitude difference between the first arrivals and the weakest reflections of interest to the limited dynamic range of the recording medium: first the paper record, then magnetic storage media, and finally the digital magnetic tape. This period can be identified with techniques known as automatic gain control (AGC). Soon after the introduction of digital recording techniques, the emphasis shifted: with intermediate digital storage, the limit to the dynamic range was no longer controlled by the properties of the storage medium. Now everything that passed through the acquisition unit could, in principle, be stored on magnetic disk or tape. At that time the aim became to record the ground motion as faithfully as possible. There were several technical developments on the way to achieve “true amplitudes” that, in turn, made exploration concepts like bright spots, seismic stratigraphy, and amplitude‐versus‐offset evaluation possible. However, the most significant innovation was what became known as floating‐point amplifier. It dominated seismic acquisition for about 25 years. Floating‐point representation of seismic signals allowed storage of the entire dynamic range in relatively economic words of about 18 bits. During the last decade, the quest for ever‐greater resolution—and the availability of mass‐produced components for hi‐fi audio equipment—led to the introduction of the sigma‐delta (Σ-δ) converter. With this device, the full range of the seismic signal (or rather the geophone output) is recorded in binary fixed‐point formats with 24 bits. With this development, the full seismic signal can be stored without distortion or loss of resolution.
Unambiguous signal recovery above the Nyquist using random‐sample‐interval imaging
Authors: Wisecup R. Daniel
Published: October 2002

Aliasing is generally understood to mean that sampling causes those frequencies above the Nyquist frequency to be irretrievably “mixed” with those below. As a result, the perceived need to prevent signal aliasing has played a major role in limiting useable signal bandwidth. Yet, the evidence of aliasing in multichannel seismic data is often paradoxical and contradictory, suggesting that aliasing may be more apparent than real. A simple, exact sample‐mapping methodology, random‐sample‐interval imaging, can be used to overcome aliasing in many of the processes used currently for the imaging of seismic data. The robust process recovers broadband signal, on both synthetic and real data, with frequencies significantly above the Nyquist limit predicted by the 1-D sampling theorem. The method appears to be applicable whenever the signal trajectory is intersected irregularly by a sampling grid of two or more dimensions. The results suggest that both spatial and temporal aliasing of signal may be resolved simultaneously by this strategy.
Instabilities in applying absorbing boundary conditions to high‐order seismic modeling algorithms
Authors: Simone Antonio , Hestholm Stig
Published: October 2002

The problem of artificial reflections from grid boundaries in the numerical discretization of elastic and acoustic wave equations has long plagued geophysicists. Even if modern computers have made it possible to extend the synthetics over more wavelengths (equivalent to larger propagation distances), efficient absorption methods are still needed to minimize interference from unwanted reflections from the numerical grid boundaries. In this study, we examine applicabilities and stabilities of the optimal absorbing boundary condition (OABC) of Peng and Toksöz (1994, 1995) for 2-D and 3-D acoustic and elastic wave modeling. As a basis for comparison, we use exponential damping (ED) (Cerjan et. al., 1985), in which velocities and stresses are multiplied by progressively decreasing terms when approaching the boundaries of the numerical grid.
Suppression of the acquisition footprint for seismic sequence attribute mapping
Authors: Marfurt Kurt J. , Scheet Ronald M. , Sharp John A. , Harper Mark G.
Published: October 2002

Seismic coherency has proven to be very effective in delineating geologic faults as well as considerably more subtle stratigraphic features, including channels, canyons, slumps, levees, glacial gouges, dewatering patterns and pinnacle reefs. Unfortunately, seismic coherency estimates, which quantitatively measure the similarity or dissimilarity of adjacent traces in 3-D, are particularly sensitive to coherent noise that passes through the acquisition and processing flow. They are also sensitive to dissimilarities in fold, offset, and azimuth distribution introduced through the 3-D acquisition and binning processes. Edge enhancement algorithms further exacerbate these linear artifacts. We define the acquisition footprint to be any pattern of noise that is highly correlated to the geometric distribution of sources and receivers on the earth’s surface. While the strong acquisition footprints such as those caused by normal moveout (NMO) stretch on vintage single‐fold data have been largely ameliorated by modern 2-D multifold recording, we see acquisition 3-D footprint in the low‐fold shallow section and throughout the entire section when recording sparse 3-D land surveys that often result in only six- to sevenfold data. One may partially suppress the acquisition footprint on the seismic coherency time or depth slices using conventional 2-D image processing. Unfortunately, such filtering is inappropriate for dip/azimuth maps, cluster analysis maps, and other maps that may not be continuous real variables or with maps that have cyclic values, such as the wavelet phase. We show that simple 3-D true‐amplitude dip filtering of the input 3-D (t, x, y) time- or depth‐migrated seismic data volume can be quite effective in minimizing the detrimental effect of the acquisition footprint on conventional 3-D seismic attributes for both marine and land data acquisition geometries. However, 3-D dip filtering of migrated data will often eliminate the fault‐plane reflections necessary for sharp coherency images. We therefore recommend that, whenever possible, suppression of acquisition footprint be performed before 3-D migration on the stacked data volume, where sharp fault truncations in depth are represented by smoothly varying diffractions in time.
3-D description of normal moveout in anisotropic inhomogeneous media
Authors: Grechka Vladimir , Tsvankin Ilya
Published: October 2002

We present a new equation for normal‐moveout (NMO) velocity that describes azimuthally dependent reflection traveltimes of pure modes from both horizontal and dipping reflectors in arbitrary anisotropic inhomogeneous media. With the exception of anomalous areas such as those where common‐midpoint (CMP) reflection time decreases with offset, the azimuthal variation of NMO velocity represents an ellipse in the horizontal plane, with the orientation of the axes determined by the properties of the medium and the direction of the reflector normal. In general, a minimum of three azimuthal measurements is necessary to reconstruct the best‐fit ellipse and obtain NMO velocity in all azimuthal directions. This result provides a simple way to correct for the azimuthal variation in stacking velocity often observed in 3-D surveys. Even more importantly, analytic expressions for the parameters of the NMO ellipse can be used in the inversion of moveout data for the anisotropic coefficients of the medium. For homogeneous transversely isotropic media with a vertical axis of symmetry (VTI media), our equation for azimuthally dependent NMO velocity from dipping reflectors becomes a relatively simple function of phase velocity and its derivatives. We show that the zero‐dip NMO velocity Vnmo(0) and the anisotropic coefficient η are sufficient to describe the P-wave NMO velocity for any orientation of the CMP line with respect to the dip plane of the reflector. Using our formalism, Vnmo(0) and η (the only parameters needed for time processing) can be found from the dip‐dependent NMO velocity at any azimuth or, alternatively, from the azimuthally dependent NMO for a single dipping reflector. We also apply this theory to more complicated azimuthally anisotropic models with the orthorhombic symmetry used to describe fractured reservoirs. For reflections from horizontal interfaces in orthorhombic media, the axes of the normal moveout ellipse are aligned with the vertical symmetry planes. Therefore, azimuthal P-wave moveout measurements can be inverted for the orientation of the symmetry planes (typically determined by the fracture direction) and the NMO velocities within them. If the vertical velocity is known, symmetry‐plane NMO velocities make it possible to estimate two anisotropic parameters equivalent to Thomsen’s coefficient δ for transversely isotropic media.
2-D Electrical Modeling over Undulated Topography
Authors: Biswas Dipankar , Bhattacharya Bimalendu B.
Published: October 2002

The electrical response of a cylindrical inclusion in topographic relief has been treated analytically for a uniform electric field. The undulated topography has been conveniently defined by a smoothly connected mathematical surface defining a hump or bump. A Born approximation of Laplace’s equation in a bipolar coordinate system has been derived by solving for the mixed‐boundary conditions, namely Neumann and Dirichlet conditions, respectively. The topographic relief causes focusing and defocusing at the transition zones of flat and topographic relief and the central zone of the hump. Consequently, the electric field is weakly linear within the flat zone and entirely nonlinear within the hump. The inclusion of a cylindrical target aggravates the field nonlinearity. The electric field and induced polarization (IP) response over the cylindrical target embedded in topographic relief are strongly dependent on the width and height of the hump and a steady function of increase in resistivity ([Formula: see text]) as well as chargeability ([Formula: see text]) contrasts. The electrical field and IP response over the cylindrical target embedded in the topographic relief, after correcting for topographic effect, resembles most closely the field measured on an equivalent flat half‐space of a particular elevation. The areas of the topographic surface above and below this unique datum bisecting the topographic relief are exactly equal.
Glacial structures in northern Germany revealed by a high‐resolution reflection seismic survey
Authors: Wiederhold Helga , Buness Hermann A. , Bram Kurt
Published: October 2002

In recent years, the sediments filling Pleistocene glacial structures have become of increasing importance to paleoclimate research. Climatic changes are documented by the deposition cycles in small, closed, trough or bowl‐like structures. A 2-D, high‐resolution, shallow reflection seismic survey was conducted in 1996 over such a structure near Tostedt in northern Germany. The objective was to obtain a more accurate picture of the structure and the underlying geology. Designed especially for shallow surveys, a newly developed impulse source provided sufficient energy to observe reflectors as deep as 400 m. Signals are characterized by a high‐frequency content with maximum energy between 80 and 180 Hz. The migrated section shows a distinct reflection pattern revealing local glacial dynamics. Reflectors at depths of 30, 40, and 45 m from inside the Tostedt structure correlate well with three interstadials of the Weichselian period. Weak reflections define the bottom of the structure, with a maximum depth of 70 m. The structure is imbedded in a much larger, previously unexpected depression of similar shape. The fill of this larger depression is seismically nearly transparent. High‐amplitude reflections delineate its lower boundary with a maximum depth of 130 m. Two major reflectors at depths of 170 and 270 m correlate with lower Miocene and middle Oligocene units. They indicate that subrosion, which might have been expected from the presence of a nearby salt diapir, is absent. This confirms the purely glacial origin of the two bowl‐like structures.
“Optimum offset” seismic reflection mapping of shallow aquifers near Bangkok, Thailand
Authors: Whiteley R. J. , Hunter J. A. , Pullan S. E. , Nutalaya P.
Published: October 2002

The “optimum offset” shallow seismic reflection technique was developed for geotechnical and groundwater applications in the early 1980s. The method was based on equipment that was “state of the art” at the time: a 10-bit engineering seismograph, a simple inhole shotgun source, and Apple II personal computers for data processing. In 1985 and 1986, this technique was successfully used in Thailand to assist in understanding the land subsidence problem around Bangkok, which is directly attributable to excessive groundwater withdrawal. The seismic sections acquired in this study were used to map subsurface structure to a depth of about 180 m, which includes several major aquifers beneath the Bangkok Clay. Much of Bangkok’s domestic water is pumped from the so‐called “second aquifer,” 80–130 m below surface, which proved to be an excellent seismic marker horizon showing lateral continuity over distances on the order of kilometers. This observation suggests that there may be good hydraulic connection within this aquifer over large areas. While the technique and equipment used in this study are dated now, the results provide a valuable demonstration of the application of inexpensive shallow reflection methods to a major engineering and groundwater problem that is of concern in many urban centers around the world. It is presented here for its societal relevance in this regard and for its historical aspect as perhaps the first application of shallow seismic reflection profiling in Southeast Asia.
Multidimensional recursive filters via a helix
Authors: Claerbout Jon
Published: October 2002

Wind a wire onto a cylinder to create a helix. I show that a filter on the 1-D space of the wire mimics a 2-D filter on the cylindrical surface. Thus 2-D convolution can be done with a 1-D convolution program. I show some examples of 2-D recursive filtering (also called 2-D deconvolution or 2-D polynomial division). In 2-D as in 1-D, the computational advantage of recursive filters is the speed with which they propagate information over long distances. We can estimate 2-D prediction‐error filters (PEFs) that are assured of being stable for 2-D recursion. Such 2-D and 3-D recursions are general‐purpose preconditioners that vastly speed the solution of a wide class of geophysical estimation problems. The helix transformation also enables use of the partial‐differential equation of wave extrapolation as though it were an ordinary‐differential equation.
Automatic NMO correction and velocity estimation by a feedforward neural network
Authors: Calderón‐Macas Carlos , Sen Mrinal K. , Stoffa Paul L.
Published: October 2002

We describe a new method of automatic normal moveout (NMO) correction and velocity analysis that combines a feedforward neural network (FNN) with a simulated annealing technique known as very fast simulated annealing (VFSA). The task of the FNN is to map common midpoint (CMP) gathers at control locations along a 2-D seismic line into seismic velocities within predefined velocity search limits. The network is trained while the velocity analysis is performed at the selected control locations. The method minimizes a cost function defined in terms of the NMO-corrected data. Network weights are updated at each iteration of the optimization process using VFSA. Once the control CMP gathers have been properly NMO corrected, the derived weights are used to interpolate results at the intermediate CMP locations. In practical situations in which lateral velocity variations are expected, the method is applied in spatial data windows, each window being defined by a separate FNN. The method is illustrated with synthetic data and a real marine data set from the Carolina Trough area.
Reciprocity properties of one‐way propagators
Authors: Wapenaar Kees
Published: October 2002

Acoustic reciprocity is a fundamental property of the wave equation for the total acoustic wavefield (Rayleigh, 1878). In its most elementary form the reciprocity principle states that an acoustic response remains the same when the source and receiver are interchanged. In terms of Green’s functions this reciprocity principle reads G(r2, r1) = G(r1, r2), with r = (x, y, z). For more general expressions and their seismic applications, see Fokkema and van den Berg (1993).
Modes of survival
Authors: Scales John A. , Snieder Roel
Published: October 2002

Scientific progress is fundamentally different from other human activities in that it involves both a venture into the unknown and a desire to change the environment. This type of work cannot be carried out on a routine basis and it requires a certain amount of mental health for its successful completion. The mental state of a researcher is to a large extent influenced by his or her environment; the environment is a crucial factor in the way people react and in a broader context on the development of one’s personality. One of the best‐known writers on personality development is Abraham Maslow (1954), who describes the various levels at which human beings actually function. His view is succinctly formulated by Takacs (1986).
Modeling dolomitized carbonate‐ramp reservoirs: A case study of the Seminole San Andres unit—Part II, Seismic modeling, reservoir geostatistics, and reservoir simulation
Authors: Wang Fred P. , Dai Jiachun , Kerans Charles
Published: October 2002

In part I of this paper, we discussed the rock‐fabric/petrophysical classes for dolomitized carbonate‐ramp rocks, the effects of rock fabric and pore type on petrophysical properties, petrophysical models for analyzing wireline logs, the critical scales for defining geologic framework, and 3-D geologic modeling. Part II focuses on geophysical and engineering characterizations, including seismic modeling, reservoir geostatistics, stochastic modeling, and reservoir simulation. Synthetic seismograms of 30 to 200 Hz were generated to study the level of seismic resolution required to capture the high‐frequency geologic features in dolomitized carbonate‐ramp reservoirs. At frequencies <70 Hz, neither the high‐frequency cycles nor the rock‐fabric units can be identified in seismic data because the tuning thickness of seismic data is much greater than the average thickness of high‐frequency cycles of 6 m. At frequencies >100 Hz, major high‐porosity and dense mudstone units can be better differentiated, while the rock‐fabric units within high‐frequency cycles can be captured at frequencies higher than 200 Hz. Seismic inversion was performed on the 30- to 200-Hz synthetic seismograms to investigate the level of seismic resolution required to recover the high‐resolution inverted impedance logs. When seismic data were noise free, wavelets were known and sampling rates were high; deconvolution techniques yielded perfect inversion results. When the seismic data were noisy, the inverted reflectivity profiles were poor and complicated by numerous high‐frequency spikes, which can be significantly removed using the moving averaging techniques. When wavelets were not known, the predictive deconvolution gave satisfactory inversion results. These results suggest that interwell information required for reservoir characterization can be recovered from low‐frequency seismic data by inversion. Outcrop data were collected to investigate effects of sampling interval and scale‐up of block size on geostatistical parameters. Semivariogram analysis of outcrop data showed that the sill of log permeability decreases and the correlation length increases with an increase of horizontal block size. Permeability models were generated using conventional linear interpolation, stochastic realizations without stratigraphic constraints, and stochastic realizations with stratigraphic constraints. The stratigraphic feature of upward‐shoaling sequences can be modeled in stochastic realizations constrained by the high‐frequency cycles and rock‐fabric flow units. Simulations of a fine‐scale Lawyer Canyon outcrop model were used to study the factors affecting waterflooding performance. Simulation results show that waterflooding performance depends strongly on the geometry and stacking pattern of the rock‐fabric units and on the location of production and injection wells.
A rock physics strategy for quantifying uncertainty in common hydrocarbon indicators
Authors: Mavko Gary , Mukerji Tapan
Published: October 2002

We present a strategy for quantifying uncertainties in rock physics interpretations by combining statistical techniques with deterministic rock physics relations derived from the laboratory and theory. A simple example combines Gassmann’s deterministic equation for fluid substitution with statistics inferred from log, core, and seismic data to detect hydrocarbons from observed seismic velocities. The formulation identifies the most likely pore fluid modulus corresponding to each observed seismic attribute and the uncertainty that arises because of natural variability in formation properties, in addition to the measurement uncertainties. We quantify the measure of information in terms of entropy and show the impact of additional data about S-wave velocity on the uncertainty of the hydrocarbon indicator. In some cases, noisy S data along with noisy P data can convey more information than perfect P data alone, while in other cases S data do not reduce the uncertainty. We apply the formulation to a well log example for detecting the most likely pore fluid and quantifying the associated uncertainty from observed sonic and density logs. The formulation offers a convenient way to implement deterministic fluid substitution equations in the realistic case when natural geologic variations cause the reference porosity and velocity to span a range of values.
A theoretical comparison of equivalent‐offset migration and dip moveout‐prestack imaging
Authors: Bednar J. Bee
Published: October 2002

Equivalent‐offset migration is a methodology for prestack‐Kirchhoff time migration that partially reverses the order of velocity analysis, normal moveout correction, stack, and migration. Though claimed to be computationally and analytically superior to earlier time‐domain approaches, it is not independent of velocity. Velocity‐independent dip moveout followed by prestack imaging is similar to equivalent‐offset migration in that it also postpones normal moveout correction to the postmigration stage, but it is independent of velocity. This paper investigates the theoretical relationship between these two processes, showing that equivalent‐offset migration and prestack imaging are asymptotically equivalent. Moreover, equivalent‐offset migration has little, if any, computational or analytic advantage. The fact that the combination of dip moveout followed by prestack imaging is independent of velocity is a major advantage and suggests that this latter method is better suited to problems of velocity estimation.
3-D preserved amplitude prestack depth migration on a workstation
Authors: Thierry Philippe , Lambaré Gilles , Podvin Pascal , Noble Mark S.
Published: October 2002

We present an algorithm based on the ray+Born approximation for 3-D preserved amplitude prestack depth migration (PAPsDM) of seismic reflection data. This ray+Born inversion scheme allows the quantitative recovery of model perturbations. The Green’s functions are estimated by dynamic ray tracing in 3-D heterogeneous smooth velocity fields with a wavefront construction (WFC) method. The PAPsDM algorithm was implemented on a single‐processor Sun Sparc 20 workstation. Special attention was paid to CPU efficiency and memory requirements. We present an application on a 3-D real marine data set (13 Gbytes). About one week of CPU time is needed to obtain a migrated image of 7 × 1 × 1 km.
Big ray‐tracing and eikonal solver on unstructured grids: Application to the computation of a multivalued traveltime field in the Marmousi model
Authors: Abgrall Rémi , Benamou Jean‐David
Published: October 2002

This paper presents a numerical computation of the multivalued traveltime field generated by a point‐source experiment in the Marmousi model. Two methods are combined to achieve this goal: a method called big ray tracing, used to compute multivalued traveltime fields, and an eikonal solver, designed to work on unstructured meshes. Big ray tracing is based on a combination of ray tracing and local solutions of the eikonal equation. Classical ray tracing first discretizes the phase space and defines local zones that possibly overlap where the traveltime field is multivalued. Then an eikonal solver computes traveltimes in these zones called big rays. It acts as an exact interpolation process between rays associated with different branches of the traveltime field. The geometry of big rays may be complicated and is better discretized using unstructured meshes. An eikonal solver designed to work on unstructured meshes is used.
Upward continuation of scattered potential field data
Authors: Fedi Maurizio , Rapolla Antonio , Russo Guido
Published: October 2002

Numerous methods have been used for upward continuation, but most of them require data on a regular grid. Gridding can introduce errors that affect the continued data in an unpredictable way. To avoid this problem, we design a continuation operator used for the direct continuation of scattered data on a 3-D basis. In this approach a harmonic function, satisfying the constraints imposed by the measured data, is developed. The continuation is written in the form of a linear combination of the measured data, but it depends on the arbitrary choice of the topographic zero level. However, the coefficients of the linear combination depend only on the position of the data points. This allows the zero level to be estimated on the basis of the continuation of synthetic anomalies calculated between the starting and ending surface. An important feature of the method is its local character, which allows the reduction of computation time. Also, the stability of the method for noisy data is reasonably good. The method is applied to both synthetic and real cases. Synthetic examples show how gridding‐related errors may affect the continuation when an irregular distribution of data points and a variable topography are considered.
Estimating shear‐wave velocities from P-wave and converted‐wave data
Authors: Levin Franklyn K.
Published: October 2002

Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.
Seismic diffracted waves from topography using 3-D discrete wavenumber‐boundary integral equation simulation
Authors: Durand Sylvette , Gaffet Stéphane , Virieux Jean
Published: October 2002

Compressional (P) and shear (S) wave diffraction by free‐surface topography plays a prominent part in the prediction of site responses for seismic risk estimation. Wave propagation modeling in 3-D media is required for an accurate estimation of these diffractions. We have extended the discrete wavenumber‐indirect boundary integral equation method for a 3-D geometry in the case of irregular topography. The Green’s functions are expressed as finite sums of analytical density functions over the horizontal wavenumbers using the spatial periodicity of the topography and a discretization of the surface. We show that the evaluation over vertical wavenumber [Formula: see text] of the analytical integral is possible because a new factor in 1/k2exists. When the force point and the receiver point are at the same vertical position, we develop a numerical strategy to choose the sign of the exponential factor, which is not given by the analytical formulation. The free‐stress boundary conditions at the topography lead to a large linear system that can be solved to obtain the source density functions. Knowing these source density functions, we can compute the diffracted wavefield anywhere inside the medium. We have determined a useful optimal, imaginary frequency to obtain the displacement directly in the frequency domain, avoiding the necessity of returning to the time domain. We have then applied this method to investigate the effect of topography on the ground motion produced by a vertical incident P- or S-wavefield. Waveforms obtained for various topographic steepnesses and shapes show deterministic correlations between the maximum amplitude zone, the geometry of the 3-D topography, and the P- or S-wave incident field characteristics. The maximum amplitude of the diffracted displacement is found near topographic zones that have horizontal or vertical dimensions closely related to the wavelength of the incident field. The predicted ground motion maximal amplifications are twice those calculated in the case of a flat topography.
Reply by the authors to the discussion by Roy E. White and Rob Simm
Authors: Ziolkowski Anton , Johnston Rodney G. K. , Underhill John R.
Published: October 2002

We thank Roy White and Rob Simm for their very entertaining discussion of our paper. We acknowledge that what we thought were obvious problems are, perhaps, not so obvious after all. Consequently, we have gone to some trouble to present the solid evidence that is required to demonstrate that these problems are real. We do this by processing synthetic data calculated using the real well log data presented in our paper (Ziolkowski et al., 1998).
Semiautomated georadar data acquisition in three dimensions
Authors: Lehmann Frank , Green Alan G.
Published: October 2002

Under favorable conditions, georadar techniques can provide vivid images of the shallow subsurface (<10–50 m). Although the significant advantages of 3-D georadar surveying strategies are well documented, they generally require much greater expenditures than traditional 2-D approaches. We introduce an efficient, semiautomated 3-D georadar acquisition and processing scheme that does not jeopardize data quality. A standard georadar acquisition unit is integrated with an innovative self‐tracking laser theodolite with automatic target recognition capabilities. Georadar and coordinate data are recorded simultaneously as the georadar antennae are transported steadily across a survey area. While tracking a target prism mounted between the antennae, the theodolite provides real‐time coordinate information with high accuracy in all directions. At ∼1 m/s (moderate walking speed) the coordinates are determined to better than ±0.04 m, and at ∼3 m/s they are better than ±0.07 m. Subsequent to acquisition, semiautomatic processing allows the georadar data to be static corrected, transferred to a regular grid using a novel 2-D Fourier transform method, amplitude modulated, filtered, and displayed. The acquisition component of the new scheme is five to ten times faster than standard step‐mode georadar techniques, and the semiautomatic processing component allows initial 3-D images to be viewed in the field. Typically, a 3-D georadar data set covering a 25 m × 25 m area may be collected and processed in less than 3 hours. One such data set recorded across a former glaciofluvial environment allows reflections from complex river channel sediments and surface features to be readily identified and interpreted.
Factors affecting spatial resolution
Authors: Vermeer Gijs J. O.
Published: October 2002

The theory of spatial resolution has been well‐established in various papers dealing with inversion and prestack migration. Nevertheless, there is a continuing flow of papers being published on spatial resolution, in particular in relation to spatial sampling. This paper continues the discussion, and deals with various factors affecting spatial resolution. The theoretical best‐possible resolution can be predicted using Beylkin’s formula. This formula gives answers on the effect on resolution of frequency, aperture, offset, and acquisition geometry. In this paper, these factors are investigated using a single diffractor in a constant‐velocity medium. Some simple resolution formulas are derived for 2-D zero‐offset data. These formulas are similar to formulas derived elsewhere in a more heuristic way, and which are in common use in the industry. The formulas are extended to 2-D common‐offset data. The width of the spatial wavelet resulting from migration of the diffraction event is compared with the resolution predicted from Beylkin’s formula for various 3-D single‐fold data sets. The measured widths confirm the theoretical prediction that zero‐offset data produce the best possible resolution and 3-D shots the worst, with common‐offset gathers and cross‐spreads scoring intermediate. The effects of sampling and fold cannot be derived directly from Beylkin’s formula; these effects are analyzed by looking at the migration noise rather than at the width of the spatial wavelet. Random coarse sampling may produce somewhat less migration noise than regular coarse sampling, though it cannot be as good as regular dense sampling. The bin‐fractionation technique (which achieves finer midpoint sampling without changing the station spacings) does not achieve higher resolution than conventional sampling. Generally speaking, increasing fold does not improve the theoretically best possible resolution. However, as noise always has a detrimental effect on the resolvability of events, fold—by reducing noise—will improve resolution in practice. This also applies to migration noise as a product of coarse sampling.
An invariant representation for the magnetic transfer function in magnetotellurics
Authors: Romo José M. , Gómez‐Treviño Enrique , Esparza Francisco J.
Published: October 2002

The magnetic transfer function in the magnetotelluric (MT) method can be represented by two simple complex functions that possess special properties in 3-D environments. This representation is obtained by means of a complex rotation matrix applied to the field measurements. One of the resulting functions is invariant with respect to rotations of the coordinate system and is closely related to the traditional concept known as tipper. The magnitude and phase of this new representation are invariant in a 3-D earth and unambiguously reduce to the corresponding formulas for 2-D cases. With these properties, the proposed representation overcomes the existing limitations of the current definition of the tipper. In the second complex function, the traditional concepts of rotation angle and skew appear naturally in the function’s real and imaginary parts, respectively. We test the new representation using the response of a 3-D model. The results are compared with those obtained using current definitions.
Magnetotelluric observations in the western Ouachita Mountains, southeastern Oklahoma
Authors: Mickus Kevin L.
Published: October 2002

The first magnetotelluric (MT) analysis of the Ouachita Mountains region is presented. Magnetotelluric data acquired at 19 sites along a 60-km profile in southeastern Oklahoma were used to image the western extension of the Ouachita Mountains and to determine the poorly known subsurface interaction between the Pennsylvanian Tishomingo‐Belton uplift and the subsurface extension of the exposed western Ouachita Mountains. Drill‐hole data, geologic mapping, seismic reflection profiles, and 1-D and 2-D MT-derived models indicate that lying beneath the low‐resistivity Gulf Coastal Plain sediments are 2–3 km of deep‐water lower Pennsylvanian (Jackfork Group) sediments and 6–8 km of Ouachita facies lithologies, mainly consisting of the Stanley Group. Beneath the profile’s northern section are 2–4 km of Atoka Formation sediments, probably deposited within the Arkoma basin, that underlie thrusted zones of the Stanley Group. The most unique feature is a high‐resistivity zone beneath stations 7–9, interpreted to be Precambrian/Cambrian granite similar to that exposed in the Tishomingo‐Belton uplift. A deep (5–6 km) low‐resistivity zone that may represent the northern border of the subsurface extension of the Broken Bow uplift is located along the Texas/Oklahoma border; however, this zone is not required by the MT data.
Magnetic mapping of Majhgawan diamond pipe of central India
Authors: Sarma B. S. P. , Verma B. K. , Satyanarayana S. V.
Published: October 2002

Magnetic response over kimberlite/lamproite pipes can be used to map their horizontal and vertical cross‐sections. A published ground magnetic vertical intensity contour map is used to map the Majhgawan kimberlite pipe near Panna in central India. Using Barnett’s (1976) method, we obtained a reasonable match between the computed and observed fields with three separate bodies. The model suggests a possible later intrusion into the main pipe. Geological studies (using drill‐hole data) imply a nearly concentric vertical lithological zoning within the pipe and thus support the hypothesis of multiple intrusions, indicated by magnetic data. The multiple intrusion hypothesis is of interest to exploration because specific intrusions within one composite pipe may differ markedly in the incidence of diamonds. The higher incidence of diamonds reported in the central part of the Majhgawan pipe, as compared to the outer part, also supports the possibility of a later intrusion into the main pipe.
Understanding CMP stacking hyperbola in terms of partial derivative wavefield
Authors: Shin Changsoo , Chung Seunghwan
Published: October 2002

Common midpoint (CMP) stacking and velocity analysis are fundamental seismic imaging concepts based on a layered velocity model. We relate these concepts to partial derivative seismograms, which give seismic amplitude variations as a function of layer coordinates. The CMP stacking hyperbola can be described kinematically by partial derivative seismograms, resulting in an interesting seismic imaging relationship.