THE USE OF FILTERED BESSEL FUNCTIONS IN DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS *

We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves. Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency.     

THE APPLICATION OF LINEAR FILTER THEORY TO THE DIRECT INTERPRETATION OF GEOELECTRICAL RESISTIVITY SOUNDING MEASUREMENTS*

Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.     

A NEW PARAMETER FOR THE INTERPRETATION OF INDUCED POLARIZATION FIELD PROSPECTING (time-domain) *

In a previous paper it has been shown that we can relate the transient IP electric field E_p , existing in a rock after a step wave of polarizing current, with the steady-state current density J_ss during the current step wave as follows: E_p =ρ' J_ss . This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m. Supposing E _p=— grad U_p and applying the divergence condition div J_ss = o, one can, for a layered earth, obtain a general expression for the depolarization potential U_p as a solution of Laplace's equation ?²U_p= o. Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'_a (defined as the product of the apparent resistivity ρ_a with the apparent chargeability m_a) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array. The most general expression of ρ'_a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'_a. Therefore it is possible to interpret a ρ'_a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching. In this manner a great deal of work is saved since there is no need to construct proper m_a graphs for the interpretation of IP soundings, as it has been done up to now. Finally some field examples are reported.     

REALIZATION OF SHARP CUT-OFF FREQUENCY CHARACTERISTICS ON DIGITAL COMPUTERS

It was found in Part I of this paper that approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length M produced a characteristic whose slope on a linear frequency scale was proportional to the length of impulse response, but whose maximum overshoot of ±9% was independent of this length (Gibbs' phenomenon). Weighting functions, based on frequency tapering or arbitrarily chosen, were used in Part II to modify the truncated impulse response of the sharp cut-off frequency characteristic, and thereby obtain a trade-off between the value of maximum overshoot and the sharpness of the resulting characteristic. These weighting functions, known as apodising functions, were dependent on the time-bandwidth product Mξ, where 2ξ, corresponded to the tapering range of frequencies. Part III now deals with digital filters where the number 2N–1 of coefficients is directly related to the finite length M of the continuous impulse response. The values of the filter coefficients are taken from the continuous impulse response at the sampling instants, and the resulting characteristic is approximately the same as that derived in Part II for the continuous finite length impulse response. Corresponding to known types of frequency tapering, we now specify a filter characteristic which is undefined in the tapering range, and determine the filter coefficients according to a mean square criterion over the rest of the frequency spectrum. The resulting characteristic is dependent on the time bandwidth product Mξ= (N–1/2)ξ up to a maximum value of 2, beyond which undesirable effects occur. This optimum partially specified characteristic is an improvement on the previous digital filters in terms of the trade-off ratio for values of maximum overshoot less than 1%. Similar to the previous optimum characteristic is the optimum partially specified weighted digital filter, where greater “emphasis is placed on reducing the value of maximum overshoot than of maximum undershoot”. Such characteristics are capable of providing better trade-off ratios than the other filters for maximum overshoots greater than 1/2%. However these filters have critical maximum numbers 2.N_C–1 of coefficients, beyond which the resulting characteristics have unsuitable shapes. This type of characteristic differs from the others in not being a biassed odd function about its cut-off frequency.     

FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*

The difficulty to use master curves as well as classical techniques for the determination of layer distribution (e_i, ρ_i) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.     

A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*

This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.     

TRAITEMENT AUTOMATIQUE DES SONDAGES ELECTRIQUES AUTOMATIC PROCESSING OF ELECTRICAL SOUNDINGS*

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.     

Study on the property of apparent resistivity changes of rock samples byin situ shear and friction test

In the strip limestone mine in Guiding county, Guizhou Province the shear and frictionin situ tests of rock body were made for the three typical inclined weak bands C ₃ ¹ /C ₃ ¹ , C ₃ ¹ /C ₂ ² and C ₂ ² /C ₂ ¹ . The tests were made according to the second scheme of cuneate sample of the standards on rock mechanics test of Water Conservancy and Electricity Ministry. The changes of the resistivity in the weak band and the acoustic speed across the weak band were measured in the same time. The apparent resistivity data, obtained for 8 samples on 27 measure lines in 38 cycle tests, show that the apparent resistivity changes have rather obvious characters as follows: 1. At shear and friction stage, the change of the apparent resistivity accelerates after the yield point, and reaches the maximum of change rate and change amplitude near fracture point (except the lines with resistivity invariant); 2. On the same sample, the resistivity changes are different on the various lines and related to the location settled the lines, there are some “sensitive” location; 3. At the stage of preloading normal stress before shearing, the resistivity decreases on most lines, but on a few lines the resistivity does not changes; 4. After unloading shear stress, the resistivity could not recover completely and the hysteresis of resistiviity takes place on a few lines.     

An algorithm for interpolation in the pyramid domain‡

With the pyramid transform, 2D dip spectra can be characterized by 1D prediction‐error filters (pefs) and 3D dip spectra by 2D pefs. These filters, contrary to pefs estimated in the frequency‐space domain (ω, x) , are frequency independent. Therefore, one pef can be used to interpolate all frequencies. Similarly, one pef can be computed from all frequencies, thus yielding robust estimation of the filter in the presence of noise. This transform takes data from the frequency‐space domain (ω, x) to data in a frequency‐velocity domain (ω, u=ω·x) using a simple mapping procedure that leaves locations in the pyramid domain empty. Missing data in (ω, x) ‐space create even more empty bins in (ω, u) ‐space. We propose a multi‐stage least‐squares approach where both unknown pefs and missing data are estimated. This approach is tested on synthetic and field data examples where aliasing and irregular spacing are present.     

AFTER-STACK MULTICHANNEL FILTERS WITHOUT MIXING EFFECTS *

Several types of multichannel filters have been introduced in the past with the purpose of rejecting, in a seismic section, coherent noise having a slope different from that of the signal. These filters, generally, tend to introduce a certain amount of mixing and therefore the output trace shows increased horizontal coherence. This is due to the model on which these filters are based, since the hypothesis is posed that the reflectors are continuous. This may be dangerous since it could lead to mistaken interpretations, for example when small faults or breaks are made to disappear in the output section. Other problems that could arise in the application of multichannel filters after-stack are space-aliasing and high-pass filtering. The former occurs when coherent noise is rejected with apparent Velocity V and frequency f_a=V/X, where X is the distance between traces. In this case, the signal also is distorted since it is rejected in the same frequency range. The high pass filtering effect occurs when the multichannel filter is designed to remove low coherent noise with high apparent velocity. In the paper a family of multichannel filters is presented based on a model of the seismic section such that minimum mixing effects appear. The filters are designed to give good results even in the case of low frequency and high velocity coherent noise. Some practical examples are shown.     

Study on the property of apparent resistivity changes of rock samples by in situ shear and friction test

In the strip limestone mine in Guiding county, Guizhou Province the shear and frictionin situ tests of rock body were made for the three typical inclined weak bands C ₃ ¹ /C ₃ ¹ , C ₃ ¹ /C ₂ ² and C ₂ ² /C ₂ ¹ . The tests were made according to the second scheme of cuneate sample of the standards on rock mechanics test of Water Conservancy and Electricity Ministry. The changes of the resistivity in the weak band and the acoustic speed across the weak band were measured in the same time. The apparent resistivity data, obtained for 8 samples on 27 measure lines in 38 cycle tests, show that the apparent resistivity changes have rather obvious characters as follows: 1. At shear and friction stage, the change of the apparent resistivity accelerates after the yield point, and reaches the maximum of change rate and change amplitude near fracture point (except the lines with resistivity invariant); 2. On the same sample, the resistivity changes are different on the various lines and related to the location settled the lines, there are some “sensitive” location; 3. At the stage of preloading normal stress before shearing, the resistivity decreases on most lines, but on a few lines the resistivity does not changes; 4. After unloading shear stress, the resistivity could not recover completely and the hysteresis of resistiviity takes place on a few lines. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 217–223, 1993. Support for this research was received from Guiding strip limestone mine, Guizhou Organic Chemistry Factory. This research is supported by the Chinese Joint Seismological Science Foundation.     

SEISMIC REFRACTION METHOD TO STUDY THE FOUNDATION ROCK OF A DAM*

Dynamic elastic moduli like E, μ, K and μ of the foundation rock of a dam have been determined by finding V_p- and V_s-velocities by seismic refraction with a hammer as source. Some parameters such as “fracture frequency” and “rock quality designation” (RQD) of the foundation rock have been derived using “average regression curves” and V_p-velocities. By comparing K/μ with V_p/V_s, a few locations showing weathered conditions have been demarcated. This compares well with RQD values of those locations.     

Mass Discharge in a Tracer Plume: Evaluation of the Theissen Polygon Method

A tracer plume was created within a thin aquifer by injection for 299 d of two adjacent “sub‐plumes” to represent one type of plume heterogeneity encountered in practice. The plume was monitored by snapshot sampling of transects of fully screened wells. The mass injection rate and total mass injected were known. Using all wells in each transect (0.77 m well spacing, 1.4 points/m² sampling density), the Theissen Polygon Method (TPM) yielded apparently accurate mass discharge (M_d) estimates at three transects for 12 snapshots. When applied to hypothetical sparser transects using subsets of the wells with average spacing and sampling density from 1.55 to 5.39 m and 0.70 to 0.20 points/m², respectively, the TPM accuracy depended on well spacing and location of the wells in the hypothesized transect with respect to the sub‐plumes. Potential error was relatively low when the well spacing was less than the widths of the sub‐plumes (>0.35 points/m²). Potential error increased for well spacing similar to or greater than the sub‐plume widths, or when less than 1% of the plume area was sampled. For low density sampling of laterally heterogeneous plumes, small changes in groundwater flow direction can lead to wide fluctuations in M_d estimates by the TPM. However, sampling conducted when flow is known or likely to be in a preferred direction can potentially allow more useful comparisons of M_d over multiyear time frames, such as required for performance evaluation of natural attenuation or engineered remediation systems.     

THE QUANTITATIVE ANALYSIS OF FREQUENCY-DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS*

Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ_∞/ρdc with ρ_∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ_∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ_∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of fe_α are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.     

TRANSFORMATION OF RESISTIVITY SOUNDING MEASUREMENTS OBTAINED IN ONE ELECTRODE CONFIGURATION TO ANOTHER CONFIGURATION BY MEANS OF DIGITAL LINEAR FILTERING*

The technique of digital linear filtering is used for transformation of apparent resistivity data from one electrode configuration into another. Usually filter spectra are determined via the discrete Fourier transforms of input and output functions: the filter characteristic is the quotient of the spectra of the output function and input function. In this paper, the transformation of the apparent resistivities is presented for four electrode configurations (Wenner, the two-electrode, Schlumberger, and dipole configurations). In our method, there is no need to use the discrete Fourier transform of the input and output functions in order to determine the filter spectrum for converting apparent resistivity in one electrode configuration to any other configuration. Sine responses for determination of the derivative of apparent resistivities are given in analytical form. If the filter spectrum for converting the apparent resistivity to the resistivity transform for one electrode configuration is known, the filter spectra for transforming the apparent resistivity to the resistivity transform for any electrode configurations can be calculated by using newly derived expressions.     

NEW RESULTS IN RESISTIVITY WELL LOGGING*

Two independent theoretical analyses show that, spacing for spacing, the two-electrode normal device investigates deeper than the seven-electrode focused Laterolog 7. The first analysis, published earlier, compares the radii of investigation of the different sondes from the portion of the ground that contributes maximum to, or fifty percent of, the measured signal. The second relates to the nature of the departure curves for the two sondes for an infinitely thick resistive formation pierced by a bore hole. With increasing spacing, the apparent resistivity for the normal device rises much faster and asymptotically approaches the true resistivity much earlier than that for Laterolog 7. These two analyses also prove that, in a Laterolog 7, the radius of investigation increases as O₁O₂ decreases relatively to A₁A₂. Since any complex point electrode system is equivalent to a superposition of elementary dipoles or two-electrode devices, it follows that no resistivity sonde of discrete point electrodes can have a radius of investigation larger than that for the normal device of the same spacing. Laboratory measurements in a model tank confirm these theoretical results. For thin highly resistive formations we find from theoretical and model studies that the normal device is markedly superior to Laterolog 7 as it gives apparent resistivity values much closer to the true. It has other advantages as well. Thus, our results on the comparative performances of the normal and Laterolog 7 devices are at variance with those published so far since the introduction of Laterolog 7 in 1951. For reasons given in the text, the chief characteristic of Laterolog 7—namely, focusing the current from the central electrode in a thin horizontal sheet into the target formation—does not endow it with any special advantage. The main reason is that the measured potential in a Laterolog 7 is caused not only by the current focused into the target formation but also by the currents from the outer two electrodes which flow, due to the same focusing process, entirely through the adjacent formations and the mud column. Indeed, the contribution to the measured signal by the outer two power electrodes is considerably larger than that from the central.     

Regional study of the anomalous change in apparent resistivity before the Tangshan earthquake (M=7.8, 1976) in China

Electrical resistivity measurements have been conducted as a possible means for obtaining precursory earthquake information. Before five great earthquakes (M>7,h<25 km) in China, the apparent resistivity _a showed systematic variations within a region 200 km from the epicenters. In particular, 9 stations in the Tangshan-Tianjin-Beijing region prior to the Tangshan earthquake (M=7.8,h=11 km, 27 July 1976) showed a consistent decrease of apparent resistivity around the epicenter, with a maximum resistivity change of 6% and a period of variation of 2–3 years. Simultaneous water table observations in this region showed a declining water table, and ground surface observations indicated a slight (5 mm) uplift in the epicenter region relative to its surroundings.In order to develop an explanation for the observed change of apparent resistivity associated with these great earthquakes, we have used Archie's Law to explore the effects of changes in rock porosity, water content and electrolyte resistivity on measured resistivity.Tentative conclusions of this study are as follows: (1) the apparent resistivity change is opposite to the effect expected from the simultaneous water table trend; (2) the dilatancy needed to give such resistivity variations (assuming Archie's Law holds) is much larger than that needed to explain the observed uplift (by 2–3 orders of magnitude); (3) salinity change in the pore electrolyte is a possible explanation for the variation in resistivity: an increase in the salinity would cause a proportional decrease in resistivity; the data needed to test this hypothesis, however, are lacking; and (4) the effect of changing geometry of rock pores or cracks due to pressure solution may provide an explanation for the decrease in apparent resistivity; it is different in nature from the effect of a volume change in response to stress although the geometry change is also closely related to the stress change.     

V p /V s anomalies in dilatant rock samples

Summary In a series of triaxial experiments we have measuredV _p ,V _s and volumetric strain simultaneously in dilating dry and saturated rocks. For the first time these data permit quantitative comparison of seismic velocities or their ratio and dilatant volumetric strain. In air-dry samplesV _p /V _s decreases by a few per cent at strains of 10^–3; in saturated materials with high pore pressure,V _p /V _s increases by a comparable amount. Decreases in seismic velocity ratio are difficult to generate in initially saturated rocks even with low pore pressures and at strain rates of 10^–4/sec. A liquid-vapor transition will not produce a significant drop inV _p /V _s . If dilatancy and fluid flow are responsible for seismic travel time anomalies prior to earthquakes, our results suggest that such anomalies will occur only in regions where pore fluid source to sink dimensions are of the order of 10 km or more, or in regions where the rocks are not saturated to begin with.     

Filter formulation and wavefield separation of cross-well seismic data

Multichannel filtering to obtain wavefield separation has been used in seismic processing for decades and has become an essential component in VSP and cross-well reflection imaging. The need for good multichannel wavefield separation filters is acute in borehole seismic imaging techniques such as VSP and cross-well reflection imaging, where strong interfering arrivals such as tube waves, shear conversions, multiples, direct arrivals and guided waves can overlap temporally with desired arrivals. We investigate the effects of preprocessing (alignment and equalization) on the quality of cross-well reflection imaging wavefield separation and we show that the choice of the multichannel filter and filter parameters is critical to the wavefield separation of cross-well data (median filters, f–k pie-slice filters, eigenvector filters). We show that spatial aliasing creates situations where the application of purely spatial filters (median filters) will create notches in the frequency spectrum of the desired reflection arrival. Eigenvector filters allow us to work past the limits of aliasing, but these kinds of filter are strongly dependent on the ratio of undesired to desired signal amplitude. On the basis of these observations, we developed a new type of multichannel filter that combined the best characteristics of spatial filters and eigenvector filters. We call this filter a ‘constrained eigenvector filter’. We use two real data sets of cross-well seismic experiments with small and large well spacing to evaluate the effects of these factors on the quality of cross-well wavefield separation. We apply median filters, f–k pie-slice filters and constrained eigenvector filters in multiple domains available for these data sets (common-source, common-receiver, common-offset and common-midpoint gathers). We show that the results of applying the constrained eigenvector filter to the entire cross-well data set are superior to both the spatial and standard eigenvector filter results.     

Regional induction studies: A review of methods and results

The geomagnetic skin-effect is specified by setting three length scales in relation to each other: L₁ for the overhead source. L₂ for the lateral non-uniformity of the subsurface conductor, L₃ for the depth of penetration of a quasi-uniform transient field into this conductor. Relations for the skin-effect of a quasi-uniform source in layered conductors are generalized to include sources of any given geometry by introducing response kernels as functions of frequency and distance. They show that only those non-uniformities of the source which occur within a distance comparable to L₃ from the point of observation are significant. The skin-effect of a quasi-uniform source in a laterally non-uniform earth is expressed by linear transfer functions for the surface impedance and the surface ratio of vertical/horizontal magnetic variations. In the case of elongated structures and E-polarisation of the source, a modified apparent resistivity is defined which as a function of depth and distance gives a first orientation about the internal distribution of conductivity. The skin-effect of a non-uniform source in a non-uniform earth is considered for stationary and “running” sources. Recent observations on the sea floor and on islands indicate a deep-seated change of conductivity at the continent—ocean transition, bringing high conductivity close to the surface, a feature which may not prevail, however, over the full width of the ocean. There is increasingly reliable evidence for high conductivities (0.02 to 0.1 micro ^?1 m^?1) at subcrustal or even at crustal depth beneath certain parts of the continents, in some cases without obvious correlation to geological structure.