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   

NOUVELLES APPLICATIONS DE LA THEORIE DES MILIEUX ALPHA HARMONIQUES A LA PROSPEGTION ELECTRIQUE EN COURANT CONTINU*     

SABBA STEFANESCU 《Geophysical Prospecting》1970,18(Z1):786-799

The equation which determines the distribution of the stationary potential ? in isotropic heterogeneous conductive media with continuously varying local conductivity σ, takes the symmetrical form if we choose as new variables For certain grounds (half-spaces) in which α is a harmonic function (Δα=ΔΨ= 0), it is possible to obtain by means of simple calculations the lines of equal apparent resistivity and the geoelectrical apparent cross-sections for the usual devices of d.c. prospecting methods. Graphical examples are also given.  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   

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   

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   

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   

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   

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   

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   

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   

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   

Mobility Enhancement of Mn Oxide during Permanganate Oxidation of TCE     

Kanwartej S. Sra 《Ground Water Monitoring & Remediation》2010,30(4):99-106

Manganese (Mn) oxide precipitation during in situ permanganate oxidation of organic compounds can cause pore clogging, reduce permeability, and increase resistance to mass transfer. Stability of Mn oxide is required to enhance oxidation effectiveness. Batch tests were conducted at eight polyphosphate (PP) to permanganate () mass ratios (0 to 8) at three MnO₄⁻¹ concentrations (500, 1000, or 2000 mg/L) for identifying mass ratios to maximize stability of Mn oxide produced in the presence of trichloroethylene (TCE). In general, stability of Mn oxide was the maximum at mass ratio of approximately 4. Three column tests were designed to investigate the impact of PP on overall removal of 4.6 or 7.0 g TCE emplaced as nonaqueous phase liquid within the column porous media. Water flush, chemical flush using alone (1000 mg/L), and chemical flush using (1000 mg/L) and PP (4000 mg/L) were conducted. Mass removal of TCE and changes in media permeability were estimated over a period of 78 to 312 h (12 to 49 pore volumes [PVs]). Column tests demonstrated enhanced removal (~90%) of TCE during chemical flush with and PP in 12 PVs as compared with approximately 64% during -only flush and approximately 26% during water flush. Pressure drop changes across the column captured change in media permeability and revealed that water flush and PP and flush caused significantly lower flow resistance as compared with -only flush. These results indicate that PP was capable of mobilizing Mn oxide away from the reaction zones, thereby reducing pore clogging and enabling better and long-term contact between TCE and the aqueous phase.  相似文献   

Equilibration of saltation     

Peter‐Jost Spies  Ian K. McEwan 《地球表面变化过程与地形》2000,25(4):437-453

A two‐dimensional numerical model of the saltation process was developed on a parallel computer in order to investigate the temporal behaviour of transport rate as well as its downwind distribution. Results show that the effects of unsteady flow on the transportation of particulates (sediment) have to be considered in two spatial dimensions (x, y). Transport rate Q(x, t) appears in the transport equation for mass M(x, t): where A = ΔxW denotes unit area composed of unit streamwise length Δx and width W. S(x, t) (units kg m⁻² s⁻¹) stands for the balance over the splash process. A transport equation for transport rate itself is suggested with U _c (x, t) a mean particle velocity at location x as the characteristic velocity of the grain cloud. For a steadily blowing wind over a 50 m long sediment bed it was found that downwind changes in Q cease after roughly 10–40 m, depending on the strength of the wind. The onset of stationarity (∂/∂t=0) was found to be a function of the friction velocity and location. The local equilibrium between transport rate and wind was obtained at different times for different downstream locations. Two time scales were found. One fast response (in the order of 1) to incipient wind and a longer time for equilibrium to be reached throughout the simulation length. Transport rate also has different equilibrium values at different locations. A series of numerical experiments was conducted to determine a propagation speed of the grain cloud. It was found that this velocity relates linearly to friction velocity. Copyright © 2000 John Wiley & Sons, Ltd.  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   

SEISMO-ELECTRIC EXPLORATION: EXPECTED SIGNAL AMPLITUDES1     

R. D. RUSSELL  A. S. BARKER 《Geophysical Prospecting》1991,39(1):105-118

For more than 20 years, Soviet scientists have published papers and registered patents describing the conversion of seismic to electromagnetic energy in geological environments and the detection of the electric or magnetic signals as a method of geophysical exploration. Because of the potential importance of a reliable geophysical technique for locating quartz veins, we have been conducting extensive laboratory and field tests of the phenomena. For the purposes of designing appropriate field tests we need to know approximate signal magnitudes, but little has been published on them. The present paper describes a simplified model from which order-of-magnitude estimates of expected electric and magnetic signal strengths can be made with sufficient accuracy for such purposes. For mathematical convenience we model the target as a homogeneous sphere in which the seismic input induces uniform, time-varying electric polarization. More realistic configurations can be described by linear superposition of the potentials of appropriate sub-elements. True piezo-electricity is, by definition, linear. Therefore, responses should have the same frequency content as the seismic input. Combining the low-frequency form of our results with the assumption that the entire thickness of a target vein responds in phase to a seismic excitation, we obtain the following estimates of the maximum electric and magnetic fields at a distance r from the target: where p is the resistivity and μ₀ the dielectric constant of the ground in which E is measured, V is the effective volume of the target, P is the polarization of the vein, s is the seismic stress at the target, and a is the effective piezo-electric coefficient. Signals observed in experiments at the Erickson Mine, British Columbia, gave electric fields in acceptable agreement with our theoretical predictions. We conclude by considering plausible relationships for the high-frequency signals observed from sulfide minerals, assuming that they represent the release of stored stress triggered by the seismic arrival.  相似文献   

A THEOREM FOR DIRECT CURRENT REGIMES AND SOME OF ITS CONSEQUENCES *     

A. ROY 《Geophysical Prospecting》1978,26(2):442-463

For any direct current regime, the theorem holds, where φ_p is the total measured or calculated potential at any point P, φ is the potential distribution known a priori, r is the distance between P and any volume element dV, the gradients are evaluated at the element, and the current sources and sinks have finite dimensions. Thus, each space element behaves as a dipole of moment (1/4π) ?φdV and contributes its share of signal or potential accordingly. By suitable summation or integration, the contribution from any assigned portion of space to the total measured signal can be determined. Except for the chargeability factor m, the formula also establishes Seigel's initial postulate for the time domain induced polarisation theory. The contribution depends on the potential gradient, not the current density, and the integration extends over the entire space. Although an insulating target carries no current, it contributes a signal that is in general larger than normal by virtue of its higher potential gradient, and thus helps in creating an overall positive anomaly or resistivity high. On the other hand, an infinitely conducting target—even though it supports a larger amount of current than normal—contributes nothing to the measured signal as the potential gradient is zero everywhere inside. Thus, by contributing less than normal, a conducting target promotes the creation of what is usually a resistivity low. In all cases, the contributions from the space elements add up exactly to the measured or total calculated value. Some other consequences of the theorem are also discussed, especially in relation to a simple two-layer earth. For instance, the contribution from the upper half-space (air) turns out to be equal to that from the lower (real ground), for all observation points on the ground surface and for any ground configuration.  相似文献   

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   

An upland soil erosion model derived from the basic principles     

K. D. Sharma  J. F. Correia 《地球表面变化过程与地形》1987,12(2):205-210

Starting from the basic erosion principles, an upland soil erosion model to predict soil loss by overland flow from individual storms on forested hillslopes can be derived in the form where Q_s is total soil loss for a storm event, n is roughness coefficient, x is down slope distance, K_f is soil erodibility factor, S is slope, α is slope exponent and Q is runoff. Values of n and α are to be determined for different environments and are 0·58 and 2·1 for a mixed pine forest ecosystem. A significant correlation (r = 0·933, n = 96) fits between the observed and predicted values using this expression, and the model fitting is good.  相似文献   

COMPUTATIONS OF NETWORK MODELS OF POROUS MEDIA*     

MANFRED RINK  JÜRGEN R. SCHOPPER 《Geophysical Prospecting》1968,16(2):277-294

In a paper presented at last year's Amsterdam meeting (viz. Geophysical Prospecting 14 (1966), 3, 301–341), J. R. Schopper derived formulas relating formation factor, permeability and porosity, by means of a statistical-network approach and by treating the electric and hydraulic resistance analogously. The model of the porous medium consists of a network of branch resistors, their values being statistically distributed about a mean R_o with a relative standard deviation (variation coefficient) s. A properly defined total resistance R of the network can be expressed by the relationship: ((1′)) Here α is a geometrical factor dependent only on the shape of the network (i.e. the number of meshes in the longitudinal and transversal direction), ε is a characteristical constant dependent only on the individual mesh shape (i.e. the number of nodes and branches within a mesh). This network constant ε enters the equations relating formation factor, permeability and porosity, ε had been found to be in the range zero to one by calculating algebraically two special limiting network cases. However, for a better understanding of which value exactly this constant will have in actual porous media, networks with various mesh shapes have to be treated generally. Because of the basically statistical approach, the networks have to be large so that a general algebraic treatment is precluded. Hence numerical methods using digital computers must be applied. The determination of the total resistance R of any resistance network leads to the problem of solving a system of linear, inhomogeneous equations; i.e. Ohm's law written in matrix form: ((2′))

• (R) is the matrix of the coefficients, composed of the individual branch resistances.
• (I) is the column vector, its components being fictitious circular mesh currents.
• (U) is the inhomogeneity column, its components being source voltages within the individual meshes.

The matrix (R) has characteristic properties that depend on the mesh shape on the one hand and on the number and arrangement of the meshes on the other hand. With the regular arrangement of identical meshes investigated here, the matrix always has a banded structure and is symmetrical with respect to the main diagonal, positive definite, and non-singular. For the numerical determination of the wanted constant ε the coefficients matrix is provided with values having a known distribution. Here, in particular, a computer-generated pseudorandom homogeneous distribution is used. The system, of equations is solved for R by a modified Cholesky method. Equation (1′) can then be solved fore. The main features of an ALGOL program written for this purpose and optimized with respect to storage space requirement and computer time are discussed. Networks of triangular, square and hexagonal meshes have been investigated. The results are discussed.  相似文献