bluuebunny/crossref_metadata_2025 huggingface dataset:
Analysis of the characteristics‐integration method for one‐dimensional wave inversion
Authors: Chen Nei‐Mao , Chu Yu‐Hua , Kuo John T.
Published: October 2002

Basing our work on the one‐dimensional (1-D) wave equation, we present an inverse method which we call the characteristics‐integration method. The method is derived from integration along characteristic families of straight lines of the wave equation in the time domain. With the source function known and reflection data recorded on the surface, the characteristics‐integration method can efficiently and economically recover the subsurface impedance profile, provided that the structure is inhomogeneous only in the depth direction. In general, when seismic data are contaminated by noise, the characteristics‐integration method, like any other 1-D inverse method, suffers from instability. We find that, for a smoothly varying impedance profile, the instability of inversions using characteristic methods depends heavily on the bandwidth of the source wavelet. We devised a resampling technique to stabilize the inverse scheme and to suppress the growth of errors. Numerical examples, including data contaminated by noise, data missing the low‐frequency component, and real data cases, show the feasibility of recovering impedance profiles using the characteristics‐integration method.
Local noise prediction filtering for central induction transient electromagnetic sounding
Authors: Spies Brian R.
Published: October 2002

Local noise prediction filtering (LNPF) is a method of noise reduction designed for use with the in‐loop transient electromagnetic (TEM) method of exploration. LNPF is based on simultaneous measurements of three orthogonal magnetic‐field components and the calculation of a time‐domain filter which predicts the vertical component from the two horizontal components. For in‐loop, or central induction, sounding over a horizontally layered earth, the TEM signal is contained wholly within the vertical component. Thus the predicted time series obtained with LNPF is the predicted electromagnetic noise which can be subtracted from the measured vertical component in subsequent processing. For low‐frequency noise, the method results in improvements in the signal‐to‐noise ratio of about a factor of five using a three‐point prediction filter. Longer filters give superior performance but are computationally intensive. The depth of exploration should increase by 40 percent, due to the five‐fold increase in signal‐to‐noise ratio, a figure which could be obtained otherwise only by increasing the transmitter power or the acquisition time by a factor of 25. In areas with lateral variations in conductivity the TEM response has both horizontal and vertical components. Applying LNPF in nonlayered areas will bias the vertical‐component TEM signal by a proportion of any horizontal TEM signal present. This bias error will generally be less than 5 to 10 percent, and usually will be insignificant in geologic environments where EM soundings are carried out. A new parameter, termed TEM tipper by analogy with magnetotellurics, is defined as the ratio of horizontal‐to‐vertical TEM response and is used to estimate the maximum LNPF bias error. The TEM tipper is useful for interpretation of TEM in‐loop data in areas of complex geology.
A method to minimize edge effects in two‐dimensional discrete Fourier transforms
Authors: Ricard Yanick , Blakely Richard J.
Published: October 2002

Fourier transforms are widely used in analysis of two‐dimensional (2-D) earth‐science data, such as gravity and magnetic surveys, topographic models, and remote‐sensing images. For example, manipulations of gridded magnetic or gravity data, such as upward and downward continuation, reduction to the pole, wavelength filters, pseudogravity transformation, and vertical derivatives (Hildenbrand, 1983), are greatly simplified with Fourier transforms, as are certain forward and inverse calculations (Parker, 1973; Parker and Huestis, 1974). Power spectra computed from 2-D Fourier transforms are used to estimate depth to the top and bottom of magnetic sources from gridded magnetic data (Spector and Grant, 1970; Connard et al., 1983) and to estimate lithospheric strength and Moho depth from gridded gravity data (Dorman and Lewis, 1970; Louden and Forsyth, 1982; McNutt, 1983).
A rapid graphical method for the interpretation of the self‐potential anomaly over a two‐dimensional inclined sheet of finite depth extent
Authors: Babu H. V. Ram , Rao D. Atchuta
Published: October 2002

The inclined sheet is an important model for interpreting self‐potential (SP) anomalies over elongated ore deposits. Many techniques (Roy and Chowdhurry, 1959; Meiser, 1962; Paul, 1965; Atchuta Rao et al., 1982; Atchuta Rao and Ram Babu, 1983; Murty and Haricharan, 1985) have been proposed for interpreting SP anomalies over this model. We propose a simple graphical procedure for locating the upper and lower edges of an inclined sheet of infinite strike extent from its SP anomaly V(x) using a few characteristics points including [Formula: see text] [Formula: see text], and [Formula: see text] The amplitude ratio [Formula: see text], is shown to vary with θ, the dip of the sheet, making it possible to estimate θ. The two edges of the sheet are equidistant from the abscissa of [Formula: see text] the zero potential point. The sheet, when extrapolated onto the line of observation, meets the x‐axis at a point where [Formula: see text] From these characteristic features of V(x), the sheet can be located easily using the simple geometrical construction presented below.
Multivariate statistical analyses applied to seismic facies recognition
Authors: Dumay Jean , Fournier Frederique
Published: October 2002

One of the most important goals of seismic stratigraphy is to recognize and analyze seismic facies with regard to the geologic environment. The first problem is to determine which seismic parameters are discriminant for characterizing the facies, then to take into account all those parameters simultaneously. The second problem is to be sure that there is a link between the seismic parameters and the geologic facies we are investigating. This paper presents a methodology for automatic facies recognition based upon two steps. The first, or learning step, begins with the definition of learning seismic traces for each facies we wish to recognize. The choice of learning traces is based upon either well data or a seismic stratigraphic interpretation. A large number of seismic parameters are then computed from the learning traces; multidimensional analyses are carried out in order to validate the choice of learning traces and to select, among all the available parameters, those that discriminate best. At this stage, a modeling step may be carried out to relate the seismic parameters to the geologic features. The second step is a predictive one which allows automatic facies recognition. We compute the previously chosen discriminant parameters on unknown seismic traces and classify the unknown traces with regard to the learning traces. We develop the methodology and successfully apply it to two examples of reservoir facies recognition. Our main conclusion is that seismic traces contain geologic information that can be extracted by multivariate data analyses of a large number of seismic parameters. Automatic facies recognition is reliable and fast; the derived facies map has the great advantage of combining simultaneously several discriminant parameters.
Three‐dimensional modeling and migration of seismic data using Fourier transforms
Authors: Wen Jing , McMechan George A. , Booth Michael W.
Published: October 2002

Programs for 3-D modeling and migration, using 3-D Fourier transforms to solve the scalar wave equation in frequency‐wavenumber space, are developed, implemented, tested, and applied to synthetic and scale‐model data. With microtasking to fully use four CRAY processors in parallel, we can solve a complete [Formula: see text] modeling problem in about 2.5 minutes (elapsed time); of this time, the two 3-D Fourier transforms take 1 minute and the wave‐equation calculations take 1.5 minutes. The corresponding migration also takes 2.5 minutes. Thus, even iterative 3-D processing is now feasible. The two main assumptions in our algorithm are that the earth has a constant velocity and that the data are zero‐offset (or stacked). Tests with model data verify that the algorithm produces the correct results when these assumptions are satisfied. Tests with scale‐model data show that approximate images may still be obtained when the assumptions are not strictly met; but the images contain a variety of distortions, primarily related to undermigration and overmigration, so caution is required in interpretation.
A technique for stabilizing interval velocities from the Dix equation
Authors: Dubose John B.
Published: October 2002

Interval velocities, the velocities at which sounds travel in the earth, can be computed from stacking or root‐mean‐square (rms) velocities by applying the Dix equation (Dix, 1955): [Formula: see text] where [Formula: see text] are the stacking velocity picks, [Formula: see text] are the associated times, and [Formula: see text] is the average interval velocity between [Formula: see text] and [Formula: see text].
On: “Seismic contouring: A unique skill” by P. M. Tucker (GEOPHYSICS, 53, 741–749, June 1988).
Authors: Gariepy Byron L.
Published: October 2002

I’ll bet you thought you were too old to receive a “Fan Letter.” “Seismic contouring: A unique skill” in the June 1988 issue of Geophysics is just exactly what will cause you to receive an alarming number of fan letters and you will deserve them. Thanks.
Laboratory and field studies of the application of electromagnetic prospecting for groundwater on Marajó Island, Brazil
Authors: Verma Om Prakesh , Bischoff Jurgen H.
Published: October 2002

On Marajó Island, Pará, Brazil, many cattle die due to lack of potable water, since a majority of the shallow groundwater is brackish. Two types of fresh‐water aquifers were delineated using resistivity methods: (1) a deep aquifer at about 100 m depth and (2) shallow buried‐stream channels filled with sand and gravel (ρ = 40 Ω ⋅ m) and embedded in clay and sand beds with brackish water (ρ = 0.8 Ω ⋅ m — 5 Ω ⋅ m). For the demarcation of the shallow buried‐stream channel aquifers, inductive electromagnetic moving source‐receiver methods were tested to replace the cumbersome galvanic resistivity methods. In order to verify the applicability of EM survey techniques for groundwater exploration in hydrogeologic conditions typical of Marajó Island, analog model studies were carried out. The groundwater‐bearing channels buried in the clays or in the sediments with brackish water represent geoelectrically a less conducting body in a more conducting environment. The buried‐channel “Guajará Mirim” on Marajó Island was chosen for test studies. A 500 times reduced model of this channel was constructed using two aluminium sheets of varying thicknesses to simulate host sediments and the sediments in the buried channel. EM profiles were measured in the laboratory across the channel model using horizontal‐coplanar vertical‐coplanar, and vertical‐coaxial coil systems in the broadside and inline modes of operation. Excellent EM model responses were obtained with all six coil configurations. Finally, EM profiles in the field were carried out using horizontal‐coplanar, vertical‐coplanar, and vertical‐coaxial coils in an inline mode of operation. Field and laboratory results are in very good qualitative agreement.
Integrated seismic analysis: Kidney area, northern Alberta, Canada
Authors: Stewart Robert R.
Published: October 2002

Integrating various seismic data via simultaneous processing or correlation can increase the accuracy and confidence in subsurface images. To this end, a multioffset VSP survey with simultaneous surface recording was acquired in the fall of 1986 near Red Earth, northern Alberta, in the Kidney prospect area. P‐wave vibrators at three locations west of the survey well were recorded by a downhole three‐component geophone at 15 m increments between depths of 225 m and 1570 m and were recorded simultaneously on a 2900 m surface spread of vertical geophones spaced 25 m apart in line with the VSP sources and just west of the well. These data, along with existing seismic lines and well logs, correlated convincingly and were used to increase confidence in the interpretation of the potential reservoir of interest—a Keg River carbonate (KRC) unit. Tomographic procedures (constrained traveltime inversion) were developed to process simultaneously the well logs, VSP, and surface seismic data. These procedures provided a macroscopic seismic interval velocity in depth. This tomographic velocity structure (TVS) was used in poststack depth migration of an existing seismic line over the region of interest. The resulting depth‐migrated section near the well matched the synthetic seismogram (computed in depth from the sonic log) reasonably well in character and depth for most of the major reflectors. The TVS was also used in a fairly conventional processing flow which included poststack time migration, maximum‐likelihood deconvolution, seismic trace inversion, and time‐to‐depth stretching. The final processed pseudosonic section in depth bore considerable resemblance to the sonic log. About 30 m of KRC was measured from the pseudosonic section, while 35 m of KRC was interpreted from the well logs. The pseudosonic section also strongly suggested thinning or discontinuity in the KRC unit on the section around a previously proposed drilling location (1.7 km west of the well). This interpretation was confirmed by another operator’s subsequent drilling at this location, which encountered only 1 m of KRC. The predicted depth of the KRC top (about 1395 m), interpreted from the pseudosonic section at the second well location, was close to the depth (1400 m) on the well logs.
Tomographic modeling of a cross‐borehole data set
Authors: Lines Larry R. , LaFehr Edward D.
Published: October 2002

In this paper we describe a methodology for estimating P‐wave velocities from a cross‐borehole seismic survey that uses straight‐ray tomography, ray tracing, and finite‐difference wave‐equation modeling to produce velocity models that fit the first‐break traveltimes. After a starting model is established by straight‐ray tomography, the velocity model is checked by ray tracing and wave‐equation modeling. Since the models for each procedure show consistent results and the modeled traveltimes closely match those traveltimes from the actual data, we felt our interpretation was confirmed. However, the fitting of cross‐well first break traveltimes is only a necessary validity check and is not sufficient to guarantee that the true solution has been found. Two wells were drilled through the areas that were anomalous on the derived tomogram and check‐shot velocity surveys were run. Due primarily to a lateral ambiguity in velocity estimation caused by too few near‐vertical raypaths, the check‐shot surveys did not agree with the tomogram velocities. However, subsequently the check‐shot traveltimes were used to place bounds on velocity in a constrained least‐squares procedure; the combined modeling of uphole and cross‐well rays produced an optimum velocity model which satisfies all available data.
On: “New prospects in shallow depth electrical surveying for archeological and pedological applications” by A. Hesse, A. Jolivet and A. Tabbagh (GEOPHYSICS, 51, 585–594, March 1986).
Authors: Goldman Mark
Published: October 2002

The forward solution given by Hesse et al. is incorrect. The error is a result of the erroneous governing differential equation [their equation (2)], which for the only nonzero component of the magnetic field has the following form: [Formula: see text]Unfortunately, the authors did not show how they arrived at this equation, but the mistake is so frequently encountered that its origin can be reconstructed quite easily. Indeed, by neglecting displacement currents in the fourth Maxwell equation and by applying the vector operator ∇× to both parts of the equation, we obtain [Formula: see text]Making use of the well known vector identity [Formula: see text]and of the first and third Maxwell equations, we obtain [Formula: see text]
Seismic detection and interpretation of porosity in Carboniferous age rocks of Kansas and Oklahoma
Authors: Thomasson M. R. , Kettle R. W. , Lloyd R. M. , McCormack R. K. , Lindsey J. P.
Published: October 2002

Many large Mississippian fields (5–130 MMBO) in south‐central Kansas and northern Oklahoma produce from discrete pods of porous chert and dolomite called “chat.” Chat has unusual acoustic properties that allow the porosity pods to be recognized on seismic sections. Integrated geologic and geophysical studies of two analog fields indicate that both reservoir quality and geometry can be interpreted from good quality seismic data. Seismic modeling on an interactive work station plays an important role in developing these interpretations.
Low‐ and high‐relief Leduc formation reefs: A seismic analysis
Authors: Anderson N. L. , Brown R. J. , Hinds R. C.
Published: October 2002

Leduc reefs have grown to widely varying heights and areal extents along the Rimbey‐Meadowbrook trend of central Alberta, resulting in significantly different seismic signatures. Three examples considered in this paper include two high‐relief or full reefs from the Leduc‐Woodbend field, an atoll and a pinnacle, each around 200 m in height but differing greatly in areal extent, about [Formula: see text] for the atoll and [Formula: see text] for the pinnacle. The third example, a low‐relief or basal reef from the Morinville field, is about 100 m high and [Formula: see text] in areal extent. The Leduc‐Woodbend and Morinville reefs exhibit quite different seismic signatures. For example, 25 ms of time‐structural drape along the top of the Devonian is observed across the Leduc‐Woodbend atoll but only 15 ms across the Morinville reef. There is 30 ms of pullup at the Beaverhill Lake level beneath the Leduc‐Woodbend atoll, 15 ms for the Morinville reef. Also, it is very difficult to differentiate the Leduc reflection from the Duvernay reflection, with which it merges, on the Morinville (basal‐reef) section. In contrast, the Leduc reflection can be correlated readily on the Leduc‐Woodbend atoll section; and reflections from the offreef shales (Duvernay and Ireton formations) terminate abruptly against the reef flank. In addition, the amplitude of the underlying Cooking Lake platform reflection varies laterally, depending on the velocity of the overlying formation (Duvernay shale or Leduc reef) and, to a lesser extent, the thickness of the overlying reef. This variation is not as useful in distinguishing between low‐relief and high‐relief reefs as it is in indicating the presence or absence of reef.
Acoustic wave propagation in composite fluid‐saturated media
Authors: Keller J. David
Published: October 2002

Biot’s linear model of stress‐wave propagation in a fluid‐saturated elastic framework is combined with a linear theoretical description of an inelastic frame to describe fluid‐saturated media in terms of a composite model. The composite model, the Constant Q (CQ) model, assumes an inelastic frame with frequency‐dependent complex elastic moduli and results in a frame response that is causal with Q exactly independent of frequency. The influence of frame inelasticity on the composite‐model Type I (compression), Type II, and shear‐wave attenuation response is found to be greatest for high and low frequencies, considering a frequency range of [Formula: see text]. The model is most sensitive to variations in permeability and pore‐size parameter for both attenuation and phase‐velocity responses. Parameter variations showed little effect on shear‐wave attenuation for a fine to course sand‐size frame matrix, indicating a fluid mechanism is responsible for the influence seen in Type I and Type II attenuations. The CQ model results fit the experimentally measured values of Type I attenuation and velocity for a fully saturated fine‐grained frame material (clay‐silt size grains) and a fully saturated coarse‐grained frame material (fine to coarse sand‐size grains). For Type I velocity, the experimentally observed dispersion clearly distinguishes the CQ model as superior to composite models that include a nondispersive frame, since such models predict very little dispersion due only to interpore fluid mechanisms.
Inversion = migration + tomography
Authors: Mora Peter
Published: October 2002

Seismic inversion, broadly enough defined, is equivalent to doing migration and reflection tomography simultaneously. Diffraction tomography and inversion work best when sources and receivers surround the region of interest, as in medical imaging applications. Theoretical studies have shown that high vertical wavenumber velocity perturbations are resolved by inverting surface seismic reflection data, but the low vertical wavenumbers must be obtained using a separate step, such as velocity analysis or reflection tomography. I propose that a nonlinear iterative inversion that updates a varying background velocity obtains all wavenumbers that are resolvable separately by migration and tomography. The background velocity must contain reflectors to provide data on both upward and downward transmission paths through the earth and hence the low wavenumbers. By considering the downward transmission paths to be between surface sources and buried image geophones and the upward transmission paths to be between surface geophones and buried image sources, the source and receiver coverage is effectively the same as in medical imaging; although the depth of the image sources and geophones must be determined in the inversion by finding the reflector depths. Synthetic examples verify the theoretical predictions and show that reflector locations and interval velocities can be obtained simultaneously even when there is no prior knowledge of reflector location. However, a good initial “very low‐wavenumber” model is normally required to ensure convergence to the global inverse solution.
Velocity analysis without picking
Authors: Toldi John L.
Published: October 2002

Conventionally, interval velocities are derived from picked stacking velocities. The velocity‐analysis algorithm proposed in this paper is also based on stacking velocities; however, it eliminates the conventional picking stage by always considering stacking velocities from the point of view of an interval‐velocity model. This view leads to a model‐based, automatic velocity‐analysis algorithm. The algorithm seeks to find an interval‐velocity model such that the stacking velocities calculated from that model give the most powerful stack. An additional penalty is incurred for models that differ in smoothness from an initial interval‐velocity model. The search for the best model is conducted by means of a conjugate‐gradient method. The connection between the interval‐velocity model and the stacking velocities plays an important role in the algorithm proposed in this paper. In the simplest case, stacking velocity is assumed to be equal to rms velocity. For the more general case, a linear theory is developed, connecting interval velocity and stacking velocity through the intermediary of traveltime. When applied to a field data set, the method produces an interval‐velocity model that explains the lateral variation in both stacking velocity and traveltime.
Borehole gravity gradiometry
Authors: Nekut A. G.
Published: October 2002

Gravity gradients measured in a borehole are of interest due to their direct, simple relation to the density of the formations surrounding the hole. Borehole gravity meters (BHGMs) are used to measure gravity differences along the borehole and from these differences, we compute averaged values for a linear combination of the gravity gradient tensor elements. One way to implement a borehole gravity gradiometer (BHGGM) is to measure the torque exerted on a pair of masses separated by a beam. A BHGGM directly measures all the elements of the gravity gradient tensor. Knowledge of these elements provides information about the direction to density anomalies in the vicinity of the borehole and enhances the analysis of dipping beds. The BHGGM may be superior to the BHGM for resolving the density of thin beds. Density variations remote from the borehole are best detected and characterized by joint interpretation of BHGM and BHGGM data.
Prestack traveltime inversion for three‐dimensional structure
Authors: Lin Tzeu‐Lie
Published: October 2002

An iterative method for determining three‐dimensional (3-D) velocity fields is presented. The input data are offset‐dependent traveltimes for primary reflections. 3-D traveltime derivatives (the Frêchet derivatives) for the 3-D structure are derived. The algorithm simultaneously determines all of the model parameters and is exceedingly robust compared to layer‐stripping algorithms, even for inaccurate data.
Autocorrelation estimation using constrained iterative spectral deconvolution
Authors: Ramaswamy Murali , Ioup George E.
Published: October 2002

Computing an autocorrelation conventionally produces a biased estimate, especially for a short data sequence. Windowing the autocorrelation can remove the bias but at the expense of violating the nonnegativity of the corresponding power spectrum. Constrained iterative deconvolution provides a basis for improving an autocorrelation estimate by reducing the bias while guaranteeing nonnegative definiteness. The length of the autocorrelation is increased in order to satisfy the nonnegativity constraints on the power spectral estimate. The constraints can also have significant effects on small, poorly determined values of the autocorrelation. The technique is applied to synthetic and real examples to show the improvements in the autocorrelation and power spectrum which are possible. The method is reasonably stable in the presence of noise and it approximately preserves the area of the power spectrum. Comparison to the maximum entropy technique shows that the iterative method gives power spectral resolution which is sometimes better and sometimes not as good, but that there are cases for which it is the more desirable approach.
Efficient computation of the gravitational field of a generalized cylindrical prism
Authors: Van Baak David A.
Published: October 2002

Various forms of geophysical modeling require a technique for computing the gravitational attraction of a specified source distribution of mass. I show in this paper that the triple integral that arises in general gravitational modeling can, under certain conditions, be reduced to a single line integral or even to a finite sum.
Discrete linear transformations of potential field data
Authors: Leão Jorge W. D. , Silva João B. C.
Published: October 2002

We present a new approach to perform any linear transformation of gridded potential field data using the equivalent‐layer principle. It is particularly efficient for processing areas with a large amount of data. An N × N data window is inverted using an M × M equivalent layer, with M greater than N so that the equivalent sources extend beyond the data window. Only the transformed field at the center of the data window is computed by premultiplying the equivalent source matrix by the row of the Green’s matrix (associated with the desired transformation) corresponding to the center of the data window. Since the inversion and the multiplication by the Green’s matrix are independent of the data, they are performed beforehand and just once for given values of N, M, and the depth of the equivalent layer. As a result, a grid operator for the desired transformation is obtained which is applied to the data by a procedure similar to discrete convolution. The application of this procedure in reducing synthetic anomalies to the pole and computing magnetization intensity maps shows that grid operators with N = 7 and M = 15 are sufficient to process large areas containing several interfering sources. The use of a damping factor allows the computation of meaningful maps even for unstable transformations in the presence of noise. Also, an equivalent layer larger than the data window takes into account part of the interfering sources so that a smaller damping factor is employed as compared with other damped inversion methods. Transformations of real data from Xingú River Basin and Amazon Basin, Brazil, demonstrate the contribution of this procedure for improvement of a preliminary geologic interpretation with minimum a priori information.
Extraction of deep crustal reflections from shallow Vibroseis data using extended correlation
Authors: Okaya David A. , Jarchow Craig M.
Published: October 2002

Lower crustal seismic reflections can be extracted from shallow crustal seismic profiles through the application of extended correlation to uncorrelated Vibroseis seismic data. “Fixed‐bandwidth” extended correlation shortens the correlation operator before crosscorrelation, producing reflections over an increased correlation time range, all with lowered bandwidth. “Self‐truncating” extended correlation preserves the full bandwidth in the original seismic reflection times but loses bandwidth in a predictable manner at the additional (later) arrival times. Correlation wavelet shape and extra correlation time are directly related and can be calculated for specific acquisition parameters. Pre‐correlation tapering is necessary to avoid undue wavelet distortion at extended correlation times. Seismic data collected in the Basin and Range province illustrate the application of the method; the results are verified with conventional correlations of long sweep records and with impulsive source data.
Identification of thermal conductivities by temperature gradient profiles: One‐dimensional steady flow
Authors: Ponzini G. , Crosta G. , Giudici M.
Published: October 2002

The comparison model method (CMM) is applied to the identification of spatially varying thermal conductivity in a one‐dimensional domain. This method deals with the discretized steady‐state heat equation written at the nodes of a lattice, a lattice which models a stack of plane parallel layers. The required data are temperature gradient and heat source (or sink) values. The unknowns of this inverse problem are not nodal values but internode thermal conductivities, which appear in the node heat balance equation. The conductivities, e.g., the solutions to the inverse problem obtained by the CMM, are a one‐parameter family. In order to achieve uniqueness (which coincides with identifiability in this case), a suitable value of this parameter must be found. To this end we consider (1) parameterization, i.e., introducing equality constraints between the unknown coefficients, (2) the use of two data sets at least in a subdomain, and (3) self‐identifiability. Each of these items formally translates the available a priori information about the system, e.g., geophysical properties of the layers. Under the assumption that an admissible solution exists, we evaluate the effects on the solution of two types of data noise: additive noise affecting temperature and a kind of multiplicative noise affecting heat‐source terms. In the numerical examples we provide, parameterization is combined with the CMM in order to obtain the unique solution to a test inverse problem, the geophysical data of which come from a well drilled across Tertiary layers in central Italy. Finally, we consider data perturbed by pseudorandom noise. More precisely, we add noise to temperature gradients and obtain stability estimates which correctly predict the numerical results. In particular, if the layers where the parameterization constraint applies contain a strong source term (e.g., due to flowing water), the solution is relatively insensitive to noise. Also, for multiplicative noise affecting heat‐source terms, theoretical stability predictions are confirmed numerically. The main advantage of the CMM is its simple algebraic formulation. Its implementation in the field by means of a pocket calculator allows both a consistency check on the data being collected and estimates of the unknown values of conductivity.
Analysis of the Rayleigh pulse
Authors: Hubral P. , Tygel M.
Published: October 2002

Seismologists make frequent use of wavelets (also referred to as signals, signatures, or pulses), particularly in such fields as seismic filtering, wavelet processing, wave‐propagation modeling, and trace inversion. Whenever possible, the actual seismic wavelet of the real source should be considered (Hosken, 1988). However, frequently, particularly in wave‐propagation modeling, one must consider a synthetic source wavelet. This should, if possible, be given by a simple mathematical formula and possess an easy description for its most important spectral properties (e.g., amplitude and phase spectrum, main frequency, Hilbert transform, etc.). Moreover, the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained.
The deconvolution of marine seismic source: An iterative approach
Authors: Alessandrini Bruno , Gasperini Marco
Published: October 2002

The purpose of this note is to compare an iterative algorithm to the Wiener technique for deconvolution of the sparker signature. The iterative algorithm, first proposed by Brigham et al. (1968), has been compared earlier to the Fourier method to obtain the inverse impulse response function of a long‐period seismic monitoring station (Alessandrini and Perazzolo, 1987).
Wrap‐around removal from one‐dimensional synthetic seismograms
Authors: Thybo Hans
Published: October 2002

One‐dimensional (1-D) synthetic seismograms are important tools in seismic exploration. They play an important role in the correlation of recorded seismograms with borehole logs and also permit the estimation of delay‐type attenuation in finely layered models. Existing computational methods for computing 1-D seismograms can be grouped according to whether the calculations are performed in the time domain or in the frequency domain.
Optimum time‐to‐depth conversion
Authors: Keydar S. , Koren Z. , Kosloff D. , Landa E.
Published: October 2002

Time‐to‐depth conversion is usually accomplished by converting zero‐offset traveltimes, interpreted from a stacked section, to depth using a known velocity field. Time‐to‐depth conversion is formulated as an iterative procedure producing a depth model which minimizes the differences between zero‐offset picked traveltimes and times derived by normal‐incidence ray tracing through the model. The input data consist of traveltimes picked from unmigrated stacked sections, as well as assumed interval velocities in each layer. The method can be applied to models with discontinuities such as pinchouts and faults. To illustrate the method, synthetic and field data examples are included.
Analytic generalized inverse for transmission + reflection tomography
Authors: Schuster Gerard T.
Published: October 2002

This short note presents a 1-D analytic generalized inverse for VSP transmission + reflection tomography. Its validity is restricted to evenly layered media and negligible ray bending. The significance of the result is that the reliability estimate of slowness for 1-D VSP tomography can be analyzed analytically, rather than by empirical guesswork. This can lead to the design of optimal tomography algorithms and field experiments. For example, Salo and Schuster (1989) observed empirically that reflection + transmission VSP data provided a better velocity reconstruction than do transmission VSP data alone. However, the underlying reason for this improvement was not clearly identified. This short note gives an unambiguous explanation.
Electromagnetic sounding in the Columbia Basin, Yakima, Washington
Authors: Wilt M. J. , Morrison H. F. , Lee K. H. , Goldstein N. E.
Published: October 2002

A controlled‐source electromagnetic (CSEM) survey was conducted near Yakima, Washington, to map the thickness and resistivity of a thick volcanic sequence overlying a sedimentary section and to infer structure in the sediments. The survey was conducted with a frequency‐domain system employing loop transmitters 400–500 m on a side and three‐component SQUID magnetometer receivers separated from the loop by 1 to 5 km. Data collected along a 30 km profile orthogonal to regional strike were interpreted initially with 1-D layered models, which were then pieced together to make a geoelectric section. Induction logs in a 5000 m exploration hole at one end of the profile agree very well with the CSEM soundings made around the hole. The geoelectric section reveals a smoothly varying thickness of volcanics with a pronounced anticlinal structure approximately concordant with a surface topographic ridge. To assess the validity of inferring lateral structure from 1-D interpretations, we made scale models of an anticlinal structure and of a surface inhomogeneity and conducted CSEM measurements over the scale models. Layered‐model inversions of these data show that the anticlinal structure and its location are very well determined by 1-D inversion, but its height and width are not accurately determined. CSEM sounding over the surface inhomogeneity model shows that this feature does not significantly degrade the interpretation of a deep target layer. In this setting, a geoelectric section made up from 1-D interpretations provides good qualitative measures of subsurface structure and also provides excellent starting models for detailed 2-D or 3-D modeling.
Attitude, velocity, and depth of a plane refractor from two line profiles
Authors: Aldridge David F.
Published: October 2002

Many refraction seismologists believe that a minimum of two reversed profiles, preferentially oriented at right angles to each other, are necessary to determine the attitude, velocity, and depth of a plane subsurface refractor. Russell et al. (1982) demonstrated that traveltimes recorded along three unreversed spreads can be analyzed to yield this same information. They state that similar measurements made on only two such profiles cannot define the three‐dimensional (3‐D) attitude of the dipping horizon. This statement, however, is incorrect. Russell et al. did not fully use the information contained in the intercept times of the traveltime curves. The purpose of the present note is to demonstrate that, in many cases, two refraction profiles are sufficient to define the 3‐D attitude, true velocity, and depth of a plane refractor. Generally speaking, the main condition required is that the two lines provide independent traveltime information about the subsurface.
Drilling‐induced isothermal remanent magnetization
Authors: Pinto Michael J. , McWilliams Michael
Published: October 2002

The recovery of core samples is important in petroleum exploration, mineral exploration, and scientific drilling projects; and often complete orientation of the samples (azimuth and plunge) is desirable. Recovered cores are usually not azimuthally oriented because of the costs associated with deployment and operation of downhole orientation tools. Inexpensive paleomagnetic orientation methods have been used with considerable success in the borehole environment (Van der Voo and Watts, 1978; Kodama, 1984; Bleakly et al., 1985a, b; Evans and Mailol, 1986; Layer et al., 1988; McWilliams and Pinto, 1988). In some cases, the technique has been hampered by secondary magnetizations associated with the drillstring and/or coring tool, magnetizations which have partially or completely overprinted the primary and secondary magnetizations used for orientation.
Pattern analysis of seismic records
Authors: Le L. H. T. , Nyland Edo
Published: October 2002

The three steps in automated analysis of seismic records are trace matching, event detection, and seismic zoning. Our algorithm matches traces by comparing sequences of peaks on neighboring traces and edits pairs of peaks identified as similar for consistency in trend across and down the record. By combining connected pairs, we obtain laterally coherent events of varying quality which divide a record into zones that may have lithologic significance. These zones can be obtained automatically by applying cluster analysis to seismic attributes and other discriminating properties of these events. On common‐shot gathers from a four‐fold survey in Saskatchewan, Canada, the coherent events which we detected this way are consistent with those recognized visually and are associated with clear formation boundaries. Strong reflections correspond to events detected with high confidence, and the seismic zones show good correlation among shot records. High detection confidence and good correlation indicate that the application of automatic analysis procedures to common‐midpoint gathers from surveys of higher multiplicity is possible and may lead to a new and quick way of obtaining velocity profiles. Zoning, if done properly, provides a compact description of seismic records that may simplify telemetry of large volumes of data.
A vertical array method for shallow seismic refraction surveying of the sea floor
Authors: Hunter J. A. , Pullan S. E.
Published: October 2002

In recent years, specific requirements of offshore geotechnical site investigations, as well as detailed defense research studies, have stimulated research interest in methods for measuring seismic velocities of sea‐floor sediments on the continental shelves. Investigations have used wide‐angie subbottom reflection measurements (McKay and McKay, 1982), bottom‐laid refraction cables (Hunter et al., 1979), and towed refraction arrays, both on the surface (Hunter and Hobson, 1974) and at depth (Fortin et al., 1987; Fagot, 1983).
Spectral analysis in airborne electromagnetics
Authors: Bartel D. C. , Becker A.
Published: October 2002

Interpretation of airborne electromagnetic (AEM) data is mainly concerned with determining the position, dip, and quality (or conductance) of an anomalous geologic feature. A new method of interpretation using spectral analysis has certain advantages over conventional methods. It is specifically applied to the interpretation of AEM anomalies observed with the INPUT1 time‐domain electromagnetic system that are related to thin rectangular conductive plates. Profiles of field data are converted to the wavenumber domain by applying a Fourier transform. Because the amplitude spectrum varies exponentially with the distance from the target to the receiver, the target depth is easily interpreted from the slope of a semilogarithmic plot of the spectrum. Analytical expressions for the amplitude spectrum of an AEM anomaly can only be obtained for a rudimentary model where the target is represented by a single filament of induced current. The spectra of more realistic models such as the dipping infinitely conductive half‐plane and the thin rectangular plate of finite conductance must be obtained numerically. The computed spectra are relatively insensitive to the target dip, except for the case of a horizontal target of finite width. For a flat‐lying target, the spectrum exhibits a distinctive modulation pattern from which the target width can be determined. A low wavenumbers the time‐decay characteristics of a given target are preserved so the its conductance can be determined. In most cases, however, this parameter as well as the target dip are just as easy to evaluate directly from the observed field data. The results obtained with the spectral analysis method of interpretation applied to field examples agree well with the known geology. Interpretation of field data requires correction for the velocity of the aircraft and the time constant of the receiver equipment. In the wavenumber domain, however, these effects are easily eliminated by a simple division. The spectral analysis method of electromagnetic interpretation is useful for determining the depth of the target because it is unaffected by dip, size, conductance, or profile position. One application of this method is in automated interpretation of portions of AEM data profiles, with large data sets over many conductors. Anomalies of interest can be picked out and interpreted automatically.
Seismic lithostratigraphy of deep subsalt Permo‐Carboniferous gas reservoirs, Northwest German Basin
Authors: Mathisen M. E. , Budny M.
Published: October 2002

Recent improvements in land seismic data quality have made it possible to initiate lithostratigraphic interpretations of deep (4000–5500 m; 2.2–2.8 s) subsalt Permo‐Carboniferous gas reservoirs in the Northwest German Basin. The first modeling and interpretation results indicate that the reflection character of Permian reservoir dolomites and sandstones can be interpreted to predict lithology and porosity variations using reflection character analysis. These formations are commonly thick enough to be resolved (>20 m) and typically have velocities 1000 to 2000 m/s slower than overlying and underlying nonreservoir rocks. Deeper Upper Carboniferous reservoir sandstones occur within a discontinuous low‐amplitude seismic facies which can be clearly differentiated from a continuous high‐amplitude facies formed by the less prospective Upper Carboniferous coal measures. The accuracy of Permian reflection character interpretations is dependent on the availability of high‐frequency, zero‐phase, relative amplitude seismic data. New 3-D data are appropriate but of limited availability. To provide suitable 2-D data, wavelet processing of selected variable vintage lines was completed. More routine use of wavelet processing and lithostratigraphic interpretation methods should help to better define reservoir facies and stratigraphic traps, lower prospect risk, and increase success ratios.
Experimental study of acoustic anisotropy and birefringence in dry and saturated Fontainebleau sandstone
Authors: Zamora M. , Poirier J. P.
Published: October 2002

The velocities of ultrasonic P, SH, and SV waves have been measured in two perpendicular directions, in samples of Fontainebleau sandstone as received or thermally cracked, dry, or saturated, under uniaxial stress. We have investigated the effect of cracking, saturation, and uniaxial stress on the velocity of P and S waves in two orthogonal directions (anisotropy) and the velocity of S waves with two orthogonal polarizations in each direction of propagation (birefringence). The effect of cracking, saturation, and uniaxial stress on Poisson’s ratio has also been investigated. The velocity anisotropy is larger for S waves than for P waves and practically disappears in saturated samples. Birefringence is attenuated in saturated samples. Inversion of the results using Crampin’s model gives values of the crack densities in three directions, in qualitative agreement with the state of cracking observed by scanning electron microscopy. In particular, the crack density is found to be near zero in sandstones with rounded pores only. After thermally induced cracking the crack density is found to be ≈20 percent; uniaxial stress closes the cracks in the plane normal to the stress. Also, in naturally cracked samples the crack density is found to be quite high. Uniaxial stress causes the density of cracks to decrease, mostly in the plane normal to the stress.
The Berlage wavelet
Authors: Aldridge David F.
Published: October 2002

Symmetric wavelets are commonly used in seismic modeling studies. However, accurate simulation of many physical wave propagation phenomena requires a causal waveform possessing a certain degree of differentiability. The purpose of this note is to quantitatively describe the characteristics of a relatively unfamiliar wavelet, called the Berlage wavelet, that is appropriate for such studies.