Showing papers in "Geophysics in 1985"

Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks

Abstract: New velocity data in addition to literature data derived from sonic log, seismic, and laboratory measurements are analyzed for clastic silicate rocks. These data demonstrate simple systematic relationships between compressional and shear wave velocities. For water-saturated clastic silicate rocks, shear wave veloci­ ty is approximately linearly related to compressional wave velocity and the compressional-to-shear velocity ratio decreases with increasing compressional velocity. Laboratory data for dry sandstones indicate a nearly constant compressional-to-shear velocity ratio with rigidity approximately equal to bulk modulus. Ideal models for regular packings of spheres and cracked solids exhibit behavior similar to the observed water­ saturated and dry trends. For dry rigidity equal to dry bulk modulus, Gassmann's equations predict velocities in close agreement with data from the water-saturated

A simplification of the Zoeppritz equations

Abstract: The compressional wave reflection coefficient R(θ) given by the Zoeppritz equations is simplified to the following: R(θ)=R0+[A0R0+Δσ(1-σ)2]sin2θ+1/2ΔVpVp(tan2θ-sin2θ). The first term gives the amplitude at normal incidence (θ = 0), the second term characterizes R(θ) at intermediate angles, and the third term describes the approach to critical angle. The coefficient of the second term is that combination of elastic properties which can be determined by analyzing the offset dependence of event amplitude in conventional multichannel reflection data. If the event amplitude is normalized to its value for normal incidence, then the quantity determined is A=A0+1(1-σ)2ΔσR0. A0 specifies the normal, gradual decrease of amplitude with offset; its value is constrained well enough that the main information conveyed is Δσ/R0, where Δσ is the contrast in Poisson’s ratio at the reflecting interface and R0 is the amplitude at normal incidence. This simplified formula for R(θ) accounts for all of the relations between R(θ...

A nonreflecting boundary condition for discrete acoustic and elastic wave equations

Abstract: I J ~ One of the nagging problems which arises in application of discrete solution methods for wave-propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh. These undesired events eventually over­ ride the actual seismic signals which propagate in the modeled region. The solution to avoiding boundary effects used to be to enlarge the numerical mesh, thus delaying the side reflections and wraparound longer than the range of times involved in the modeling. Obviously this solution considerably increases the expense of computation. More recently, nonreflecting bound­ ary conditions were introduced for the finite-difference method (Clayton and Enquist, 1977: Reynolds, (978). These boundary conditions are based on replacing the wave equation in the boundary region by one-way wave equations which do not permit energy to propagate from the boundaries into the nu­ merical mesh. This approach has been relatively successful, except that its effectiveness degrades for events which impinge on the boundaries at shallow angles. It is also not clear how to apply this type of boundary condition to global discrete meth­ ods such as the Fourier method for which all grid points are coupled. In this note we describe an alternative scheme for construct­ ing a nonreflecting boundary condition. It is based on gradual reduction of the amplitudes in a strip of nodes along the bound­ aries of the mesh. The method appears extremely simple and robust, and it can be applied to a wide variety of time­ dependent problems. Unlike other methods, the effectiveness of this boundary condition does not decrease for shallow angles of incidence.

Tomographic determination of velocity and depth in laterally varying media

Abstract: Estimation of reflector depth and seismic velocity from seismic reflection data can be formulated as a general inverse problem. The method used to solve this problem is similar to tomographic techniques in medical diagnosis and we refer to it as seismic reflection tomography. Seismic tomography is formulated as an iterative Gauss‐Newton algorithm that produces a velocity‐depth model which minimizes the difference between traveltimes generated by tracing rays through the model and traveltimes measured from the data. The input to the process consists of traveltimes measured from selected events on unstacked seismic data and a first‐guess velocity‐depth model. Usually this first‐guess model has velocities which are laterally constant and is usually based on nearby well information and/or an analysis of the stacked section. The final model generated by the tomographic method yields traveltimes from ray tracing which differ from the measured values in recorded data by approximately 5 ms root‐mean‐square. The i...

Evaluation of anisotropy by shear‐wave splitting

Abstract: The polarizations of three‐component shear wavetrains carry unique information about the internal structure of the rock through which they pass: specifically, commonly observed shear‐wave splitting may contain information about the orientation of crack distributions. This information cannot usually be recovered from shear waves recorded at the free surface because of interference with the interaction of the shear wave with the surface, even for nearly vertical incidence. However, shear‐wave splitting in synthetic three‐component vertical seismic profiles, in some cases, may be interpreted directly in terms of the direction of strike of vertical cracks. Because the human eye is not skilled at identifying the phase relationships between three‐component seismograms played out conventionally as parallel time‐series, the polarizations are displayed in orthogonal sections of the particle displacements to facilitate recognition and evaluation of the shear‐wave splitting. Estimating the orientations of cracks, an...

Low-frequency electrical properties.

Abstract: In the interpretation of induced polarization data, it is commonly assumed that metallic mineral polarization dominantly or solely causes the observed response. However, at low frequencies, there is a variety of active chemical processes which involve the movement or transfer of electrical charge. Measurements of electrical properties at low frequencies (such as induced polarization) observe such movement of charge and thus monitor many geochemical processes at a distance. Examples in which this has been done include oxidation‐reduction of metallic minerals such as sulfides, cation exchange on clays, and a variety of clay‐organic reactions relevant to problems in toxic waste disposal and petroleum exploration. By using both the frequency dependence and nonlinear character of the complex resistivity spectrum, these reactions may be distinguished from each other and from barren or reactionless materials.

Scattering characteristics of elastic waves by an elastic heterogeneity

Abstract: Elastic wave scattering by a general elastic heterogeneity having slightly different density and elastic constants from the surrounding medium is formulated using the equivalent source method and Born approximation In the low‐frequency range (Rayleigh scattering) the scattered field by an arbitrary heterogeneity having an arbitrary variation of density and elastic constants can be equated to a radiation field from a point source composed of a unidirectional force proportional to the density contrast between the heterogeneity and the medium, and a force moment tensor proportional to the contrasts of elastic constant It is also shown that the scattered field can be decomposed into an “impedance‐type” field, which has a main lobe in the backscattering direction and no scattering in the exact forward direction, and a “velocity type” scattered field, which has a main lobe in the forward scattering direction and no scattering in the exact backward direction For Mie scattering we show that the scattered far f

Curie point depths of the Island of Kyushu and surrounding areas, Japan

Abstract: As part of a comprehensive, nationwide evaluation of geothermal resources for Japan, the first of the Curie point depth maps, covering the island of Kyushu, has been prepared. The map was created by inverting gridded, regional aeromagnetic data. Two satisfactory algorithms were developed to invert the gridded data based upon a distribution of point dipoles. The first algorithm estimates x0,y0, and z0, the coordinates of the centroid of the distribution, by computing a least‐squares fit to the radial frequency of the Fourier transform; the second algorithm estimates centroid depth only by computing a least‐squares fit to the squared amplitude of the frequency estimates. The average depth to the top, zt of the collection of point dipoles, was estimated by a variation of the second algorithm. The depth to the bottom of the dipoles, inferred Curie point depth, is zb=2z0-zt. The depth estimates are hand contoured to produce the final map. The Curie point depth map is then compared to regional geology and heat ...

Velocity-stack and slant-stack stochastic inversion

Abstract: 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 LT (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 LT is a generalization of the inversion problem of computerized tomography: deconvolving out the point‐spread function after back projection. The inversion process is complicated ...

Nonlinear inversion, statistical mechanics, and residual statics estimation

Abstract: Nonlinear inverse problems are usually solved with linearized techniques that depend strongly on the accuracy of initial estimates of the model parameters. With linearization, objective functions can be minimized efficiently, but the risk of local rather than global optimization can be severe. I address the problem confronted in nonlinear inversion when no good initial guess of the model parameters can be made. The fully nonlinear approach presented is rooted in statistical mechanics. Although a large nonlinear problem might appear computationally intractable without linearization, reformulation of the same problem into smaller, interdependent parts can lead to tractable computation while preserving nonlinearities. I formulate inversion as a problem of Bayesian estimation, in which the prior probability distribution is the Gibbs distribution of statistical mechanics. Solutions are then obtained by maximizing the posterior probability of the model parameters. Optimization is performed with a Monte Carlo te...

Migration and inversion of seismic data

Abstract: Seismic migration and inversion describe a class of closely related processes sharing common objectives and underlying physical principles. These processes range in complexity from the simple NMO‐stack to the complex, iterative, multidimensional, prestack, nonlinear inversion used in the elastic seismic case. By making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data. NMO‐stack can be modified to solve for these parameters, as can prestack migration. Linearized, wave‐equation inversion does not inordinately increase the complexity of data processing. The principal part of a migration‐inversion algorithm is the migration. Practical difficulties are considerable, including both correctable and intrinsic limitations in data quality, limitations in current algorithms (which we hope are correctable), and correctable (or perhaps intrinsic) limitations in computer power.

Applications of algebraic reconstruction techniques to crosshole seismic data

Abstract: Tomographic imaging techniques were applied to two crosshole data sets to determine the velocity structures and the reliability and resolution of the algorithms on real data. The experiments were carried out at the Retsoff salt mine in New York and at the underground radioactive waste study site at the Stripa mine facility in Sweden. The traveltimes at Restoff were high quality and were obtained over raypaths of up to 500 m in length. The structure was quite complicated with velocity contrasts up to 50 percent. The Stripa site was in granitic rock with velocity contrasts of only a few percent. The dimensions of the experiment were small with maximum ray lengths of just over 10 m. The data at this site were collected with very high accuracy, source and receiver locations were measured to better than 1.0 mm, and traveltimes were read to 0.001 ms. A number of algorithms similar to the algebraic reconstruction techniques (ART) used in medical imaging have been applied to the data. Some modifications of the algorithms, such as the application of weighting schemes, damping parameters, and curved raypaths, were performed. The resulting velocity fields were compared to the known fields and with each other to determine an optimal method. The algorithms were found to be a rapid, reliable means of reconstructing the slowness field of real data. Low-velocity zones were recovered with accuracy in location and value. It was also found that great care was necessary in application of the techniques to ensure that proper damping parameters are used and the proper number of iterations taken; otherwise poor reconstructions will result.

World oil outlook

Abstract: Thank you for inviting me to testify at your hearings on the world oil outlook. You have also asked for comments on other subjects such as the Treasury Department’s tax reform proposals affecting the oil industry. I will briefly comment on this issue following my discussion on the world oil outlook.

Vertical seismic profiling

Abstract: Vertical seismic profiling is one of the rapidly developing areas of geophysical technology for exploring in mature basins. The measurement basically involves recording the total upgoing and downgoing seismic wave fields propagating through a stratigraphic section by means of geophones clamped to the wall of a drilled well.

The influence of pore pressure and confining pressure on dynamic elastic properties of Berea Sandstone

Abstract: Compressional- and shear-wave velocities of water-saturated Berea sandstone have been measured as functions of confining and pore pressures to 2 kbar. The velocities, measured by the pulse transmission technique, were obtained at selected pressures for the purpose of evaluating the relative importance of confining pressure and pore pressure on elastic wave velocities and derived dynamic elastic constants. Changes in Berea sandstone velocities resulting from changes in confining pressure are not exactly canceled by equivalent changes in pore pressure. For properties that involve significant bulk compression (compressional-wave velocities and bulk modulus) an incremental change in pore pressure does not entirely cancel a similar change in confining pressure. On the other hand, it is shown that a pore pressure increment more than cancels an equivalent change in confining pressure for properties that depend significantly on rigidity (shear-wave velocity and Poisson's ratio). This behavior (as well as observed wave amplitudes) is related to the presence of high-compressibility clay that lines grains and pores within the quartz framework of the Berea sandstone.

The joint use of coincident loop transient electromagnetic and Schlumberger sounding to resolve layered structures

Abstract: One-dimensional earth models consisting of uniform horizontal layers are useful both as actual representations of earth structures and as host models for more complex structures. However, there are often inherent difficulties in establishing layer thicknesses and resistivities from one type of measurement alone. For example, the dc resistivity method is sensitive to both conductive and resistive layers, but as these layers become thin, nonuniqueness becomes a severe problem. Electromagnetic (EM) methods are good for establishing the parameters of conductive layers, but they are quite insensitive to resistive layers.The use of both coincident loop transient EM (TEM) and Schlumberger methods, together with a joint inverse computer program, can vastly improve interpretation of layered-earth parameters. The final model is less dependent upon starting guesses, error bounds are much improved, and nonuniqueness is much less of a problem. These advantages are illustrated by interpretation of real field data as well as by a theoretical study of four different types of earth models.

Surface-consistent residual statics estimation by stack-power maximization

Abstract: Application of incorrect static shifts will decrease the power of the common‐depth‐point stack. Conversely, static shifts can be estimated by maximizing the stack power. We tried it and it worked well enough that we recommend it in routine practice for data with low signal‐to‐noise ratio. Likewise, stack power was maximized by adjustment of surface‐consistent phase correction.

Plane-wave Q deconvolution

Abstract: Often the information content of measured signals from distance sources is hidden, because the signal distorts, weakens, and loses resolution as it propagates. For seismic energy traveling in the earth, these propagation effects can be approximated by the constant (frequency-independent) Q model for attenuation and dispersion. For a propagating plane wave, this model leads to a spatial attenuation factor that is an unbounded function of frequency. Consequently, the broadband inverse of the constant-Q filter does not exist. For a fixed distance between the source and receiver the effects of the propagation path can be deconvolved (removed) within the seismic band by reversing the propagation of the plane wave. This propagation reversal is done by a time reversal with Q replaced by -Q, thereby changing absorption to gain in the complex wavenumber.Normally, measured seismic traces contain returns from a variety of depths. The interference of waves with different amounts of attenuation complicates the inversion process. From a superposition of plane waves with reversed propagation, a general inverse to an attenuation earth filter is proposed. To account for the increased attenuation with depth, the plane-wave inverse filter is now time-varying. This time-varying inverse filter has a simple Fourier integral representation where the wavenumber is complex, and the direction of propagation is chosen such that the wave is growing rather than attenuating with distance. To control the wavelet side lobes a frequency-domain window function (Hanning window) is applied to the trace. This two-step plane-wave deconvolution scheme was demonstrated to be superior to conventional deconvolution procedures. Tests with field data indicate the method is effective in removing attenuation effects from both VSP (Vertical Seismic Profile) and surface measurements. Phase distortions are eliminated and interference between events is reduced within the seismic band.This inverse is nearly exact for events where the time-bandwidth (propagation time-signal bandwidth) product is less than the effective Q. For depths where the time-bandwidth product is greater than Q eff large wavelet side lobes appear. The wavelet side lobes can be partially suppressed by tapering the edges of the spectrum. However, the large side lobes of wavelets from shallow reflectors limit the bandwidth that can be recovered from the deeper events to aproximately 2Q eff /t, where t is the propagation time to the event. Advances in the inversion algorithm (e.g., a Wiener filter could be used in place of the Hanning window to control side lobes) could probably improve upon our results, but in most cases even a small amount of measurement noise limits the reflection sequences to time-bandwidth products that are less than twice the effective Q.

Non-Gaussian reflectivity, entropy, and deconvolution

Abstract: Standard deconvolution techniques assume that the wavelet is minimum phase but generally make no assumptions about the amplitude distribution of the primary reflection coefficient sequence. For a white reflection sequence the assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible; however, a non‐Gaussian distribution in theory allows recovery of the phase. It is generally recognized that primary reflection coefficients typically have a non‐Gaussian amplitude distribution. Deconvolution techniques that assume whiteness but seek to exploit the non‐Gaussianity include Wiggins’ minimum entropy deconvolution (MED), Claerbout’s parsimonious deconvolution, and Gray’s variable norm deconvolution. These methods do not assume minimum phase. The deconvolution filter is defined by the maximization of a function called the objective. I examine these and other MED‐type deconvolution techniques. Maximizing the objective by setting derivatives to zero results in most case...

Applications of gravity and magnetic surveys: The state-of-the-art in 1985

Abstract: There is a continuous large demand for gravity and magnetic surveys all over the world for a variety of exploration applications, all of which require the geophysicist to provide some new insight into the geology of an area at scales ranging from very large to very small. To achieve this objective, (a) surveys must be carried out accurately, and (b) their results must be interpreted in sympathy with what is already known of the geology. The methodology for acquiring and compiling data appears to be keeping pace with modern technology. Methods of quantitatively interpreting anomalies in terms of models of causative bodies are adapting rapidly to the burgeoning availability of computing power, from large, powerful machines to inexpensive and field‐portable microcomputers. Geologic interpretation, or the identification of physical property distributions in terms of realistic geologic models and processes, is still relatively neglected—in practice and, regretably, in the geophysical literature. Research into ...

Biot-consistent elastic moduli of porous rocks; low-frequency limit

Abstract: The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the...

Velocity Analysis Without Picking

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

Finite Difference Synthetic Acoustic Logs

Abstract: The finite‐difference method is a powerful technique for studying the propagation of elastic waves in boreholes. Even for the simple case of an open borehole with vertical homogeneity, the snapshot format of the method displays clearly the interaction between the borehole and the rock, and the origin and evolution of phases. We present an outline of the finite‐difference method applied to the acoustic logging problem, including a boundary condition formulation for liquid‐solid cylindrical interfaces which is correct to second order in the space increments. Absorbing boundaries based on the formulations of Reynolds (1978) and Clayton and Engquist (1977) were used to reduce reflections from the grid boundaries. Results for a vertically homogeneous sharp interface model are compared with the discrete‐wavenumber method and excellent agreement is obtained. The technique is also demonstrated by considering sharp and continuous transitions (damaged zones) at the borehole wall and by considering the effects of wa...

Seismic wave propagation in a porous medium

Abstract: A complete set of equations to describe low‐frequency seismic wave phenomena in fluid‐filled porous media is presented. The approach is based on the mathematics of volume‐averaging, aided by order‐of‐magnitude and physical arguments. The results are immediately utilizable by practicing seismologists. Our equations and those of Biot (1956a) are found to be largely consistent in form, and we suggest how Biot’s parameters may be defined in terms of basic physical parameters. The theory predicts two dilatational waves and two rotational waves. Under certain conditions these behave differently than would be expected on the basis of Biot’s theory.

Distortion of magnetotelluric sounding curves by three-dimensional structures

Abstract: Distortions of magnetotelluric fields caused by three‐dimensional (3‐D) structures can be severe and are not predictable using one‐dimensional or two‐dimensional modeling. I used a 3-D modeling algorithm based upon an extension of a generalized thin sheet analysis due to Ranganayaki and Madden (1980) to examine field distortions in crustal environments. Three major physical mechanisms cause these distortions. These mechanisms are resistive coupling between the electrical mantle and upper crust, resistive coupling between conductive features within the upper crust, and local induction of current loops within good conductors. Each mechanism produces different spatial and frequency effects upon the background field, so identification of the dominant mechanism can be used as an interpretational aid. I finally use this analysis to identify distortion mechanisms seen in magnetotelluric data from Beowawe, Nevada to aid in an interpretation of that area.

Dielectric properties of reservoir rocks at ultra-high frequencies

Abstract: Conventional resistivity and induction tools measure the electrical conductivity of the formation. Interpretation of these logs is difficult in situations where the formation water resistivity is variable or unknown as a result, for example, of water, steam, or chemical flooding. Recent introduction of several dielectric tools offers a new technique in well logging. These sondes measure the relative dielectric permittivity of the formation at very‐high and ultra‐high radio frequencies. Because water has a much higher relative dielectric permittivity (about 80) than oil (about 2) or gas (about 1), the dielectric tool can distinguish hydrocarbon‐bearing zones from water‐bearing zones even when the formation fluid is nonconducting. However, in order to quantify the oil saturation in the formation, one needs an accurate formula that can relate the measured relative dielectric permittivity of the rock to the oil saturation in the rock. Present interpretation formulas have only a limited range of applicability....

Absorbing boundary conditions for acoustic media

Abstract: By decomposing the acoustic wave equation into incoming and outgoing components, an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation. This boundary condition is characterized by a first‐order differential operator. The differential operator, or absorbing boundary operator, is the basic element from which more complicated boundary conditions can be constructed. The absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions. By combining two or more absorption operators, boundary conditions can be created which absorb plane waves propagating in any number of directions. Absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems.

State-of-the-art geophysical exploration for geothermal resources

Abstract: At the present stage of development, use of geothermal energy saves about 77 million barrels of oil per year worldwide that would otherwise be required for electrical power generation and direct heat applications. More than a dozen countries are involved in development of geothermal resources. Currently, only the moderate- and high-temperature hydrothermal convective type of geothermal system can be economically used for generating electric power. Lower-temperature resources of several types are being tapped for space heating and industrial processing. Geophysics plays important roles both in exploration for geothermal systems and in delineating, evaluating, and monitoring production from them. The thermal methods, which detect anomalous temperatures directly, and the electrical methods are probably the most useful and widely used in terms of siting drilling targets, but gravity, magnetics, seismic methods, and geophysical well logging all have important application.Advances in geophysical methods are needed to improve cost effectiveness and to enhance solutions of geologic problems. There is no wholly satisfactory electrical system from the standpoint of resolution of subsurface resistivity configuration at the required scale, depth of penetration, portability of equipment, and survey cost. The resolution of microseismic and microearthquake techniques needs improvement, and the reflection seismic technique needs substantial improvement to be cost effective in many hard-rock environments. Well-logging tools need to be developed and calibrated for use in corrosive wells at temperatures exceeding 200 degrees C. Well-log interpretation techniques need to be developed for the hard-rock environment. Borehole geophysical techniques and geotomography are just beginning to be applied and show promise with future development.

Numerical computation of individual far-field arrivals excited by an acoustic source in a borehole

Abstract: In this paper, I model the acoustic logging problem and numerically compute individual arrivals at far-field receivers. The ability to compute individual arrivals is useful for examining the sensitivities of each arrival to various factors of interest, as opposed to examining the full waveform as a whole. While the numerical computation of the mode arrivals (Peterson, 1974) and the numerical computation of the first head waves (Tsang and Rader, 1979) have been previously reported, the numerical computation of the entire set of head-wave arrivals is new and is the major contribution of this paper.Following Roever et al. (1974) and others, the full wave field is represented as a sum of contributions from both poles and branchcuts in the complex wavenumber plane. The pole contributions correspond to mode arrivals while the branch cuts are associated with body waves (i.e., head waves). Both the pole and branch cut contributions are computed numerically and results are presented for the cases of a slow and a fast formation. The shear event in the slow formation is found to be relatively small, consistent with observations in measured data. Contrary to existing knowledge, the shear event in the fast formation is also relatively small. The apparent strong shear arrival in the full waveforms is due primarily to the trapped mode pole in the vicinity of cutoff.

Geophysical exploration with audiofrequency natural magnetic fields

Abstract: Experience with the AFMAG method has demonstrated that an electromagnetic exploration system using the Earth’s natural audiofrequency magnetic fields as an energy source is capable of mapping subsurface electrical structure in the upper kilometer of the Earth’s crust. We resolved the limitations of this method by adapting the tensor analysis and remote reference noise bias removal techniques from the geomagnetic induction and magnetotelluric methods to computation of the tippers. After a thorough spectral study of the natural magnetic fields, we designed lightweight magnetic field sensors capable of measuring the magnetic field throughout the year. We also built a digital acquisition and processing system with the ability to provide audiofrequency tipper results in the field. This new instrumentation was used in a study of the Mariposa, California site previously mapped with AFMAG. This study once again demonstrates the usefulness of natural magnetic field data in mapping an electrically conductive body. ...