bluuebunny/crossref_metadata_2025 huggingface dataset:
Inversion of azimuthally dependent NMO velocity in transversely isotropic media with a tilted axis of symmetry
Authors: Grechka Vladimir , Tsvankin Ilya
Published: October 2002

Just as the transversely isotropic model with a vertical symmetry axis (VTI media) is typical for describing horizontally layered sediments, transverse isotropy with a tilted symmetry axis (TTI) describes dipping TI layers (such as tilted shale beds near salt domes) or crack systems. P-wave kinematic signatures in TTI media are controlled by the velocity [Formula: see text] in the symmetry direction, Thomsen’s anisotropic coefficients ε and δ, and the orientation (tilt ν and azimuth β) of the symmetry axis. Here, we show that all five parameters can be obtained from azimuthally varying P-wave NMO velocities measured for two reflectors with different dips and/or azimuths (one of the reflectors can be horizontal). The shear‐wave velocity [Formula: see text] in the symmetry direction, which has negligible influence on P-wave kinematic signatures, can be found only from the moveout of shear waves. Using the exact NMO equation, we examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parameters and establish the necessary conditions for a stable inversion procedure. Since the azimuthal variation of the NMO velocity is elliptical, each reflection event provides us with up to three constraints on the model parameters. Generally, the five parameters responsible for P-wave velocity can be obtained from two P-wave NMO ellipses, but the feasibility of the moveout inversion strongly depends on the tilt ν. If the symmetry axis is close to vertical (small ν), the P-wave NMO ellipse is largely governed by the NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η. Although for mild tilts the medium parameters cannot be determined separately, the NMO-velocity inversion provides enough information for building TTI models suitable for time processing (NMO, DMO, time migration). If the tilt of the symmetry axis exceeds 30°–40° (e.g., the symmetry axis can be horizontal), it is possible to find all P-wave kinematic parameters and construct the anisotropic model in depth. Another condition required for a stable parameter estimate is that the medium be sufficiently different from elliptical (i.e., ε cannot be close to δ). This limitation, however, can be overcome by including the SV-wave NMO ellipse from a horizontal reflector in the inversion procedure. While most of the analysis is carried out for a single layer, we also extend the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation. A synthetic example for a strongly anisotropic, stratified TTI medium demonstrates a high accuracy of the inversion (subject to the above limitations).
The 3-D geometry of the Linglong granitic complex from 2-D gravity forward modeling, Shandong Province, east China
Authors: Zeng Hualin , Wan Tianfeng , Teyssier Christian , Yao Changli , Tikoff Basil
Published: October 2002

The 3-D geometry of the Linglong granitic complex, Shandong Province, east China, is derived from 2-D gravity forward modeling constrained by geological data. A study of the geometry of the granite body at depth is particularly significant to better understand emplacement mechanisms and to guide gold exploration. The geometry of the granitic complex is analyzed using 2-D gravity forward modeling, constrained by the outcrops of the granites along each modeled profile. Anomalies along the profile were modeled using an interactive program derived from 2-D forward‐modeling techniques. The results show the Linglong granitic complex is a sheet‐like body of 3100 km2 in areal extent and a maximum thickness of 8 km. It is not a deeply rooted batholith as previously inferred.
Estimating the amount of gas hydrate and free gas from marine seismic data
Authors: Ecker Christine , Dvorkin Jack , Nur Amos M.
Published: October 2002

Marine seismic data and well‐log measurements at the Blake Ridge offshore South Carolina show that prominent seismic bottom‐simulating reflectors (BSRs) are caused by sediment layers with gas hydrate overlying sediments with free gas. We apply a theoretical rock‐physics model to 2-D Blake Ridge marine seismic data to determine gas‐hydrate and free‐gas saturation. High‐porosity marine sediment is modeled as a granular system where the elastic wave velocities are linked to porosity; effective pressure; mineralogy; elastic properties of the pore‐filling material; and water, gas, and gas‐hydrate saturation of the pore space. To apply this model to seismic data, we first obtain interval velocity using stacking velocity analysis. Next, all input parameters to the rock‐physics model, except porosity and water, gas, and gas hydrate saturation, are estimated from geologic information. To estimate porosity and saturation from interval velocity, we first assume that the entire sediment does not contain gas hydrate or free gas. Then we use the rock‐physics model to calculate porosity directly from the interval velocity. Such porosity profiles appear to have anomalies where gas hydrate and free gas are present (as compared to typical profiles expected and obtained in sediment without gas hydrate or gas). Porosity is underestimated in the hydrate region and is overestimated in the free‐gas region. We calculate the porosity residuals by subtracting a typical porosity profile (without gas hydrate and gas) from that with anomalies. Next we use the rock‐physics model to eliminate these anomalies by introducing gas‐hydrate or gas saturation. As a result, we obtain the desired 2-D saturation map. The maximum gas‐hydrate saturation thus obtained is between 13% and 18% of the pore space (depending on the version of the model used). These saturation values are consistent with those measured in the Blake Ridge wells (away from the seismic line), which are about 12%. Free‐gas saturation varies between 1% and 2%. The saturation estimates are extremely sensitive to the input velocity values. Therefore, accurate velocity determination is crucial for correct reservoir characterization.
Electric field of a horizontal antenna above a homogeneous half‐space: Implications for GPR
Authors: Baumann Christoph E. , Sampaio Edson E. S.
Published: October 2002

Inverse modeling and interpretation of subsurface structures depend on accurate knowledge of the undisturbed field. This is especially true in the analysis of radargrams, in which it is difficult to resolve the upper homogeneous medium from the less shallow scatterers. The available forward models based on plane‐wave and ray approximation are not accurate enough for this task. To improve resolution capabilities, we determine the undisturbed field using exact expressions for the electric field of a sine‐shaped ground‐penetrating radar (GPR) signal antenna above a homogeneous half‐space. In the frequency domain it consists of the sum of two improper integrals with complex integrands. Each integrand contains a kernel multiplied by a Bessel function of the first kind and of order zero or one. In the general case these integrals do not have a solution in closed form, and their integrands are poorly convergent. Therefore, to solve the integrals we must use a special formalism involving integrals around branch points. When we assume that both the transmitter and the receiver are on the boundary of the half‐space, there exist analytic solutions for the first integral without further restrictions and for the second integral for two special cases: free space and half‐space, neglecting displacement currents. We check our corresponding numerical results against these analytic solutions. In the time domain we represent the electric field as a function of transmitter‐receiver offset and time. For a purely dielectric half‐space the backtransformation of the first integral is analytical under the assumed simplification, allowing us to check the numerical results obtained with a fast Fourier transform (FFT) algorithm. These results allowed us to design radargrams for five different models of a homogeneous earth, and they are fundamental for interpretation and further research of GPR modeling.
Multicomponent Kirchhoff migration
Authors: Hokstad Ketil
Published: October 2002

This paper presents a method for elastic and viscoelastic imaging of multicomponent seismic data. The method is based on Claerbout’s survey‐sinking concept and the (visco)elastic Kirchhoff integral for the displacement field. Assuming a multishot and multireceiver experiment, the migration process is formulated as a wavefield reconstruction problem, using the (visco)elastic Kirchhoff integral twice. First, the receiver coordinates are downward continued. Second, the source coordinates are downward continued. The multicomponent seismic data are treated as a vector wavefield in which the data measurements may be displacement velocity or traction (pressure). The theoretical formulation is based on the viscoelastic Hooke’s law and Newton’s equation of motion as the physical model for seismic wave propagation. It is valid for linear viscoelastic media with any anisotropic symmetry. When the lowest‐order ray approximation is introduced, the migration equation takes a form similar to conventional Kirchhoff migration. To obtain the imaging equations, the downward‐continued wavefield is related to the ray‐Born approximation. Numerical results are shown from elastic imaging of synthetic and real marine walkaway vertical seismic profiling (VSP) data.
A blind interpretation of drill‐bit signals
Authors: Poletto Flavio
Published: October 2002

The role of kurtosis in evaluating the quality of vertical seismic profiling (VSP) drill‐bit data is investigated. The calculations show how kurtosis depends on the dominant frequency, bandwidth, and phase content of a seismic signal. This analysis is applied to synthetic and real common‐offset and common‐shot drill‐bit seismograms to evaluate the prominence and quality of the first arrival and other coherent events. High values of kurtosis correspond to an isolated first arrival or to a compressed coherent noise event, while low values are typical of low S/N (distributed) ratio traces. Kurtosis analysis applied to drill‐bit VSP data while drilling proved to be successful at identifying high‐quality traces with little interpretational input.
A sparse spectrum technique for gridding and separating potential field anomalies
Authors: Guspí Fernando , Introcaso Beatriz
Published: October 2002

The separation of regional and residual potential field anomalies, regarded as a spectral problem, can be greatly facilitated when a spectrum estimate shows a clear break between low‐ and high‐frequency components, a feature that normal fast‐Fourier‐transform (FFT) methods fail to present. In this work, we model the discrete Fourier transform of a potential field, measured at stations irregularly distributed on a surface, by means of a high‐resolution sparse estimate derived originally for seismic signal processing. The coefficients of this estimate, which are distributed according to the Cauchy probability law, produce a model with only few components having a significant value. A steepest‐descent algorithm gives a computing alternative to large matrix multiplications and inversions. Advantages of taking this approach are twofold. First, the high‐resolution transform can be used as a gridding tool to evaluate the potential field either on a horizontal plane or on the topographic surface. The enhancement of the spectral peaks and the virtual absence of sidelobes prevents oscillations and edge effects in the result. Secondly, the sparse distribution of the spectral elements allows the interpreter to locate clearly the low‐frequency components related to the regional field. After a second and faster pass, the values of those coefficients can be redefined in order to obtain a more robust separation, ajusting the residuals by the Cauchy criterion. A theoretical noise‐free example to separate the magnetic anomaly of a prism from a polynomial background illustrates well the difference between sparse and FFT spectra. An example with real Bouguer anomalies in the Interserrana basin, Argentina, shows that gridding results, in this case reduced to sea level, compare well with those obtained by other gridding methods, and that the separation procedure is able to outline well defined areas of positive and negative residual anomalies.
Fresnel zones and spatial resolution for P- and SH-waves in transversely isotropic media
Authors: Okoye Patrick N. , Uren Norm F.
Published: October 2002

In an elastically anisotropic medium where the seismic wave velocity is a function of direction, the wavefront shape is nonspherical and, in most cases, assumes a nonelliptical shape. Numerical modelling techniques have been used to calculate the Fresnel‐zone diameter for compressional (P) and shear (SH) waves in transversely isotropic and isotropic media, respectively. The size of the Fresnel zone is found to be predominantly dependent on the curvatures and wavelength of the wavefront as well as the dip angle of the reflector. In addition, the anisotropic elastic parameters δ* (critical near‐vertical anisotropy), ε (the P-wave anisotropy), and γ (the SH-wave anisotropy) are found to significantly affect the size of the Fresnel zone. Numerical modeling results show considerable differences between the Fresnel zones for anisotropic and isotropic velocity functions at various reflector dips. In addition, the Fresnel‐zone dimensions for anisotropic media exhibit asymmetry and considerable change with dip. By way of contrast, those of the corresponding isotropic velocity field exhibit symmetry and negligible variation with dip. The spatial resolution of unmigrated seismic data in an anisotropic medium would consequently be significantly different from that determined for the same medium if it is assumed to be isotropic. Physical modeling results demonstrate that anisotropy can significantly affect the spatial resolving power of seismic waves. The degree of these effects depends on the wavefront curvature, which changes with dip and orientation of the symmetry axis. This observation indicates that the spatial imaging of unmigrated reflection events from the base of thick shale sediments will be affected by anisotropy.
Kirchhoff modeling, inversion for reflectivity, and subsurface illumination
Authors: Duquet Bertrand , Marfurt Kurt J. , Dellinger Joe A.
Published: October 2002

Because of its computational efficiency, prestack Kirchhoff depth migration is currently one of the most popular algorithms used in 2-D and 3-D subsurface depth imaging. Nevertheless, Kirchhoff algorithms in their typical implementation produce less than ideal results in complex terranes where multipathing from the surface to a given image point may occur, and beneath fast carbonates, salt, or volcanics through which ray‐theoretical energy cannot penetrate to illuminate underlying slower‐velocity sediments. To evaluate the likely effectiveness of a proposed seismic‐acquisition program, we could perform a forward‐modeling study, but this can be expensive. We show how Kirchhoff modeling can be defined as the mathematical transpose of Kirchhoff migration. The resulting Kirchhoff modeling algorithm has the same low computational cost as Kirchhoff migration and, unlike expensive full acoustic or elastic wave‐equation methods, only models the events that Kirchhoff migration can image. Kirchhoff modeling is also a necessary element of constrained least‐squares Kirchhoff migration. We show how including a simple a priori constraint during the inversion (that adjacent common‐offset images should be similar) can greatly improve the resulting image by partially compensating for irregularities in surface sampling (including missing data), as well as for irregularities in ray coverage due to strong lateral variations in velocity and our failure to account for multipathing. By allowing unstacked common‐offset gathers to become interpretable, the additional cost of constrained least‐squares migration may be justifiable for velocity analysis and amplitude‐variation‐with‐offset studies. One useful by‐product of least‐squares migration is an image of the subsurface illumination for each offset. If the data are sufficiently well sampled (so that including the constraint term is not necessary), the illumination can instead be calculated directly and used to balance the result of conventional migration, obtaining most of the advantages of least‐squares migration for only about twice the cost of conventional migration.
The offset‐midpoint traveltime pyramid in transversely isotropic media
Authors: Alkhalifah Tariq
Published: October 2002

Prestack Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an offset‐midpoint traveltime equation, Cheop’s pyramid equivalent equation for VTI media. The derivation of such an equation for VTI media requires approximations that pertain to high frequency and weak anisotropy. Yet the resultant offset‐midpoint traveltime equation for VTI media is highly accurate for even strong anisotropy. It is also strictly dependent on two parameters: NMO velocity and the anisotropy parameter, η. It reduces to the exact offset‐midpoint traveltime equation for isotropic media when η = 0. In vertically inhomogeneous media, the NMO velocity and η parameters in the offset‐midpoint traveltime equation are replaced by their effective values: the velocity is replaced by the rms velocity and η is given by a more complicated equation that includes summation of the fourth power of velocity.
Least‐squares DMO and migration
Authors: Ronen Shuki , Liner Christopher L.
Published: October 2002

Conventional processing, such as Kirchhoff dip moveout (DMO) and prestack full migration, are based on independent imaging of subsets of the data before stacking or amplitude variation with offset (AVO) analysis. Least‐squares DMO (LSDMO) and least‐squares migration (LSMig) are a family of developing processing methods which are based on inversion of reverse DMO and demigration operators. LSDMO and LSMig find the earth model that best fits the data and a priori assumptions which can be imposed as constraints. Such inversions are more computer intensive, but have significant advantages compared to conventional processing when applied to irregularly sampled data. Various conventional processes are approximations of the inversions in LSDMO and LSMig. Often, processing is equivalent to using the transpose of a matrix which LSDMO/LSMig inverts. Such transpose processing is accurate when the data sampling is adequate. In practice, costly survey design, real‐time coverage quality control, in‐fill acquisition, redundancy editing, and prestack interpolation, are used to create a survey geometry such that the transpose is a good approximation of the inverse. Normalized DMO and migration are approximately equivalent to following the application of the above transpose processing by a diagonal correction. However, in most cases, the required correction is not actually diagonal. In such cases LSDMO and LSMig can produce earth models with higher resolution and higher fidelity than normalized DMO and migration. The promise of LSMig and LSDMO is reduced acquisition cost, improved resolution, and reduced acquisition footprint. The computational cost, and more importantly turn‐around time, is a major factor in the commercialization of these methods. With parallel computing, these methods are now becoming practical.
Seismic exploration in complex terrains: A processing experience in the Southern Apennines
Authors: Mazzotti Alfredo P. , Stucchi Eusebio , Fradelizio Gian Luigi , Zanzi Luigi , Scandone Paolo
Published: October 2002

We discuss a data‐processing sequence adopted to reprocess a seismic line that crosses the Italian southern Apennines from the Tyrrhenian Sea to the Adriatic margin and investigate both the overthrust and foreland areas. We first determine the main causes of the very low S/N ratio in the field data and then propose a processing sequence aimed at exploiting the signal content, also making use of a priori geological knowledge of this area. Our work indicates a combination of causes for the very low quality of the seismic data. These include length of the spread (about 20 km) that is unfavorable because of the rapid variation in the near‐surface geology, tectonic complexity, crooked‐line acquisition, and the rough topography associated with outcropping rocks characterized by highly variable velocities. Based on the outcome of this data analysis, we present a processing sequence driven by knowledge of the regional tectonic setting and by knowledge of the shallow subsurface geology. The main effort is in removing the large, near‐surface related noise components. The low S/N ratio makes it impossible or nearly impossible to successfully apply highly sophisticated techniques such as depth migration or wave equation datuming. Thus, we used robust techniques specifically designed to solve each problem that degraded data quality. The most relevant of these techniques were the removal of bad traces where unacceptably low quality was detected by energy and frequency decay criteria; estimation and correction for static time shifts attributable to near‐surface conditions; optimization of common midpoint (CMP) sorting to attenuate the deleterious effects of the crooked‐line acquisition; application of a weighted stacking technique to maximize stack power and application of prestack f-x deconvolution to attenuate uncorrelated noise. The outcome of this processing sequence is compared with the result of a more standard sequence that was previously applied to the same data and is also discussed in terms of the possible geological model it might evidence. The realization of a seismic section showing rather continuous and structured events down to 8 s which, depending on the interpretation, may be related to Moho discontinuity or to very deep sedimentary layers supports the efficacy of the processing approach we propose.
Smooth inversion of induction logs for conductivity models with mud filtrate invasion
Authors: de Groot—Hedlin Catherine D.
Published: October 2002

A robust, efficient method of inversion of induction logging data for smooth 2-D models, appropriate to an environment in which mud filtrate invades flat‐lying layers, is described. An infinite number of solutions exist to the problem of determining a conductivity structure from a finite number of imprecise induction data. Therefore, the inverse problem is regularized such that the smoothest model is sought subject to the condition that the resulting computed log agrees with the field log to a given preset level. At each iteration, the Jacobian sensitivities are approximated using the distorted Born approximation. In most cases, the algorithm converges in 3 to 4 iterations. The resulting maximally smooth models reflect the resolution power of the induction data and are unlikely to result in overinterpretation of the data. Inversion of both synthetic and field data indicates that layer boundaries are well resolved but radial boundaries are poorly resolved by conventional induction logging data.
The usefulness of geophone ground‐coupling experiments to seismic data
Authors: Drijkoningen Guy G.
Published: October 2002

Ground‐coupling devices measure local conditions around a geophone and are therefore useful for geophone design. For purposes of gathering seismic data, the data from local ground‐coupling experiments must be related to seismic data. In particular, the geophysicist wants to know whether a local measurement could help in detecting a ground‐coupling problem or in correcting the seismic data for it. Two sets of field experiments have been carried out to investigate these effects. Our experimental data of coupling‐measurement devices show that the behavior of well‐planted spiked geophones is determined by shear along the spike, while the behavior of poorly planted geophones is determined by its weight. However, when a link is established between the data from a coupling‐measurement device to seismic data, it becomes clear that the usefulness of this device for predicting problematic ground‐coupling phenomena in seismic data is very limited.
Mapping of the resistivity, susceptibility, and permittivity of the earth using a helicopter‐borne electromagnetic system
Authors: Huang Haoping , Fraser Douglas C.
Published: October 2002

Interpretation of helicopter‐borne electromagnetic (EM) data is commonly based on the mapping of resistivity (or conductivity) under the assumption that the magnetic permeability is that of free space and dielectric permittivity can be ignored. However, the data obtained from a multifrequency EM system may contain information about the magnetic permeability and dielectric permittivity as well as the conductivity. Our previous work has shown how helicopter EM data may be transformed to yield the resistivity and magnetic permeability or, alternatively, the resistivity and dielectric permittivity. A method has now been developed to recover the resistivity, magnetic permeability, and dielectric permittivity together from the transformation of helicopter EM data based on a half‐space model. A field example is presented from an area which exhibits both permeable and dielectric properties. This example shows that the mapping of resistivity, magnetic permeability, and dielectric permittivity together yields more credible results than if the permeability or permittivity is ignored.
Engineering and environmental geophysics at the millennium
Authors: Steeples Don W.
Published: October 2002

Near‐surface geophysics is being applied to a broader spectrum of problems than ever before, and new application areas are arising continually. Currently, the tools used to examine the near‐surface environment include a variety of noninvasive methods employing electrical, electromagnetic, or mechanical energy sources, along with passive techniques that measure the physical parameters of the earth. Some of the advances of recent years have emerged from breakthroughs in instrumentation and computer‐processing techniques, and some have been driven by societal needs, such as the increasing demand for the accurate geophysical characterization of polluted sites. Other compelling factors, such as the ever‐expanding need for groundwater, the enactment of laws that have spurred geophysical surveying for archaeological purposes, and the necessity for better soil‐physics information in geotechnical engineering and agriculture, are present worldwide. For historical context, the reader is referred to an excellent review concerning the status of shallow exploration techniques in the mid-1980s (Dobecki and Romig, 1985).
Common‐reflection‐surface stack: Image and attributes
Authors: Jäger Rainer , Mann Jürgen , Höcht German , Hubral Peter
Published: October 2002

The common‐reflection‐surface stack provides a zero‐offset simulation from seismic multicoverage reflection data. Whereas conventional reflection imaging methods (e.g. the NMO/dip moveout/stack or prestack migration) require a sufficiently accurate macrovelocity model to yield appropriate results, the common‐reflection‐surface (CRS) stack does not depend on a macrovelocity model. We apply the CRS stack to a 2-D synthetic seismic multicoverage dataset. We show that it not only provides a high‐quality simulated zero‐offset section but also three important kinematic wavefield attribute sections, which can be used to derive the 2-D macrovelocity model. We compare the multicoverage‐data‐derived attributes with the model‐derived attributes computed by forward modeling. We thus confirm the validity of the theory and of the data‐derived attributes. For 2-D acquisition, the CRS stack leads to a stacking surface depending on three search parameters. The optimum stacking surface needs to be determined for each point of the simulated zero‐offset section. For a given primary reflection, these are the emergence angle α of the zero‐offset ray, as well as two radii of wavefront curvatures [Formula: see text] and [Formula: see text]. They all are associated with two hypothetical waves: the so‐called normal wave and the normal‐incidence‐point wave. We also address the problem of determining an optimal parameter triplet (α, [Formula: see text], [Formula: see text]) in order to construct the sample value (i.e., the CRS stack value) for each point in the desired simulated zero‐offset section. This optimal triplet is expected to determine for each point the best stacking surface that can be fitted to the multicoverage primary reflection events. To make the CRS stack attractive in terms of computational costs, a suitable strategy is described to determine the optimal parameter triplets for all points of the simulated zero‐offset section. For the implementation of the CRS stack, we make use of the hyperbolic second‐order Taylor expansion of the stacking surface. This representation is not only suitable to handle irregular multicoverage acquisition geometries but also enables us to introduce simple and efficient search strategies for the parameter triple. In specific subsets of the multicoverage data (e.g., in the common‐midpoint gathers or the zero‐offset section), the chosen representation only depends on one or two independent parameters, respectively.
Effective elastic properties of solid clays
Authors: Wang Zhijing (Zee) , Wang Hui , Cates Michael E.
Published: October 2002

Clay minerals are perhaps the most abundant materials in the earth’s upper crust. As such, their elastic properties are extremely important in seismic exploration, seismic reservoir characterization, and sonic‐log interpretation. Because little exists in the literature on elastic properties of clays, we have designed a method of measuring effective elastic properties of solid clays (clays without pores). In this method, clay minerals are mixed with a material with known elastic properties to make composite samples. Elastic properties of these clay minerals are then inverted from the measured elastic properties of the composite samples using the weighted Hashin‐Shtrikman average. Using this method, we have measured 66 samples of 16 types of clays. In this paper, we present a comprehensive data set of elastic properties of solid clays that commonly occur in, or are related to, petroleum reservoirs. Although uncertainties (up to 10%) exist, the data set reported here is by far the most comprehensive set of elastic properties in the literature. These data can be used potentially in modeling the seismic properties of clay‐bearing rocks.
Twelve years of vertical birefringence in nine‐component VSP data
Authors: Winterstein Donald F. , De Gopa S. , Meadows Mark A.
Published: October 2002

Since 1986, when industry scientists first publicly showed data supporting the presence of azimuthal anisotropy in sedimentary rock, we have studied vertical shear‐wave (S-wave) birefringence in 23 different wells in western North America. The data were from nine‐component vertical seismic profiles (VSPs) supplemented in recent years with data from wireline crossed‐dipole logs. This paper summarizes our results, including birefringence results in tabular form for 54 depth intervals in 19 of those 23 wells. In the Appendix we present our conclusions about how to record VSP data optimally for study of vertical birefringence. We arrived at four principal conclusions about vertical S-wave birefringence. First, birefringence was common but not universal. Second, birefringence ranged from 0–21%, but values larger than 4% occurred only in shallow formations (<1200 m) within 40 km of California’s San Andreas fault. Third, at large scales birefringence tended to be blocky. That is, both the birefringence magnitude and the S-wave polarization azimuth were often consistent over depth intervals of several tens to hundreds of meters but then changed abruptly, sometimes by large amounts. Birefringence in some instances diminished with depth and in others increased with depth, but in almost every case a layer near the surface was more birefringent than the layer immediately below it. Fourth, observed birefringence patterns generally do not encourage use of multicomponent surface reflection seismic data for finding fractured hydrocarbon reservoirs, but they do encourage use of crossed‐dipole logs to examine them. That is, most reservoirs were birefringent, but none we studied showed increased birefringence confined to the reservoir.
A constrained global inversion method using an overparameterized scheme: Application to poststack seismic data
Authors: Ma Xin‐Quan
Published: October 2002

A global optimization algorithm using simulated annealing has advantages over local optimization approaches in that it can escape from being trapped in local minima and it does not require a good initial model and function derivatives to find a global minimum. It is therefore more attractive and suitable for seismic waveform inversion. I adopt an improved version of a simulated annealing algorithm to invert simultaneously for acoustic impedance and layer interfaces from poststack seismic data. The earth’s subsurface is overparameterized by a series of microlayers with constant thickness in two‐way traveltime. The algorithm is constrained using the low‐frequency impedance trend and has been made computationally more efficient using this a priori information as an initial model. A search bound of each parameter, derived directly from the a priori information, reduces the nonuniqueness problem. Application of this technique to synthetic and field data examples helps one recover the true model parameters and reveals good continuity of estimated impedance across a seismic section. This approach has the capability of revealing the high‐resolution detail needed for reservoir characterization when a reliable migrated image is available with good well ties.
Alford rotation, ray theory, and crossed‐dipole geometry
Authors: Dellinger Joe A. , Nolte Bertram , Etgen John T.
Published: October 2002

Two generalizations of Alford rotation have been proposed for processing 2 × 2-component data containing nonorthogonal split shear waves: singular value decomposition (SVD) and eigenvector‐eigenvalue decomposition (EED). Using a simple crossed‐dipole synthetic model, we demonstrate that the physical model behind the EED method is invalid. It incorrectly assumes that a vector source aligned with the particle motion of an anisotropic pure mode will excite only that one mode. Ray theory shows that a vector point‐force source embedded in a homogeneous anisotropic medium instead excites all those modes with particle motions that are not perpendicular to the direction of the applied force, just as a vector point receiver detects all modes with polarizations that are not perpendicular to the receiver. Correctly generalized Alford rotation synthesizes vector sources and receivers such that each component is perpendicular to all but one of the pure modes of the medium. Although this ray‐theory result does not allow for the possibility of a source or receiver on a free surface and so is not yet completely general, it does apply to the idealized homogeneous crossed‐dipole geometry of our example. The new method, symmetric Alford diagonalization, differs from previous methods by becoming unstable when applied over excessively short time windows. This behavior is consistent with the physics of the problem: If nonorthogonal modes are allowed, then there is not enough information at a single time sample to determine a unique solution. Any method that can find a unique solution at a single time sample, including both the EED and SVD methods, does not respect the physics of the nonorthogonal problem. Although there appears to be no problem that recommends the EED method over standard Alford rotation for its solution, the SVD method is still applicable to the problem it was originally designed to solve: orthogonal modes with an unknown source or receiver orientation.
Hybrid shortest path and ray bending method for traveltime and raypath calculations
Authors: Van Avendonk Harm J. A. , Harding Alistair J. , Orcutt John A. , Holbrook W. Steven
Published: October 2002

The shortest path method (SPM) is a robust ray‐tracing technique that is particularly useful in 3-D tomographic studies because the method is well suited for a strongly heterogeneous seismic velocity structure. We test the accuracy of its traveltime calculations with a seismic velocity structure for which the nearly exact solution is easily found by conventional ray shooting. The errors in the 3-D SPM solution are strongly dependent on the choice of search directions in the “forward star,” and these errors appear to accumulate with traveled distance. We investigate whether these traveltime errors can be removed most efficiently by an SPM calculation on a finer grid or by additional ray bending. Testing the hybrid scheme on a realistic ray‐tracing example, we find that in an efficient mix ray bending and SPM account for roughly equal amounts of computation time. The hybrid method proves to be an order of magnitude more efficient than SPM without ray bending in our example. We advocate the hybrid ray‐tracing technique, which offers an efficient approach to find raypaths and traveltimes for large seismic refraction studies with high accuracy.
Parabolic Radon transform, sampling and efficiency
Authors: Schonewille M. A. , Duijndam A. J. W.
Published: October 2002

A good choice of the sampling in the transform domain is essential for a successful application of the parabolic Radon transform. The parabolic Radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform Fourier transform. This leads to new and useful insights in the parabolic Radon transform. Using nonuniform Fourier theory, we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling. A significantly smaller sampling interval requires stabilization. If diagonal stabilization is used, no gain in resolution is obtained. In contrast to conventional implementations, the curvature sampling interval is proposed to be inversely proportional to the temporal frequency. This results in improved quality of the transform and yields significant savings in computation time.
The impact of common‐offset migration on porosity estimation by AVO inversion
Authors: Buland Arild , Landrø Martin
Published: October 2002

The impact of prestack time migration on porosity estimation has been tested on a 2-D seismic line from the Valhall/Hod area in the North Sea. Porosity is estimated in the Cretaceous chalk section in a two‐step procedure. First, P-wave and S-wave velocity and density are estimated by amplitude variation with offset (AVO) inversion. These parameters are then linked to porosity through a petrophysical rock data base based on core plug analysis. The porosity is estimated both from unmigrated and prestack migrated seismic data. For the migrated data set, a standard prestack Kirchhoff time migration is used, followed by simple angle and amplitude corrections. Compared to modern high‐cost, true amplitude migration methods, this approach is faster and more practical. The test line is structurally fairly simple, with a maximum dip of 5°; but the results differ significantly, depending on whether migration is applied prior to the inversion. The maximum difference in estimated porosity is of the order of 10% (about 50% relative change). High‐porosity zones estimated from the unmigrated data were not present on the porosity section estimated from the migrated data.
3-D traveltime computation using Huygens wavefront tracing
Authors: Sava Paul , Fomel Sergey
Published: October 2002

Traveltime computation is widely used in seismic modeling, imaging, and velocity analysis. The two most commonly used methods are ray tracing and numerical solutions to the eikonal equation. Eikonal solvers are fast and robust but are limited to computing only the first‐arrival traveltimes. Ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers. We propose a robust and complete method of traveltime computation. It is based on a system of partial differential equations, which is equivalent to the eikonal equation but formulated in the ray‐coordinates system. We use a first‐order discretization scheme that is interpreted very simply in terms of the Huygens’s principle. Our explicit finite‐difference solution to the eikonal equation solved in the ray‐coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step. The finite‐difference method has proven to be a robust alternative to conventional ray tracing, while being faster and having a better ability to handle rough velocity media and penetrate shadow zones.
Velocity analysis for tilted transversely isotropic media: A physical modeling example
Authors: Grechka Vladimir , Pech Andres , Tsvankin Ilya , Han Baoniu
Published: October 2002

Transverse isotropy with a tilted symmetry axis (TTI media) has been recognized as a common feature of shale formations in overthrust areas, such as the Canadian Foothills. Since TTI layers cause serious problems in conventional imaging, it is important to be able to reconstruct the velocity model suitable for anisotropic depth migration. Here, we discuss the results of anisotropic parameter estimation on a physical‐modeling data set. The model represents a simplified version of a typical overthrust section from the Alberta Foothills, with a horizontal reflector overlaid by a bending transversely isotropic layer. Assuming that the TTI layer is homogeneous and the symmetry axis stays perpendicular to its boundaries, we invert P-wave normal‐moveout (NMO) velocities and zero‐offset traveltimes for the symmetry‐direction velocity V0and the anisotropic parameters ε and δ. The coefficient ε is obtained using the traveltimes of a wave that crosses a dipping TTI block and reflects from the bottom of the model. The inversion for ε is based on analytic expressions for NMO velocity in media with intermediate dipping interfaces. Our estimates of both anisotropic coefficients are close to their actual values. The errors in the inversion, which are associated primarily with the uncertainties in picking the NMO velocities and traveltimes, can be reduced by a straighforward modification of the acquisition geometry. It should be emphasized that the moveout inversion also gives an accurate estimate of the thickness of the TTI layer, thus reconstructing the correct depth scale of the section. Although the physical model used here was relatively simple, our results demonstrate the principal feasibility of anisotropic velocity analysis and imaging in overthrust areas. The main problems in anisotropic processing for TTI models are likely to be caused by the lateral variation of the velocity field and overall structural complexity.
A THEORY OF THE DISTRIBUTION OF RADIOACTIVITY IN MARINE SEDIMENTARY ROCKS
Authors: Weaver Paul
Published: October 2002

Gamma‐ray measurements of marine sedimentary rocks indicate that in general the slower the rate of deposition the greater the radioactivity. The most recent measurements of the radioactivity of sea water suggest an increase with depth, which indicates a very slow settling of small particles. It is believed that a geologic time‐scale of sedimentation can be established, subject to certain corrections due to fixation of radioactive minerals by organisms.
FAULTING IN THE BILLINGS OILFIELD, OKLAHOMA, AS INTERPRETED FROM TORSION BALANCE DATA, AND FROM SUBSEQUENT DRILLING
Authors: Klaus H.
Published: October 2002

The results of an experimental torsion balance survey of the Billings Oilfield are shown by means of the conventional maps, and of second derivative contour maps. The latter show good and consistent anomalies, which are interpreted as faulting. The survey was made in July, 1937, some time after discovery of Ordovician production in the field, but long before faulting was clearly defined by drilling, and the results were communicated to several oil companies interested in the area or in the method of interpretation. In the meantime, one of the faults limiting the field has been defined in detail by drilling, and the present subsurface interpretation is compared with the original torsion balance predictions with respect to this fault. From the amount of agreement between the two sets of data, it is concluded that the torsion balance can still be used effectively for specialized purposes, particularly the investigation of faulting.
Geologic Correlation of Areal Gravitational and Magnetic Studies in New Jersey and Vicinity. George P. Woollard. Bulletin of the Geological Society of America, Vol. 54, Pages 791 to 818, June 1, 1943.
Authors: Nettleton L. L.
Published: October 2002

This paper gives the geophysical results and interpretation for a rather close net of gravity and magnetic stations in the southern two‐thirds of New Jersey and eastern Pennsylvania. Over most of the New Jersey parts, the stations are at intervals of about 31/2 miles on profiles roughly ten miles apart, running approximately NW‐SE, or across the strike of the Appalachian trends. This work is supplemented by a zone of much closer control extending in a band about four miles wide reaching from Barnegat Bay on the coast, northwestward through Princeton and Flemington to the Delaware River at Phillipsburg, New Jersey.
GEOPHYSICS LOOKS FORWARD
Authors: Wyckoff R. D.
Published: October 2002

We speak of the war emergency and what it has done to our domestic oil reserves. I would not attempt to minimize the effects of the war demand upon our current production facilities nor imply that the extra demand, the purely military consumption, is a minor quantity. But considered in the light of the total quantity of oil that has been taken from the ground in the past and that which is to be added to the grand total by future production, it does not loom out of all proportion as some current discussion would imply. Rather it appears as the warning that has jarred us out of our normal complacency and into an admission that, after all, our domestic oil is limited, that it is being depleted at an alarming pace, and that new reserves are not forthcoming in the accustomed manner at a rate sufficient to replenish the reservoir.
Magneto‐gravity response function and its application to the Daito Ridge
Authors: Ueda Yoshio , Kubota Ryuji , Segawa Jiro
Published: October 2002

A magneto‐gravity response function, which shows a phase relationship between magnetic and gravity anomalies caused by a common source body with a constant density‐to‐magnetization ratio, is derived for determining the magnetization direction of a source body for 2‐D and 3‐D cases. The validity of the method is demonstrated through application to test data and to field anomalies from the Daito Ridge. The Daito Ridge is found to be magnetized in the present main field direction, contrary to shallow inclinations suggested by studies of Deep Sea Drilling Project (DSDP) sediment cores. The strong normal magnetization is ascribed to high magnetic susceptibility and/or viscous remanent magnetization.