VSP traveltime inversion for anisotropy in a buried layer     

Michael A. Slawinski  Michael P. Lamoureux  Raphael A. Slawinski  R. James Brown 《Geophysical Prospecting》2003,51(2):131-140

We present a method for calculating the anisotropy parameter of a buried layer by inverting the total traveltimes of direct arrivals travelling from a surface source to a well‐bore receiver in a vertical seismic profiling (VSP) geometry. The method assumes two‐dimensional media. The medium above the layer of interest (and separated from it by a horizontal interface) can exhibit both anisotropy and inhomogeneity. Both the depth of the interface as well as the velocity field of the overburden are assumed to be known. We assume the layer of interest to be homogeneous and elliptically anisotropic, with the anisotropy described by a single parameter χ. We solve the function describing the traveltime between source and receiver explicitly for χ. The solution is expressed in terms of known quantities, such as the source and receiver locations, and in terms of quantities expressed as functions of the single argument x_r, which is the horizontal coordinate of the refraction point on the interface. In view of Fermat's principle, the measured traveltime T possesses a stationary value or, considering direct arrivals, a minimum value, . This gives rise to a key result ‐‐ the condition that the actual anisotropy parameter . Owing to the explicit expression , this result allows a direct calculation of in the layer of interest. We perform an error analysis and show this inverse method to be stable. In particular, for horizontally layered media, a traveltime error of one millisecond results in a typical error of about 20% in the anisotropy parameter. This is almost one order of magnitude less than the error inherent in the slowness method, which uses a similar set of experimental data. We conclude by detailing possible extensions to non‐elliptical anisotropy and a non‐planar interface.  相似文献   

MATHEMATICAL MODELS OF CONDUCTING ORE BODIES FOR DIRECT CURRENT ELECTRICAL PROSPECTING *     

S. STEF&#x;NESCU  D. STEF&#x;NESCU 《Geophysical Prospecting》1974,22(2):246-260

The authors generalize a method expounded in a previous paper (1971, Geoph. Prosp. 18, 786-799) to the case of a local conductivity σ(M) of the infinite medium satisfying the relation where the R_i's are the distances from the point M to n fixed points S_i (i= 1,. n), k is a positive real constant and C_i, C_ii are constants ensuring the condition α > O. The sub-surface conductivity distributions (half-spaces) complying with (1) provide a wide variety of conducting structures, which can fit quite successfully the rather complicated distributions of conductivity occurring in natural ore bodies. An exact algebraic calculation of the apparent resistivity for these grounds, valid for any dc electrical prospecting devices (Wenner, Schlumberger, dipole, etc.) leads to a set of simultaneous linear equations, with a matrix which is invariant with respect to the position of the quadrupole being used. This greatly simplifies the numerical computation. We also present some examples of cross sections for the real and apparent resistivity obtained by this method.  相似文献   

TRAITEMENT AUTOMATIQUE DES SONDAGES ELECTRIQUES AUTOMATIC PROCESSING OF ELECTRICAL SOUNDINGS*     

G. KUNETZ  J. P. ROCROI 《Geophysical Prospecting》1970,18(2):157-198

I. Introduction In this section the problem is stated, its physical and mathematical difficulties are indicated, and the way the authors try to overcome them are briefly outlined. Made up of a few measurements of limited accuracy, an electrical sounding does not define a unique solution for the variation of the earth resistivities, even in the case of an isotropic horizontal layering. Interpretation (i.e. the determination of the true resistivities and thicknesses of the ground-layers) requires, therefore, additional information drawn from various more or less reliable geological or other geophysical sources. The introduction of such information into an automatic processing is rather difficult; hence the authors developped a two-stage procedure:

• a) the field measurements are automatically processed, without loss of information, into more easily usable data;
• b) some additional information is then introduced, permitting the determination of several geologically conceivable solutions.

The final interpretation remains with the geophysicist who has to adjust the results of the processing to all the specific conditions of his actual problem. II. Principles of the procedure In this section the fundamental idea of the procedure is given as well as an outline of its successive stages. Since the early thirties, geophysicists have been working on direct methods of interpreting E.S. related to a tabular ground (sequence of parallel, homogeneous, isotropic layers of thicknesses h_i and resistivities ρ_i). They generally started by calculating the Stefanesco (or a similar) kernel function, from the integral equation of the apparent resistivity: where r is the distance between the current source and the observation point, S₀ the Stefanesco function, ρ(z) the resistivity as a function of the depth z, J₁ the Bessel function of order 1 and λ the integration variable. Thicknesses and resistivities had then to be deduced from S₀ step by step. Unfortunately, it is difficult to perform automatically this type of procedure due to the rapid accumulation of the errors which originate in the experimental data that may lead to physically impossible results (e.g. negative thicknesses or resistivities) (II. 1). The authors start from a different integral representation of the apparent resistivity: where K₁ is the modified Bessel function of order I. Using dimensionless variables t = r/2h₀ and y(t)=ζ (r)/ρ₁ and subdividing the earth into layers of equal thicknesses h₀ (highest common factor of the thicknesses h_i), ø becomes an even periodic function (period 2π) and the integral takes the form: The advantage of this representation is due to the fact that its kernel ø (function of the resistivities of the layers), if positive or null, always yields a sequence of positive resistivities for all values of θ and thus a solution which is surely convenient physically, if not geologically (II.3). Besides, it can be proved that ø(θ) is the Fourier transform of the sequence of the electric images of the current source in the successive interfaces (II.4). Thus, the main steps of the procedure are: a) determination of a non-negative periodic, even function ø(θ) which satisfies in the best way the integral equation of apparent resistivity for the points where measurements were made; b) a Fourier transform gives the electric images from which, c) the resistivities are obtained. This sequence of resistivities is called the “comprehensive solution”; it includes all the information contained in the original E.S. diagram, even if its too great detail has no practical significance. Simplification of the comprehensive solution leads to geologically conceivable distributions (h, ρ) called “particular solutions”. The smoothing is carried out through the Dar-Zarrouk curve (Maillet 1947) which shows the variations of parameters (transverse resistance R_i= h_i.ρ_i–as function of the longitudinal conductance C_i=h_i/ρ_i) well suited to reflect the laws of electrical prospecting (principles of equivalence and suppression). Comprehensive and particular solutions help the geophysicist in making the final interpretation (II.5). III. Computing methods In this section the mathematical operations involved in processing the data are outlined. The function ø(θ) is given by an integral equation; but taking into account the small number and the limited accuracy of the measurements, the determination of ø(θ) is performed by minimising the mean square of the weighted relative differences between the measured and the calculated apparent resistivities: minimum with inequalities as constraints: where t_l are the values of t for the sequence of measured resistivities and p_l are the weights chosen according to their estimated accuracy. When the integral in the above expression is conveniently replaced by a finite sum, the problem of minimization becomes one known as quadratic programming. Moreover, the geophysicist may, if it is considered to be necessary, impose that the automatic solution keep close to a given distribution (h, ρ) (resulting for instance from a preliminary interpretation). If φ(θ) is the ø-function corresponding to the fixed distribution, the quantity to minimize takes the form: where: The images are then calculated by Fourier transformation (III.2) and the resistivities are derived from the images through an algorithm almost identical to a procedure used in seismic prospecting (determination of the transmission coefficients) (III.3). As for the presentation of the results, resorting to the Dar-Zarrouk curve permits: a) to get a diagram somewhat similar to the E.S. curve (bilogarithmic scales coordinates: cumulative R and C) that is an already “smoothed” diagram where deeper layers show up less than superficial ones and b) to simplify the comprehensive solution. In fact, in arithmetic scales (R versus C) the Dar-Zarrouk curve consists of a many-sided polygonal contour which múst be replaced by an “equivalent” contour having a smaller number of sides. Though manually possible, this operation is automatically performed and additional constraints (e.g. geological information concerning thicknesses and resistivities) can be introduced at this stage. At present, the constraint used is the number of layers (III.4). Each solution (comprehensive and particular) is checked against the original data by calculating the E.S. diagrams corresponding to the distributions (thickness, resistivity) proposed. If the discrepancies are too large, the process is resumed (III.5). IV. Examples Several examples illustrate the procedure (IV). The first ones concern calculated E.S. diagrams, i.e. curves devoid of experimental errors and corresponding to a known distribution of resistivities and thicknesses (IV. 1). Example I shows how an E.S. curve is sampled. Several distributions (thickness, resistivity) were found: one is similar to, others differ from, the original one, although all E.S. diagrams are alike and characteristic parameters (transverse resistance of resistive layers and longitudinal conductance of conductive layers) are well determined. Additional informations must be introduced by the interpreter to remove the indeterminacy (IV.1.1). Examples 2 and 3 illustrate the principles of equivalence and suppression and give an idea of the sensitivity of the process, which seems accurate enough to make a correct distinction between calculated E.S. whose difference is less than what might be considered as significant in field curves (IV. 1.2 and IV. 1.3). The following example (number 4) concerns a multy-layer case which cannot be correctly approximated by a much smaller number of layers. It indicates that the result of the processing reflects correctly the trend of the changes in resistivity with depth but that, without additional information, several equally satisfactory solutions can be obtained (IV. 1.4). A second series of examples illustrates how the process behaves in presence of different kinds of errors on the original data (IV.2). A few anomalous points inserted into a series of accurate values of resistivities cause no problem, since the automatic processing practically replaces the wrong values (example 5) by what they should be had the E.S. diagram not been wilfully disturbed (IV.2.1). However, the procedure becomes less able to make a correct distinction, as the number of erroneous points increases. Weights must then be introduced, in order to determine the tolerance acceptable at each point as a function of its supposed accuracy. Example 6 shows how the weighting system used works (IV.2.2). The foregoing examples concern E.S. which include anomalous points that might have been caused by erroneous measurements. Geological effects (dipping layers for instance) while continuing to give smooth curves might introduce anomalous curvatures in an E.S. Example 7 indicates that in such a case the automatic processing gives distributions (thicknesses, resistivities) whose E.S. diagrams differ from the original curve only where curvatures exceed the limit corresponding to a horizontal stratification (IV.2.3). Numerous field diagrams have been processed (IV. 3). A first case (example 8) illustrates the various stages of the operation, chiefly the sampling of the E.S. (choice of the left cross, the weights and the resistivity of the substratum) and the selection of a solution, adapted from the automatic results (IV.3.1). The following examples (Nrs 9 and 10) show that electrical prospecting for deep seated layers can be usefully guided by the automatic processing of the E.S., even when difficult field conditions give original curves of low accuracy. A bore-hole proved the automatic solution proposed for E.S. no 10, slightly modified by the interpreter, to be correct.  相似文献   

Comment on ‘Aspects of 1D seismic modelling using the Goupillaud principle’ by Evert Slob and Anton Ziolkowski1     

Edward Szaraniec 《Geophysical Prospecting》1994,42(1):81-83

The paper by Slob and Ziolkowski (1993) is apparently a comment on my paper (Szaraniec 1984) on odd-depth structure. In fact the basic understanding of a seismogram is in question. The fundamental equation for an odd-depth model and its subsequent deconvolution is correct with no additional geological constraints. This is the essence of my reply which is contained in the following points.

• 1 The discussion by Slob and Ziolkowski suffers from incoherence. On page 142 the Goupillaud (1961) paper is quoted: “… we must use a sampling rate at least double that… minimum interval…”. In the following analysis of such a postulated model Slob and Ziolkowski say that “… two constants are used in the model: Δt as sampling rate and 2Δt as two-way traveltime”. By reversing the Goupillaud postulation all the subsequent criticism becomes unreliable for the real Goupillaud postulation as well as the odd-depth model.
• 2 Slob and Ziolkowski take into consideration what they call the total impulse response. This is over and above the demands of the fundamental property of an odd-depth model. Following a similar approach I take truncated data in the form of a source function, S(z), convolved with a synthetic seismogram (earth impulse response), R?(z), the free surface being included. The problem of data modelling is a crucial one and will be discussed in more detail below. By my reasoning, however, the function may be considered as a mathematical construction introduced purely to work out the fundamental property. In this connection there is no question of this construction having a physical meaning. It is implicit that in terms of system theory, K(z) stands for what is known as input impedance.
• 3 Our understandings of data are divergent but Slob and Ziolkowski state erroneously that: “Szaraniec (1984) gives (21) as the total impulse response…”. This point was not made. This inappropriate statement is repeated and echoed throughout the paper making the discussion by Slob and Ziolkowski, as well as the corrections proposed in their Appendix A, ineffective. Thus, my equation (2) is quoted in the form which is in terms of the reflection response G^sc and holds true at least in mathematical terms. No wonder that “this identity is not valid for the total impulse response” (sic), which is denoted as G(z). None the less a substitution of G for G^sc is made in Appendix A, equation (A3). The equation numbers in my paper and in Appendix A are irrelevant, but (A3) is substituted for (32) (both numbers of equations from the authors’ paper). Afterwards, the mathematical incorrectness of the resulting equation is proved (which was already evident) and the final result (A16) is quite obviously different from my equation (2). However, the substitution in question is not my invention.
• 4 With regard to the problem of data modelling, I consider a bi-directional ID seismic source located just below the earth's surface. The downgoing unit impulse response is accompanied by a reflected upgoing unit impulse and the earth response is now doubled. The total impulse response for this model is thus given by where (—r₀) =— 1 stands for the surface reflection coefficient in an upward direction. Thus that is to say, the total response to a unit excitation is identical with the input impedance as it must be in system theory. The one-directional 1D seismic source model is in question. There must be a reaction to every action. When only the downgoing unit impulse of energy is considered, what about the compensation?
• 5 In more realistic modelling, an early part of a total seismogram is unknown (absent) and the seismogram is seen in segments or through the windows. That is why in the usual approach, especially in dynamic deconvolution problems, synthetic data in the presence of the free surface are considered as an equivalent of the global reflection coefficient. It is implicit that model arises from a truncated total seismogram represented as a source function convolved with a truncated global reflection coefficient.

Validation or invalidation of the truncation procedure for a numerically specified model may be attempted in the frame of the odd-depth assumption. My equations (22) and (23) have been designed for investigating the absence or presence of truncated energy. The odd-depth formalism allows the possibility of reconstructing an earlier part of a seismogram (Szaraniec 1984), that is to say, a numerical recovery of unknown moments which are unlikely designed by Slob and Ziolkowski for the data.  相似文献   

PERFORMANCE OF 2000 AND 6000 PSI AIR GUNS: THEORY AND EXPERIMENT*     

R.C. JOHNSTON 《Geophysical Prospecting》1980,28(5):700-715

Air guns have been used in various applications for a number of years. They were first used in coal-mining operations and were operated at up to 16000 psi charge pressures. Later, single air guns, operated at 2000 psi, found application as an oceanographic survey tool. Air gun arrays were first used in offshore seismic exploration in the mid-1960's. These early arrays were several hundred cubic inches in total volume and were operated at 2000 psi; they were either tuned arrays or several large guns of the same size with wave-shape kits. Today's arrays have total volumes greater than 5000 cu in. and are typically operated at 2000 psi. Recently, higher-pressure, lower-volume arrays operated at 4000–5000 psi have been introduced; guns used in these arrays are descendants of the coal-mining gun. On first thought one would equate increased gun pressure linearly with the amplitude of the initial pulse. This is approximately true for the signature radiated by a “free-bubble” (no confining vessel) and recorded broadband. The exact relation depends on the depth at which the gun is operated; from solution of the free-bubble oscillation equation, the relation is If P_c,1= 6014.7 psia, P_c,2= 2014.7 psia and P_{O, 1}=P_{O, 2}= 25.8 psia (corresponding to absolute pressure at 25 ft water depth), then Experiments were conducted offshore California in deep water to determine the performance of several models of air guns at pressures ranging from 2000 to 6000 psi and gun volumes ranging from 5 to 300 cu in. At a given gun pressure, the initial acoustic pulse P_a correlated with gun volume V_c according to the classical relation For 1 ms sampled data the ratio varied between 4.5 and 5.5 dB depending on gun model. Pulse width of the 2000 psi signatures indicated they are compatible with 2 ms sample-rate recording while pulse width of the 6000 psi signatures was greater, indicating they are less compatible with 2 ms sample-rate recording. Conclusions reached were that 2000 psi air guns are more efficient than higher pressure guns and are more compatible with 2 ms sample-rate requirements.  相似文献   

A SIMPLE DERIVATION OF SEIGEL'S TIME DOMAIN INDUCED POLARIZATION FORMULA *     

A. Roy  M. Poddar 《Geophysical Prospecting》1981,29(3):432-437

It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability m_a, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation where the symbols have the usual meanings.  相似文献   

FAST HANKEL TRANSFORMS*     

H. K. JOHANSEN  K. S RENSEN 《Geophysical Prospecting》1979,27(4):876-901

Inspired by the linear filter method introduced by D. P. Ghosh in 1970 we have developed a general theory for numerical evaluation of integrals of the Hankel type: Replacing the usual sine interpolating function by sinsh (x) =a· sin (ρx)/sinh (aρx), where the smoothness parameter a is chosen to be “small”, we obtain explicit series expansions for the sinsh-response or filter function H*. If the input function f(λ exp (iω)) is known to be analytic in the region o < λ < ∞, |ω|≤ω₀ of the complex plane, we can show that the absolute error on the output function is less than (K(ω₀)/r) · exp (?ρω₀/Δ), Δ being the logarthmic sampling distance. Due to the explicit expansions of H* the tails of the infinite summation ((m?n)Δ) can be handled analytically. Since the only restriction on the order is ν > ? 1, the Fourier transform is a special case of the theory, ν=± 1/2 giving the sine- and cosine transform, respectively. In theoretical model calculations the present method is considerably more efficient than the Fast Fourier Transform (FFT).  相似文献   

MEASURED UNDERWATER NEAR-FIELD E-PATTERNS OF A PULSED,HORIZONTAL DIPOLE ANTENNA IN AIR: COMPARISON WITH THE THEORY OF THE CONTINUOUS WAVE,INFINITESIMAL ELECTRIC DIPOLE1     

W. A. WENSINK  G. GREEUW  J. HOFMAN  J. K. VAN DEEN 《Geophysical Prospecting》1990,38(7):805-830

At Delft Geotechnics the technique of ground-penetrating radar is in use for the detection of buried objects such as pipes. To enable us to give our ‘measurements in the field’ a more quantitative interpretation than can be deduced from these alone, a series of experiments has been started under well-defined conditions. A cylindrical vessel containing water simulates wet soil. Mounted horizontally above the water surface is a pulsed triangular half-wave dipole which is used as a transmitting antenna (TA). It has a carrier-frequency of about 160 MHz and a pulse repetition-frequency of about 50 kHz. A movable receiving dipole (‘probe’) in the water measures the transverse, mutually orthogonal E_φ,- and E_θ-components of the pulses as a function of probe-position (r, θ, φ) and of the height h of the TA above the water surface. When these pulses are Fourier-transformed, the transverse electric fields E_φ and E_θ at 200 MHz are obtained. The resulting field patterns are compared with computational results on the basis of the theory of the continuous wave, infinitesimal electric dipole (‘point dipole’). It can be concluded that:

• 1 Far-field conditions have not fully developed at a depth of about 2.50 m, the largest value of the radius r at which field patterns were measured, although it represents a distance of about 15 wavelengths.
• 2 The attenuation constant of the tapwater used, as deduced from E-field measurements for θ= 0, 2.50 m < r < 2.75 m, is slightly less than the value measured using a network analyser and air line combination, in agreement with (1).
• 3 E _φ field patterns calculated using the value of the conductivity σ corresponding to the former value of the attenuation constant agree reasonably well with the measured patterns for r≤ 2.50 m and for θ < 20° at all antenna heights considered. Calculated Eφ patterns do not agree so well with the measured patterns when h is close to zero. With increasing height the agreement inproves.
• 4 In accordance with the theory of the point-dipole, the angular distribution of the radiation patterns of the TA becomes wider as the frequency decreases.
• 5 The normalized underwater pulse-spectra shift to lower frequencies with increasing r. This can be explained since the attenuation constant of the water rises with rising frequency.

  相似文献   

Frictional resistance to accelerating slip     

J. C. Gu 《Pure and Applied Geophysics》1984,122(5):662-679

General analytical expressions for the friction stress and state variable, based on a rate and state-dependent constitutive friction law proposed by Dieterich and Ruina, have been obtained as an explicit function of slip rateV or slip timet or slip displacement δ under the assumption that slip accelerationa is constant or piecewise constant. Properties of the solutions have been discussed, and reviewed, for uniformly accelerating (or decelerating) slip, the following.

1. Frictional stress increases (or decreases) with increasing time, or slip rate, or slippage at the beginning of motion, until a maximum (or a minimum) value (when it exists) has been reached, then decreases (or increases), and finally approaches a special frictional state, namely a steady state, for which stress depends on instantaneous slip rate.
2. The maximal value of frictional stress is dependent on accelerationa; the larger thea, the larger the magnitude of the maximum.

The energy expense ε needed to overcome the frictional stress has been estimated. And therefore the optimal value of acceleration for saving energy for a slipping mechanical system has been obtained. The energy release rateG for an abrupt rupture process of a crack or fault has been estimated.  相似文献   

A COMPARISON OF IP TRANSIENT SHAPES OVER DISSEMINATED AND MASSIVE SULFIDE SHEETS IN THE LOWER PILLOW LAVAS OF CYPRUS*     

G. MALIOTIS  M. AFTAB KHAN 《Geophysical Prospecting》1981,29(6):906-922

A number of time-domain IP traverses were carried out across two parallel mineralized sheets in the Lower Pillow Lavas, near Mitsero, Cyprus with Huntec Mark III equipment using the pole-dipole array. In one sheet the mineralization was disseminated (2%S), and in the other it was massive (30%S). The transients were recorded at separation n= 2 at a number of points to give the complete shape of the curves. The normalized time integrals were anomalous over the two sheets, but were not significantly different; the highest values being observed over the disseminated sheet. Both sheets were also associated with high electromagnetic components of the decay curve. The chargeability and resistivity values obtained over the disseminated body were considerably higher. The metal factor was also of value in discriminating between massive ore, disseminated mineralization, and barren rock. The values of P₂ and P₃ for the two bodies were also compared (P₂ and P₃ are defined by where M₁ to M₄ are the amplitudes of the decay curve at 55, 130, 280 and 580 ms respectively). For the massive ore, P was inversely related to M, but for the disseminated ore P was independent of M. Four simple parameters from the decay curves show that indices of curve shape offer the best prospect of grade discrimination.  相似文献   

IMPEDANCE OF A PLANE ELECTROMAGNETIC WAVE AT THE SURFACE OF A LAYERED CONDUCTING EARTH WITH DIPPING ANISOTROPY*     

J. G. NEGI  P. D. SARAF 《Geophysical Prospecting》1972,20(4):785-799

The problem of a plane wave incident on a non-isotropic dipping layer lying over an isotropic conducting substratum has been studied and some numerical results are presented to show the effects of

• 1) degree of anisotropy m,
• 2) conductivity contrast between the substratum to the upper layer b,
• 3) angle of inclination of the axis of anisotropy α,

on the variation of amplitude and phase difference of the wave impedance with the normalized skin-depth (d/δ₁).  相似文献   

ESTIMATION OF THE PRIMARY SEISMIC PULSE *     

R. E. WHITE  P. N. S. O'BRIEN 《Geophysical Prospecting》1974,22(4):627-651

A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, α_j is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and n_j is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.  相似文献   

Pore pressure profiles in fractured and compliant rocks1     

zdoan Yilmaz  Richard C. Nolen-Hoeksema  Amos Nur 《Geophysical Prospecting》1994,42(6):693-714

Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. We define the permeability compliance γ= 1/k(k/δp_p)_pc, which is the sensitivity of the permeability k to the pore pressure p_p at a constant confining pressure p_c, and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. We expect this phenomenon to occur in highly fractured and compliant rock systems where γ may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where δp_p/δx is a maximum, decreases with time approximately as and the amplitude of the profile also dissipates with time (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when γ is large. The large near-wellbore pressure gradients caused during withdrawal by large γ can cause sanding and wellbore collapse due to excessive production rates.  相似文献   

ON THE BREMMER SERIES DECOMPOSITION: EQUIVALENCE BETWEEN TWO DIFFERENT APPROACHES*     

F. AMINZADEH  J.M. MENDEL 《Geophysical Prospecting》1980,28(1):71-84

A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is where the y_j(t) are physically meaningful constituents (i.e., y₁(t) are primaries, y₂(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.  相似文献   

On the form of the space‐time domain reflection function for a simple flat‐lying interface     

C.J. Thomson 《Geophysical Prospecting》2012,60(1):49-63

  相似文献   

A STUDY ON THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDING DATA MEASURED BY WENNER ELECTRODE CONFIGURATION*     

SIEW HUNG CHAN 《Geophysical Prospecting》1970,18(2):215-235

This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K₁(λ) is the kernel and B₁(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions.  相似文献   

Non-adiabatic motion of charged particles traversing a weak magnetic field: Pitch angle scattering     

Sydney Chapman  Peter C. Kendall 《Pure and Applied Geophysics》1964,59(1):100-122

Summary A charged particle moves with velocityv in a constant non-uniform magnetic fieldH, spiralling with Larmor radiusR. IfR is small compared with the scale lengthL of the field, the magnetic moment associated with the Larmor motion of the particle is nearly constant. Consequently , the (pitch) angle betweenv andH, varies as arcsinH ^1/2. Hence in such adiabatic motion is approximately the same at points on the path whereH has the same value. But the magnetic moment and the pitch angle may differ materially at two such points, each in the region whereR/L is small, if between them the particle traverses a region whereR/L is not small. This region of non-adiabatic motion scatters the pitch angles.Such scattering is investigated for regions of weak field (R large), with and without the presence of a neutral line along whichH=0. Either type of region, it is found, can scatter the pitch angles. This gives support to the theory proposed byAkasofu andChapman to explain why auroral arcs and bands are very thin.The scattering here examined is of interest also in connection with magnetic mirror devices for nuclear energy transformation. It may also have applications to phenomena of solar and stellar atmospheres.  相似文献   

Reflection points and surface points1     

Franklyn K. Levin 《Geophysical Prospecting》1995,43(6):831-841

A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z-axis perpendicular to the surface and a primed one with a z-axis perpendicular to the reflector, we have where θ is the dip angle, φ is the profile angle, X is the source-to-receiver separation, and D is the depth of the reflector. The reflection point is (x, y_p, D) and the surface midpoint is (x_c, y_c, 0). Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture.  相似文献   

LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*     

A. TARANTOLA 《Geophysical Prospecting》1984,32(6):998-1015

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).  相似文献   

Studies on the Toxicity of a few Pesticides on Colisa fasciatus and Notopterus notopterus with Reference to Histopathology and Histochemistry. Part 1: Bioassay Studies     

S. P. Gupta  S. R. Verma  R. C. Dalela 《洁净——土壤、空气、水》1979,7(2):223-238

An attempt has been made to study the toxicity of two commonly used pesticides aldrin (organochlorine) and ethyl-parathion (organophosphorus) to the fish Colisa fasciatus (Anabantidae) and Notopterus notopterus (Notopteridae). During bioassay studies, the behaviour of the fishes was recorded. The aldrin concentration used lies between 0.021 mg/1 and 0.042 mg/1 for C. fasciatus and 0.00056 mg/1 and 0.00135 mg/1 for N. notopterus. The ethyl-parathion concentration used lies between 1.8 mg/1 and 3.7 mg/1 for C. fasciatus and 0.49 mg/1 and 1.00 mg/1 for N. notopterus.

• – The effect of lethal aqueous concentrations of pesticides on the Fishes prior to death are usually manifested by excitation, erratic swimming ability, difficulty in respiration, increasing in ventilation rate, jerky movements of body and fin fast, up- and downward movements, convulsions, loss of equilibrium, loss of the original colour of the body skin and the excess secretion of mucus by the gills and the body wall.
• – the TL_m values for 24, 48 and 96 hours of exposition are determined for both species of fish and both pesticides at the following variables:

• ? three levels of temperature,
• ? three levels of dissolved oxygen,
• ? three levels of pH,
• ? three fish sizes.

• – statistical analysis of variance shows, that all variables have a significant effect on the TL_m values of both pesticides for both fish species;
• – Aldrin (chlorinated hydrocarbon) is more toxic than ethylparathion (organophosphate) at all variables;
• – Colisa fasciatus is the more resistant species than Notopterus notopterus.
• – the relationship between the total number of the fishes N₀, survival numbers N and time t can be expressed by a mathematical formula as:
• – the harmless concentration to C. fasciatus ranged from 0.0049 mg/1 to 0.0161 for aldrin, 0.54 mg/1 to 0.99 mg/1 for ethyl-parathion and to N. notopterus from 0.00012 mg/1 to 0.00045 mg/1 for aldrin, 0.10 mg/1 to 0.21 mg/1 for ethyl-parathion;
• – the aldrin should be diluted at least 4000 times and ethyl-parathion 320 times of its actual concentration.

  相似文献