bluuebunny/crossref_metadata_2025 huggingface dataset:
Velocity‐stack and slant‐stack stochastic inversion
Authors: Thorson Jeffrey R. , Claerbout Jon F.
Published: October 2002

Normal moveout (NMO) and stacking, an important step in analysis of reflection seismic data, involves summation of seismic data over paths represented by a family of hyperbolic curves. This summation process is a linear transformation and maps the data into what might be called a velocity space: a two‐dimensional set of points indexed by time and velocity. Examination of data in velocity space is used for analysis of subsurface velocities and filtering of undesired coherent events (e.g., multiples), but the filtering step is useful only if an approximate inverse to the NMO and stack operation is available. One way to effect velocity filtering is to use the operator [Formula: see text] (defined as NMO and stacking) and its adjoint L as a transform pair, but this leads to unacceptable filtered output. Designing a better estimated inverse to L than [Formula: see text] is a generalization of the inversion problem of computerized tomography: deconvolving out the point‐spread function after back projection. The inversion process is complicated by missing data, because surface seismic data are recorded only within a finite spatial aperture on the Earth’s surface. Our approach to solving the problem of an ill‐conditioned or nonunique inverse [Formula: see text], brought on by missing data, is to design a stochastic inverse to L. Starting from a maximum a posteriori (MAP) estimator, a system of equations can be set up in which a priori information is incorporated into a sparseness measure: the output of the stochastic inverse is forced to be locally focused, in order to obtain the best possible resolution in velocity space. The size of the resulting nonlinear system of equations is immense, but using a few iterations with a gradient descent algorithm is adequate to obtain a reasonable solution. This theory may also be applied to other large, sparse linear operators. The stochastic inverse of the slant‐stack operator (a particular form of the Radon transform), can be developed in a parallel manner, and will yield an accurate slant‐stack inverse pair.
Supercritical reflections observed in P- and S- wave data
Authors: Winterstein D. F. , Hanten J. B.
Published: October 2002

We have observed a conspicuous example of supercritical reflection in both P- and SH- wave seismic data. Data were recorded in the Midland Basin (Texas) Project of the Conoco Shear Wave Group Shoot in 1977–1978. P- and S- wave critical angle phenomena, as observed in the data, are remarkably similar. Event amplitudes are small or undetectable at offsets out to about 2 000 ft, but at offsets from 2 500 to 3 600 ft amplitudes are higher than those of any other event. Head waves originating at the critical distance are weak but detectable. Long path multiplies of the supercritical parts of P and SH events appear at expected times and offsets. Constant velocity moveout corrections helped identify them. Sonic logs in combination with a knowledge of the lithology made it possible to model P- wave critical angle phenomena. Agreement of model results with the data was good when we assumed cylindrical wavefronts. As expected, modeling based on plane waves was unable to match observed phase and amplitude behavior. A number of potential uses for supercritical reflections in exploration and data processing readily come to mind, many of them related to the recording of relatively high amplitudes at distances where source noise is low. Observed rise in amplitude near the critical offset was very abrupt, particularly for SH-waves. This suggests that variations in the onset of high amplitudes may be useful for monitoring changes in velocity contrast at the reflecting interface.
A method to analyze and verify deep crustal reflections offshore Costa Rica
Authors: Tsai C. J.
Published: October 2002

A multichannel seismic reflection profile across the oceanic crust seaward of the Middle America Trench off the Nicoya Peninsula, Costa Rica, shows discontinuous, low‐frequency events at 6.5 to 7.0 s. These events might first be interpreted as reflections from the Moho. However, careful analysis of the seismic data suggests that these events represent three‐dimensional (3-D) scattered energy from the rough basaltic basement. Velocity analysis indicates that root‐mean‐square (rms) velocities for these deep “reflection events” are too low to emanate from the Moho. Also, the ghost separation caused by the streamer depth decreases for increasing record time, suggesting that incident angle for these “reflections” increases with time. Furthermore, these events are approximately 13 dB stronger than would be expected for a Moho reflection. Common‐depth‐point (CDP) stacking and velocity filtering were used to attenuate the scattered noise and sideswipe from the basalt. The results show a 21 dB total reduction of scattered energy. However, Moho reflections still cannot be discerned. The results suggest (1) ambient noise after processing is 20 dB below the expected Moho level and is not a factor in detection of the Moho; (2) Moho reflectivity may be smaller than 0.1 (reflectivity is calculated from assumed velocities and densities) and could be as small as 0.05 (the detection threshold); (3) the Moho may not be a discrete reflector and may therefore represent a transition zone; and (4) Moho events may be disorganized by transmission through rough basalt so the CDP stacking process is not effective.
P-SV wave scattering by coal‐seam inhomogeneities
Authors: Edwards S. A. , Asten M. W. , Drake L. A.
Published: October 2002

The dynamic finite‐element method is used to calculate the normal incidence P-SV guided‐wave scattering spectra of 124 models of coal‐seam obstructions commonly encountered in in‐seam seismology. The models are faults of varying throw and dip; thick faults with an associated region of fracturing; dikes of varying width, hardness, and dip; sills of varying hardness; stone rolls of varying height; and seam washouts. Reflection and transmission spectra including mode conversion are studied for incident fundamental symmetric P-SV seam modes. The dynamic finite‐element method is adapted to the calculation of scattering parameters through the consistent boundary condition of Lysmer and Waas. The results complement an earlier study of SH seam‐wave scattering. They show that faults reflect a much higher percentage of SH-wave energy than P-SV, but that P-SV-waves undergo substantially greater mode conversion on scattering from faults. Dikes exhibit thin film interferometric effects for both SH- and P-SV-waves. Sills do not reflect P-SV-waves substantially. Stone rolls cause conversion between symmetric and antisymmetric modes. From the results it is evident that reflection and transmission spectra contain sufficient information on the nature (not merely the existence) of a seam obstruction to justify further efforts in the design of in‐mine seismic observations aimed at allowing characterization as well as location of the obstruction. The names Evison wave and Krey wave are proposed and defined for guided SH-waves and P-SV-waves, respectively.
On: “A least‐squares approach to depth determination from gravity data” by G. P. Gupta,(GEOPHYSICS, 48, 357‐360, March 1983).
Authors: Abdelrahman El‐Sayed M. , Bayoumi Abdel‐Rhim I. , Amin Yehia A.
Published: October 2002

In his paper, Gupta was able to transform the problem of depth estimation of buried structures into a problem of finding a solution of a nonlinear equation in the form of [Formula: see text]. Gupta also indicated that such a numerical approach is found to be capable of determining optimum depths particularly from residual anomaly profiles even if small segments of the gravity profiles are observed. No doubt this numerical approach has its point of view both in theory and practice over any other depth estimation techniques such as those defined by the [Formula: see text] rule (Nettleton, 1940, 1942; Telford et al., 1976). However, Gupta’s technique would be much more effective if applied not to residuals but to derivative anomalies, particularly when the regional field has few extrema in it; this is obviously due to the following.
A numerical solution for the electromagnetic scattering by a two‐dimensional inhomogeneity
Authors: Lee K. H. , Morrison H. F.
Published: October 2002

A numerical solution for electromagnetic scattering from a two‐dimensional earth model of arbitrary conductivity distribution has been developed and compared with analog model results. A frequency‐domain variational integral is Fourier transformed in the strike direction, and a solution is obtained using the finite‐element method for each of a finite number of harmonics or wavenumbers in transform space. The solution is obtained in terms of the secondary electric fields. Principally due to the inaccuracy associated with numerical derivatives of electric fields, the secondary magnetic field is computed by integrating over the scattering currents in harmonic space and is then inverse Fourier transformed.
A statistical analysis of bottom‐hole temperature data in southern Alberta
Authors: Lam H. ‐L. , Jones F. W. , Majorowicz J. A.
Published: October 2002

When bottom‐hole temperatures (BHT) are plotted as functions of depth for different areas, the plots exhibit differences in the spread of the data. The regional variations in spread in southern Alberta were mapped in detail on the basis of 33 653 BHT data from 18 711 wells. There are local areas with anomalously high spread values, and the spread generally increases westward toward the Disturbed Belt. Also, the spread values for data below the Paleozoic erosional surface are greater than those above. Greater spread in the data appears to be associated with the occurrence of faults, steeply dipping strata of different thermal conductivity, and rough topography. The increased spread associated with faults and steeply dipping strata is probably due to water movement. This suggests that bottom‐hole temperatures may provide information about subsurface structure and phenomena as well as information on temperature.
Inversion of seismic data using precritical reflection and refraction data
Authors: Carrion Philip M. , Foster Douglas J.
Published: October 2002

We present a two‐step inversion procedure to extract subsurface velocity estimates from large‐offset seismic data. The first step is the automatic iterative large‐offset inverse method (AILOIM) which we test in the presence of strong water‐bottom multiples. Since this method is based on finding the locus of critically reflected points, low‐velocity zones cannot be resolved and the reconstruction is only an average estimate. In the presence of low‐velocity zones, the second step of the inversion process is required. This second step is a generalized least‐squares inverse scheme applied to the precritical reflections. We computed the inverse solution using a perturbation technique and determined the reference model from an estimate of the average velocity given by the first step. Two major features of this inversion method are: amplitudes of reflection arrivals are incorporated into analysis, and accurate results can be achieved without human interaction (picking the traveltime curves). Numerical examples using synthetic and field data demonstrate the accuracy of our inversion procedure.
Transient response from a planar acoustic interface by a new point‐source decomposition into plane waves
Authors: Hubral Peter , Tygel Martin
Published: October 2002

For the wave field of a point source in full space there currently exist two classical decompositions into plane waves. The wave field can be decomposed into either (a) homogeneous and horizontally propagating (vertically attenuated) inhomogeneous plane waves by using the so‐called Sommerfeld‐Weyl integral, or (b) upgoing and downgoing homogeneous plane waves only using the Whittaker integral. Transient representations of both integrals exist. We propose a new decomposition integral that has a greater flexibility than both classical decompositions. Solutions for the point‐source reflection/transmission response from a planar interface, if based on the Sommerfeld‐Weyl integral, have for instance inherently an infinite integration limit. With the new formula, by which the wave field of a transient point source is decomposed into upgoing and downgoing homogeneous as well as horizontally propagating inhomogeneous transient plane waves, the point‐source response is directly obtained in the form of an integral with a finite integration limit. It can also be interpreted in terms of certain plane waves by which the point source is simulated in a new manner. For that matter, solutions based on the new integral readily reveal the “evanescent” or “nonray” character of the point source. The new formula may be considered an extension of the Sommerfeld‐Weyl or Whittaker integral. It can be used to compute reflection/transmission responses in a compact form in situations where the Sommerfeld‐Weyl integral was hitherto considered fundamental.
Estimation of seabottom reflection characteristics and source signature from seabed reflected waves
Authors: Berteussen K. A. , Alstad O. J.
Published: October 2002

We describe a procedure for modeling the primary and multiple reflected seabed pulses as a function of distance. The assumption is made that the registered pulse can be constructed as a sum of elementary pulses, that is, the time and relative size of the arrivals are calculated for each source‐receiver position. This is done using both angle‐dependent and angle‐independent reflection coefficients at the seabottom. For each receiver channel on the cable, the predicted seismogram is calculated as the sum of the registrations in each hydrophone included in that channel. It is demonstrated first how the shape of the seabottom reflections changes with the sea depth and source‐receiver distance because of geometry effects, and because of the extended sources and receivers applied in marine seismic exploration. Next, We show that angle‐dependent reflection coefficients do introduce additional and sometimes quite drastic variations in the shape of the different pulses. Finally, we demonstrate that the predicted pulses can be matched quite well to observed data from the North Sea. This gives a possibility to estimate the geophysical characteristics of the seabed.
A case study in seismic diffraction near a Gulf Coast salt dome
Authors: Linville A. F. , Dablain M. A.
Published: October 2002

The diffraction response from a sequence of truncated dipping beds is examined. It is shown that standard velocity analysis and interpretation can emphasize the diffracted energy in the common‐depth‐point (CDP) stack. This energy can then produce a distorted image in the poststack migration of the data. In our case this distortion took the form of smaller estimates for the structural dip, which was independently confirmed by well control. Wave‐equation synthetics are also used to support the role of truncated dipping beds as strong diffractors. It is shown that the diffraction from these beds will give rise to certain identifiable characteristics in the CDP data. These characteristics are demonstrated by examining the ideal case of a truncated reflector with dip. It is shown that in the presence of dip, a proper choice for the stacking velocity will lead to the enhancement of the reflected energy at the expense of the diffraction. These stacking velocities can then be used to improve the interval velocity estimates for migration. In this study the application of these ideas brought the structural dip as derived from the surface seismics into good agreement with the well data. In comparison with model data, there was also some evidence that the gas‐water contact could be identified in the reprocessed migration.
Temperature distribution in flowing liquid wells
Authors: Beck A. E. , Shen P. Y.
Published: October 2002

The temperature distribution in flowing liquid wells is usually calculated from a simple equation, advanced by Boldizsar (1958) and Ramey (1962), under the assumption that the vertical temperature gradient is negligibly disturbed by the fluid flow. The crucial parameter in this equation is a time function derived by considering the heat conduction in a region bounded internally by a circular cylinder. The present results, obtained by the alternating direction, implicit, finite‐difference method, confirm the validity of this equation for elapsed time of intermediate range from days to months. Caution must be exercised, however, when the equation is used for very small or very large times. For the impractical case of very small times (< 1 day), the time function should be calculated from the correct model of heat conduction which takes into account the nonzero heat capacity of the borehole fluid. On the other hand, for very large times (> 1 year), the assumption of negligible net heat transfer in the vertical direction, upon which the equation is based, ceases to hold. This leads to the introduction of systematic errors which reach 10 percent after about 11 years, when the equation is used to estimate the formation temperature gradient and/or thermal conductivity.
Compressional and shear arrivals in a multipole sonic log
Authors: Winbow Graham A.
Published: October 2002

A sound source in a liquid‐filled borehole generates, among other excitations, compressional and shear waves in the rock which are detected in the fluid as refractions. It is practical to be able to separate the latter components. I show that this can always be achieved in principle by appropriately choosing the properties of the source. Solutions of the acoustic wave equation in the “far field” of the source are analyzed in detail. Suppose the source radiation depends upon the azimuthal angle η through some function F(η). The refracted waves are analyzed conveniently in terms of Fourier components [Formula: see text], where n and η are Fourier conjugates. For a source symmetrical about the axis of the borehole, as conventional sources are, [Formula: see text] vanishes except for n = 0. Our principal results concern the z dependence of the pressure radiation field in the drilling mud p (r, η, z) (using cylindrical polar coordinates). For a fixed n, as z → ∞, the refracted P‐wave is proportional to [Formula: see text] for n = 0, 1, … . The refracted S‐wave signal is proportional to [Formula: see text]. Thus, for an axially symmetric source, the P‐wave refraction generally dominates the S‐wave refraction as z → ∞. For an axially asymmetric source the S‐wave dominates the P‐wave. An example of an n = 1 source is a horizontally pointing dipole on the borehole axis. Higher order multipole sources also effectively produce nearly pure S‐wave signals in a borehole.
The effect of a conductive half‐space on the transient electromagnetic response of a three‐dimensional body
Authors: SanFilipo William A. , Eaton Perry A. , Hohmann Gerald W.
Published: October 2002

The transient electromagnetic (TEM) response of a three‐dimensional (3-D) prism in a conductive half‐space is not always approximated well by three‐dimensional free‐space or two‐dimensional (2-D) conductive host models. The 3-D conductive host model is characterized by a complex interaction between inductive and current channeling effects. We numerically computed 3-D TEM responses using a time‐domain integral‐equation solution. Models consist of a vertical or horizontal prismatic conductor in conductive half‐space, energized by a rapid linear turn‐off of current in a rectangular loop. Current channeling, characterized by currents that flow through the body, is produced by charges which accumulate on the surface of the 3-D body and results in response profiles that can be much different in amplitude and shape than the corresponding response for the same body in free space, even after subtracting the half‐space response. Responses characterized by inductive (vortex) currents circulating within the body are similar to the response of the body in free space after subtracting the half‐space contribution. The difference between responses dominated by either channeled or vortex currents is subtle for vertical bodies but dramatic for horizontal bodies. Changing the conductivity of the host effects the relative importance of current channeling, the velocity and rate of decay of the primary (half‐space) electric field, and the build‐up of eddy currents in the body. As host conductivity increases, current channeling enhances the amplitude of the response of a vertical body and broadens the anomaly along the profile. For a horizontal body the shape of the anomaly is distorted from the free‐space anomaly by current channeling and is highly sensitive to the resistivity of the host. In the latter case, a 2-D response is similar to the 3-D response only if current channeling effects dominate over inductive effects. For models that are not greatly elongated, TEM responses are more sensitive to the conductivity of the body than galvanic (dc) responses, which saturate at a moderate resistivity contrast. Multicomponent data are preferable to vertical component data because in some cases the presence and location of the target are more easily resolved in the horizontal response and because the horizontal half‐space response decays more quickly than does the corresponding vertical response.
Transient analytic point‐source response of a layered acoustic medium: Part I
Authors: Tygel Martin , Hubral Peter
Published: October 2002

The exact transient responses (e.g., reflection or transmission responses) of a transient point source above a stack of parallel acoustic homogeneous layers between two half‐spaces can be analytically obtained in the form of a finite integral strictly in the time domain. (The theory is presented in part II of this paper, this issue.) The transient acoustic potential of the point source is decomposed into transient plane waves, which are propagated through the layers at any angle of incidence as well in the time domain; finally, they are superposed to obtain the total point‐source response. The theory dealing with transient analytic plane wave propagation is described here. It constitutes an essential part of computing the synthetic seismogram by the new transient method proposed in part II. The plane‐wave propagation is achieved by an exact discrete recursion that automatically handles the conversion of homogeneous waves into inhomogeneous transient plane waves at layer boundaries. A particularly efficient algorithm is presented, that can be viewed as a natural extension of the popular normal‐incidence Goupillaud (1961)-type algorithm to the nonnormal incidence case.
How to include prespecified horizons into minimum‐variance deconvolution and maximum‐likelihood deconvolution
Authors: Mendel J. M.
Published: October 2002

I am frequently asked how to include prespecified horizon (time) information in both minimum‐variance deconvolution (MVD) and maximum‐likelihood deconvolution (MLD) (e.g., Mendel, 1983). To explain how this is done, I briefly review the convolutional model, which is the starting point for MVD and MLD; explain how MVD and MLD are modified to incorporate the known‐horizon information; and finally, discuss two detectors used in MLD to see how they must be modified. Fortunately, few modifications are needed in MVD or MLD, and it is quite straightforward to incorporate known‐horizon information into these techniques.
Asymptotic formula of the transform function for the layered‐earth potential and its applications to interpretation of resistivity sounding data
Authors: Gai‐shan Zhao
Published: October 2002

With the development of computation techniques based on the digital linear filter method and the wide use of computers, automatic interpretation of vertical electric sounding (VES) data has become practical and common. The digital linear filter method developed in Ghosh (1971a, b) makes solving the inverse problem of VES easier and more practical, because it requires less computer time and storage space, is more accurate than other methods, and does not restrict the number of layers, electrode spacings, and layer depths. However, considerable ambiguity in the interpretation may result when many layers are involved. This means that strongly differing layer distributions may yield apparent resistivity sounding curves that, although not equal, differ so slightly that they cannot be accurately distinguished. In other words, the interpretation provided is only one of many acceptable interpretations, all of which are consistent with the field curves within the accuracy of measurements. Some combination parameters obtained may be useful in this case, and they are needed sometimes. I present a new method to interpret resistivity sounding data, by which some combination parameters such as total longitudinal conductance, total transverse resistance, and the resistivity of the substratum can be obtained.
t-x reflection curves for arbitrary three‐dimensional media in terms of geometry of a reflector and a near‐reflector wavefront
Authors: Nedlin G.
Published: October 2002

A general relation between a normal‐moveout velocity (NMOV) for t-x (time‐offset) reflection curves and the geometrical properties of a reflector and a wavefront in the vicinity of the reflector has been found. Furthermore, by considering the reflector as a set of zero‐offset reflecting points for different shot locations on the earth’s surface, a new formulation of the special “seismic” parametric description of a reflecting surface allows the arrival times to be related directly to the wavefront equation, without introducing any earth model above the reflector. The NMOV is expressed in terms of the local velocity near the reflector and the curvatures of the reflector and of the near‐reflector wavefront. New equations for geometrical migration make it possible to do direct wavefront modeling without earth modeling (above the reflector). If t-x curves are approximated by hyperbolas (i.e., terms higher than those quadratic in the offsets are neglected), all rays in a common‐midpoint (CMP) panel with a fixed midpoint have the same reflecting point, for any earth model.
Effects of geologic noise on cross‐borehole electrical surveys
Authors: Zhao J. X. , Rijo L. , Ward S. H.
Published: October 2002

Using a finite‐element algorithm which allows for subsurface current and potential electrodes in dc resistivity, we have analyzed the detection of a thin, 2-D, conductive inhomogeneity in the presence of several sources of geologic noise. The pole‐pole array with the current electrode fixed in one borehole and the potential electrode movable in adjacent boreholes is the main array of concern. The sources of noise are surface topography, buried topography, random geologic noise, quasi‐random geologic noise (nontarget inhomogeneities), layering, and a vertical contact. For several positions of a downhole source electrode, normalized apparent resistivities have been computed. These resistivities have been contoured in section view as appropriate to cross‐borehole investigations. For the models studied here, surface topography, buried topography, random and quasi‐random geologic noise do not obscure the anomaly due to the thin conductive inhomogeneity. In a vertically or horizontally layered earth, the anomaly due to the inhomogeneity is almost totally obscured. Normalization of the apparent resistivity by the variable apparent resistivity of a layered half‐space can help alleviate the problem. However, it may not be possible to apply such normalization in field studies. Other arrays such as the cross‐borehole dipole‐dipole array, with the dipoles moved simultaneously, may then be required.
On the effect of recording aperture in migration of vertical seismic profile data
Authors: McMechan George A. , Hu Liang‐Zie
Published: October 2002

Miller et al. (1984) presents examples of different images of a pattern of point diffractors obtained by migrating data from various sources and receivers. In particular, they consider combinations of vertical seismic profile (VSP) and surface survey data. Related VSP studies by Kohler and Koenig (1984), Hu and McMechan (1986), Chang and McMechan (1986), and by Sun and McMechan (1986) suggest the importance of multiple offsets for imaging of complicated structures in VSP experiments. The key point is similar to that made by Berkhout (1980), namely, image resolution varies directly with recording aperture. Physically, of course, reconstruction of a structural image by migration can utilize only those waves that were recorded. Partial data produce partial images.
On: “High‐resolution common‐depth point profiling: Field acquisition parameter design,” by R. Knapp and D. Steeples (GEOPHYSICS, 51, 283–294, February, 1986).
Authors: Mayne W. Harry
Published: October 2002

I have read your article with interest and congratulate you on an excellent overview of this topic. There are a couple of points on which I would like to comment, however.
Attenuation measurements on shallow seismic refraction data
Authors: Hatherly P. J.
Published: October 2002

Techniques of making seismic attenuation measurements are of interest in engineering geophysics because they allow rock type and quality to be estimated. The measurements may be made on field data from spectral amplitudes, amplitude decay curves, or observed pulse broadening. With shallow seismic refraction data, attenuation is best measured from the pulse broadening. I discuss the problem and demonstrate a computer technique for making routine measurements.
Applications and advantages of the Slingram electromagnetic method for archaeological prospecting
Authors: Tabbagh Alain
Published: October 2002

The electromagnetic Slingram method can provide three types of information simultaneously: (1) the apparent resistivity of the ground; (2) its apparent susceptibility; and (3) the characteristic signatures of buried metallic objects. To build an apparatus with these three measurement capabilities requires an appropriate choice of parameters, including frequency, coil separation, and coil orientation as well as calculations which take into account the electrical resistivity and the magnetic susceptibility of the ground. The value of the Slingram method for archaeological applications is shown by two examples: (1) a Gallo‐Roman pottery workshop investigated with measurements of the apparent susceptibility using a reduced sampling wide mesh grid technique; and (2) the study of a Bronze hoard site located in a marsh. Capabilities of the Slingram method may be improved by further study of an apparatus using several receivers which would increase the depth of investigation. Use of several frequencies would overcome difficulties related to resolving the magnetic quadrature susceptibility.
Seismic mis‐tie adjustment procedure (SMAP) using a minimax‐minisum strategy
Authors: Indelicato G. J. , Moore G. C.
Published: October 2002

Seismic mis‐ties in a grid of control reduce the reliability of the interpretation. This is especially important in areas of low relief where minor changes in dip are critical. Existing methods for adjusting mis‐tie errors generally alter the dip along individual lines. We present a linear programming formulation for adjusting the individual seismic mis‐tie errors surface without altering the dip seen on the individual seismic line. First we minimize the maximum intersectional error (minimax objective) and then, given that objective, we minimize the sum of the remaining errors in the grid (minisum objective). This is subject to the constraint that the adjustments along any given line produce no rotation. Thus the original geometry (dip) identified by the interpreter is preserved. The results of a sample problem show that the method substantially reduces mis‐tie errors without rotation, and that the adjusted data produce interpretable contours.
Apparent axial properties of transversely isotropic media
Authors: Byun Bok S. , Cheng Shi‐Chen W.
Published: October 2002

Byun (1984) described some important surface seismic characteristics (such as “apparent” velocities) for transversely isotropic media. His theoretical development was based on the elliptical surface fit to the actual wave surface of energy propagation from a point source to describe local properties of the ray. In this note we give more theoretical insight into the apparent axial properties of the surface observations made in Byun’s (1984) paper. More comprehensive studies were reported in Helbig (1983) and Hake et al. (1984) for other surface seismic properties of transversely isotropic media.
Synthetic full‐waveform acoustic logs in cased boreholes, II—Poorly bonded casing
Authors: Tubman Kenneth M. , Cheng C. H. , Cole S. P. , Toksöz M. Nafi
Published: October 2002

A generalization of the technique of Tubman et al. (1984) allows the inclusion of intermediate fluid layers in the theoretical study of elastic wave propagation in a layered borehole. The number and location of fluid layers are arbitrary. The only restrictions are that the central cylinder is fluid and the outermost formation is solid. Synthetic full‐waveform microseismograms in poorly bonded cased holes can be generated, allowing investigation of free pipe and cement sheathed pipe with no bond to the formation. If there is a fluid layer between the steel and the cement, the steel is free to ring. The first arrival in this situation is from the casing, even with an extremely thin fluid layer or microannulus. The amplitude and duration of the pipe signal depend upon the thickness of the fluid layer. While the first arrival is from the casing, the formation body‐wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small, it is possible to distinguish the formation P-wave arrival. If the fluid layer is between the cement and the formation, then the steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thicknesses of the fluid and cement layers are important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe and make it possible to distinguish formation arrivals. If there is less cement bonded to the steel, the cement does not damp out the steel ringing but the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends upon the velocities and thicknesses of the steel and cement layers.
The effect of structure and anisotropy on resistivity measurements
Authors: Matias M. J. S. , Habberjam G. M.
Published: October 2002

When conducting resistivity investigations over steeply dipping geologic structures, large orientational variations in resistivity response are commonly encountered. These variations can arise from resistivity contrasts between constituent layers or from anisotropy within the beds. When such structures are concealed, a thorough sampling of these orientational variations must be conducted. Field experience and model studies have shown that such sampling can be conveniently conducted using the crossed‐square array and that the orientational variations encountered can be adequately summarized by the anisotropically defined parameters of apparent resistivity, anisotropy, and strike derived from these array measurements.
Analysis of multiple‐source bipole‐quadripole resistivity surveys using the apparent resistivity tensor
Authors: Bibby H. M.
Published: October 2002

Measurements of apparent resistivity made using the bipole‐dipole method depend upon the location and orientation of the current source relative to the body under study. Although it has been recognized that this dependence on orientation can be partially overcome by use of two current bipoles with different orientations, no agreement on the method of analysis of multiple source surveys has been reached. The most general form of presentation of such results is an apparent resistivity tensor. Various rotation invariants derived from the apparent resistivity tensor can be regarded as mean values of apparent resistivity, independent of the direction of the electric field, thus greatly reducing the “false anomalies” typical of single‐source bipole‐dipole survey results. Two of the tensor invariants obey the principle of reciprocity: if the roles of the current and potential electrodes are interchanged, the invariants are unchanged. The properties of the apparent resistivity tensor are demonstrated for selected simple models. For a horizontally layered medium, when the receiver array is far from the current source, the tensor is symmetric and has invariants which depend only on the distance from the current source. The extreme values of apparent resistivity occur when the electric field vector is tangential and radial relative to the current source. These extreme values correspond to the Schlumberger apparent resistivity and the “polar” dipole apparent resistivity, respectively. Lateral discontinuities in resistivity are modeled with both a single vertical discontinuity and a hemispherical model. The source‐dependent variations in the apparent resistivity derived from a single‐current bipole are greatly reduced in plots of the tensor invariants. For a vertical discontinuity, the tensor trace (the sum of the diagonal elements) is close to the resistivity underlying the receiver site, whereas for a hemisphere, the square root of the tensor determinant gives the best representation. Near lateral discontinuities in resistivity, the apparent resistivity tensor indicates strong dependence of apparent resistivity on the direction of the measured electric field. This apparent anisotropy can be used as an indicator of such discontinuities, yielding both position and orientation of the discontinuity.
Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results
Authors: Gauthier Odile , Virieux Jean , Tarantola Albert
Published: October 2002

The nonlinear problem of inversion of seismic waveforms can be set up using least‐squares methods. The inverse problem is then reduced to the problem of minimizing a lp;nonquadratic) function in a space of many [Formula: see text] variables. Using gradient methods leads to iterative algorithms, each iteration implying a forward propagation generated by the actual sources, a backward propagation generated by the data residuals (acting as if they were sources), and a correlation at each point of the space of the two fields thus obtained, which gives the updated model. The quality of the results of any inverse method depends heavily on the realism of the forward modeling. Finite‐difference schemes are a good choice relative to realism because, although they are time‐consuming, they give excellent results. Numerical tests performed with multioffset synthetic data from a two‐dimensional model prove the feasibility of the approach. If only surface‐recorded reflections are used, the high spatial frequency content of the model (but not the low spatial frequencies) is recovered in few (≃5) iterations. By using transmitted data also (e.g., between two boreholes), all the spatial frequencies are recovered. Since the problem is nonlinear, if the initial guess is far enough from the true solution, the iterative algorithm may converge into a secondary solution. A nonlinear inversion with 8 shots, each shot recorded at 400 receiver locations, with 700 samples in each seismogram, corresponding to a 2-D model described by 40 000 grid points, takes approximately 1 hour in a CRAY 1S supercomputer.
The use and misuse of apparent resistivity in electromagnetic methods
Authors: Spies Brian R. , Eggers Dwight E.
Published: October 2002

Problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly. Several definitions of apparent resistivity are available for use in electromagnetic methods; however, those most commonly used do not always exhibit the best behavior. Many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used. It is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve. For the in‐loop transient electromagnetic (TEM) method, apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response. A comparison of “exact” and “asymptotic” formulas for the TEM method reveals that automated schemes for distinguishing early‐time and late‐time branches are at best tenuous, and those schemes are doomed to failure for a certain class of resistivity structures (e.g., the loop size is large compared to the layer thickness). For the magnetotelluric (MT) method, apparent resistivity curves defined from the real part of the impedance exhibit much better behavior than curves based on the conventional definition that uses the magnitude of the impedance. Results of using this new definition have characteristics similar to apparent resistivity obtained from time‐domain processing.
Three‐dimensional determination of structure and velocity by seismic tomography
Authors: Chiu S. K. L. , Kanasewich E. R. , Phadke S.
Published: October 2002

A computerized seismic tomographic method was developed to obtain body‐wave velocities and three‐dimensional (3-D) structure of interfaces from reflection data simultaneously. The medium consists of layers with continuous arbitrary 3-D curved interfaces separating homogeneous material with different acoustic properties. The interface is defined by a polynomial surface. The elastic waves are assumed to be transmitted or reflected at curved interfaces in which the raypaths satisfy Snell's law. The ray tracing for each source‐receiver pair is determined by solving a system of nonlinear equations. This method of 3-D ray tracing is effective in computing many seismic rays, including converted phases and multiples. A damped least‐squares inversion scheme is formulated to reconstruct the interval velocity and 3-D structure of the interface by minimizing the difference between observed traveltimes and computed traveltimes. The results from a synthetic model indicate that the solutions converge quickly to the true model. The seismic tomographic method was applied to a Vibroseis seismic section obtained in 1984 on Vancouver Island as part of PROJECT LITHOPROBE. The method was found to be useful for imaging the 3-D subsurface of subducting plates by taking advantage of crooked lines in the nominally two‐dimensional seismic reflection survey.
A simplified fast method of deriving weathering corrections
Authors: Morsi M. H.
Published: October 2002

I propose a method for deriving static corrections to a subsurface datum where a constant ratio can be assumed between the velocity of the weathered layer and the velocity of the subweathered layer. This ratio determines the proportionality constant for the relationship between the static correction to the datum and a refracted arrival time at a certain distance to its elevation above the datum. The advantage of the method lies in its rapid computation of the static corrections where the assumed velocity distribution applies.
A comparison of methods for approximating the vertical gradient of one‐dimensional magnetic field data
Authors: Paine J. W.
Published: October 2002

The vertical gradient of a one‐dimensional magnetic field is known to be a useful aid in interpretation of magnetic data. When the vertical gradient is required but has not been measured, it is necessary to approximate the gradient using the available total‐field data. An approximation is possible because a relationship between the total field and the vertical gradient can be established using Fourier analysis. After reviewing the theoretical basis of this relationship, a number of methods for approximating the vertical gradient are derived. These methods fall into two broad categories: methods based on the discrete Fourier transform, and methods based on discrete convolution filters. There are a number of choices necessary in designing such methods, each of which will affect the accuracy of the computed values in differing, and sometimes conflicting, ways. A comparison of the spatial and spectral accuracy of the methods derived here shows that it is possible to construct a filter which maintains a reasonable balance between the various components of the total error. Further, the structure of this filter is such that it is also computationally more efficient than methods based on fast Fourier transform techniques. The spacing and width of the convolution filter are identified as the principal factors which influence the accuracy and efficiency of the method presented here, and recommendations are made on suitable choices for these parameters.
Reflection coefficients at pore‐fluid contacts as a function of offset
Authors: Wright J.
Published: October 2002

It has been recognized for some time that seismic amplitude variations with offset contain lithologic and pore‐fluid information. However, the exact formulas for plane‐wave reflection coefficients are not easily interpreted in terms of the effects expected from classes of geologic models. For fluid contacts within a rock unit (which may show up as “flat spots” in seismic data), simplified approximate formulas can be derived to predict reflection coefficients for compressional (P) and shear (S) waves. The formulas derived in this note predict (under the assumption that changes in pore fluid do not affect the elastic properties of the rock matrix) that the P and S reflection coefficients from a gas‐brine, gas‐oil, or oil‐brine contact increase monotonically with offset, and that for a gas‐ brine contact, the ratio of the two coefficients is sensitive to gas saturation.
A new variable‐magnetization terrain correction method for aeromagnetic data
Authors: Grauch V. J. S.
Published: October 2002

Terrain effects in aeromagnetic data are produced by rugged, magnetic topography. These effects mimic the shape of topography and can often be so large that they obscure anomalies of interest. Thus it is desirable to remove terrain effects from aeromagnetic data in order to isolate the anomalies to be investigated. However, removal of aeromagnetic terrain effects has been a longstanding problem. Previously developed methods have succeeded only in certain, specific geologic situations. I present a new aeromagnetic terrain‐correction method that is superior to the previously developed methods for the general case. This method takes into account the highly variable magnetic properties of rocks and can remove terrain effects whether the sources of interest are shallow or deep. The new method is based on the assumption that magnetic sources of interest are often geometrically unrelated to terrain. It finds the magnetization that gives a magnetic‐field residual with minimum correlation to terrain effects for a window of data within a grid of magnetic‐field values. By repeating the calculation for windows covering the entire grid, a grid of variable‐magnetization values is produced which is combined with topography to calculate a magnetic‐terrain correction. The variable‐magnetizaton method was extensively tested using theoretical models (where the answer is known) and using real data from the Lake City caldera area in the San Juan Mountains of southern Colorado. The tests demonstrated the method’s effectiveness in removing terrain effects from aeromagnetic data. Valid terrain corrections were not obtained where anomalies of interest correlated with terrain effects. However, these places are readily recognizable and easily corrected by editing some of the magnetization values.