Exploration Geophysics - Volume 15, Issue 3, 1984

Geophysical surveys across the Salt Creek and Mons Cupri volcanogenic massive sulphide bodies of the Pilbara area of Western Australia show them to be chargeable, but not conductive. Pervasive silicification, isolation of conductive minerals by sphalerite and tectonic disruption all appear to contribute to prevent these accumulations of normally conductive sulphides from responding to electromagnetic systems.

During an exploration programme for volcanogenic massive sulphides in the Mt Windsor belt of north-east Queensland a variety of transient electromagnetic (TEM) profiles were measured over a particular prospect. On the basis of separated-loop SIROTEM and fixed-loop EM 37 profiles the most distinctive anomaly was initially interpreted to be due to a steeply dipping bedrock conductor, but drilling and down-hole SIROTEM could not adequately explain the anomaly. Subsequent coincident-loop SIROTEM and fixed-loop EM 37 and UTEM surveys utilizing a transmitter loop on each side of the interpreted conductor demonstrated that its source was not within bedrock but was actually the edge of a conductive surf icial layer. Comparison of the field data with analogue model profiles confirms this interpretation. As it is apparent that similar geological situations will commonly be encountered during TEM surveys in conductive environments, caution in interpretation is required. In a number of cases apparent bedrock conductors may need to be re-surveyed with a different field configuration to confirm their validity before drill testing.

The contamination of the geophysical signal by variations in the geomagnetic field, by natural EM signals, and by mechanical motion of the receiving inductor in the earth's field is studied in detail. It is shown that the noise in the data of the more sensitive EM systems is subject to substantial variations of a seasonal, diurnal, and regional nature that may combine to yield a ~ 10⁴ variation in extreme cases. Operational procedures that minimize the effects of noise upon the geophysical data are enunciated. The amplitude distribution of sferics is measured, and used to evalute the effectiveness of sferic suppression techniques.

Regional differences are observed in the severity of telluric noise interference in induced polarization surveys. In some areas, of which Cobar (New South Wales) is an extreme example, surveys must often be postponed or confined to particular times of day. Using simple resistivity and magnetotelluric models, and typical magnetic micro-pulsation spectra, we show how this arises. The situation is worst when a very resistive basement is overlain by a thick conductive cover. In that case the IP signal is small on account of the conductive cover, while telluric voltages are large because of the resistive basement. For typical IP frequencies, and for the values of overburden resistivity found at Cobar, noise to signal ratio is shown to be greatest for overburden thicknesses of 200-300 m. This compares with the 80-150 m thicknesses actually observed. Noise to signal ratio is relatively insensitive to dipole length for a given separation of dipole centres.

The Hoggar Region of Algeria, situated in the central part of the Sahara, is geologically complex and logistically difficult. Programmes of geological mapping and mineral exploration are being conducted by Algerian Government Agencies in which geophysical studies are playing useful roles. The region is covered by aerogeophysical surveys at regional scale. The interpretation of this data, integrated with the results of ground magnetic, radiometric and gravity traverses and of measurements of geophysical properties of outcrop samples is the first stage in the mapping programmes. Examples of results from the Timissao-Timgaouine region are presented. The several episodes of granite were identified and mapped by their radiometric expressions. The sequence of granites is interpreted, from older (early Pan African) to younger (Eocambrian), as Timgaouine granite, migmatitic granite, Abankor and Timissao magmatic granites and finally the intrusive granites of Taourirt and Bahouinet. The various magnetic bodies (conformable metavolcanics, diorite and gabbro intrusives, effusive complexes and mafic dikes) show characteristic aeromagnetic signatures by which they can be mapped. Source body parameters are calculated from magnetic and gravity data. The evolution of the Pharusian Chain west of the great 4°50' submeridional fault has been re-interpreted in the light of modern theories of global tectonics. In the Timgaouine region, the computed structures, the distribution of magnetic units and the systems of faults all support the hypothesis that the Pharusian Chain evolved as a back-arc basin during a period of separation of the West African Craton from the Touareg Shield as a result of the Pan African Orogeny.

It is known that in the North Sea basin the depths to major reflectors as determined from surface seismic data are often larger than the well-log depths. From a study of data sets which tie 21 wells, I found a strong correlation between the occurrence of the depth error and the presence of shales in the subsurface. Assuming that the error is caused by elliptical velocity anisotropy in shales, I measured the anisotropy from a comparison of the well-log sonic data and the interval velocity profile obtained from the surface seismic data and also from a comparison of the seismic depth and the well-log depth. It was found that the two methods of measurement agree with each other and also agree qualitatively with the previous laboratory measurements of anisotropy in shale samples. The results strongly suggest that the depth anomaly in the North Sea basin is caused by the velocity anisotropy of shales. A simple method to correct the seismic depth is given.

Compressional waves are sensitive to the type of pore fluid within rocks, but shear waves are only slightly affected by changes in fluid type. This suggests that a comparison of compressional- and shear-wave seismic data recorded over a prospect may allow an interpreter to discriminate between gas-related anomalies and those related to lithology. This case study documents that where a compressional-wave ‘bright spot’ or other direct hydrocarbon indicator is present, such a comparison can be used to verify the presence of gas. In practice, the technique can only be used for a qualitative evaluation. However, future improvement of shear-wave data quality may enable the use of more quantitative methods as well.

Velocity sensitive (wide propagation angle) seismic data do not comply with the r.m.s. small propagation angle approximation. A hyperbolic velocity spectrum and Dix’s equation cannot use wide-angle arrivals to estimate interval velocity accurately. The linear moveout method measures interval velocity exactly in stratified media. Snell midpoint coordinates are constructed to image the data before velocity estimation. Energy focuses at the arrival coordinates of a fixed reference Snell wavefront as required by the linear moveout method. The image of a common-midpoint seismic gather in Snell midpoint coordinates, for a nonvertical reference Snell wave, defines the wave-equation velocity spectrum. Two important properties of the velocity spectrum are locality, where energy is a local function of velocity; and linearity, that is invertible using linear transformations. Velocity sensitivity of wave-equation extrapolation operators increases with the angle of propagation. In Snell midpoint coordinates, angles are measured relative to an arbitrary slanted reference Snell wave. At this particular angle wave-equation operators are exact, independent of velocity. Approximations of the wave equation in Snell midpoint coordinates satisfactorily image wide-angle energy. To compute the velocity spectrum, we use the 15-degree finite-difference wave equation in the frequency domain. This equation is insensitive to the downward continuation velocity. This formation resolves multivalued, wide velocity spectrum data using in-homogeneous, offset and depth dependent, downward continuation velocity. Stepout filtering concurrent with downward continuation eliminates wide-angle propagation energy not modeled by the 15-degree wave equation.

The significance of entropy-like terms is examined within the context of the finite-difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central-difference scheme, and (2) the Lax–Wendroff two-step scheme. Numerical results are presented comparing the short-wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one-dimensional source is used.

The seismic rays and wavefront curvatures are determined by solving a system of nonlinear ordinary differential equations. For media with constant velocity and for media with constant velocity gradient, simplified solutions exist. In a general inhomogeneous medium these equations must be solved by numerical approximations. The integration of the ray-tracing and wavefront curvature equations is then performed by a modified divided difference form of the Adams PECE (Predict–Evaluate–Correct–Evaluate) formulas and local extrapolation. The interfaces between the layers are represented by bicubic splines. The changes in ray direction and wavefront curvature at the interfaces are computed using standard formulas. For three-dimensional media, two quadratic traveltime approximations have been proposed. Both are based on a Taylor series expansion with reference to a ray from a reference source point to a reference receiver point. The first approximation corresponds to expanding the square root of the result. The second approximation corresponds to expanding the traveltime in a Taylor series. The two traveltime approximations may be expressed in source–receiver coordinates or in midpoint-half-offset coordinates. Simplified expressions are obtained when the reference source and receiver coincide, giving zero-offset approximations, for which the reference ray is a normal-incidence ray. A new method is proposed for computing the second derivatives of the normal-incidence traveltime with respect to the source-receiver midpoint coordinates. By considering a beam of normal-incidence rays it is shown that the second-derivative matrix may be found by computing the wavefront curvature along a reference normal-incidence ray starting at the reflection point with the wavefront curvature equal to the curvature of the reflecting interface. From this second-derivative matrix the normal moveout velocity can be computed for any seismic line through the reference source–receiver midpoint. It is also shown how a reverse wavefront curvature calculation may be used, in a time-to-depth migration scheme, to compute the curvature of the reflecting interface from the estimated second derivatives of the normal-incidence traveltime. Numerical results for different three-dimensional models indicate that the first traveltime approximation, based on an expansion of the square of the traveltime, is the most accurate for shallow reflectors and for simple models. For deeper reflectors the two approximations give comparable results, and for models with complicated velocity variations the second approximation may be slightly better than the first one, depending on the particular model chosen. A simplified traveltime approximation may be used in a three-dimensional seismic velocity analysis. Instead of estimating the stacking velocity one must estimate three elements in a 2 × 2 symmetric matrix. The accuracy and range of validity of the simplified traveltime approximation are investigated for different three-dimensional models.

Point source responses from a planar acoustic and/or elastic layer boundary (as well as from a stack of planar parallel layers) are generally obtained by using as a starting point the Somerfeld-Weyl integral, which can be viewed as decomposing a time-harmonic spherical source into time-harmonic homogeneous and inhomogeneous plane waves. This paper gives a powerful extension of this integral by providing a direct decomposition of an arbitrary transient spherical source into homogeneous and inhomogeneous transient plane waves. To demonstrate with an example the usefulness of this new point source integral representation, a transient solution is formulated for the reflected/transmitted response from a planar acoustic reflector. The result is obtained in the form of a relatively simple integral and essentially corresponds to the solution obtained by Bortfeld (1962). It, however, is arrived at in a physically more transparent way by strictly superimposing the reflected/transmitted transient waves leaving the interface in response to the incident transient homogeneous and in-homogeneous plane waves coming from the centre of the point source.

The use of summary representation for electromagnetic modeling The method of summary representation developed by G. N. Polozhii is a quasi-analytical method for solving self-adjoint, finite-difference boundary value problems expressed on regular meshes. In principle, the method should allow considerable savings in computing time as well as improved accuracy when compared to commonly used finite-difference schemes. We have used summary representation as the basis for a new hybrid scheme to solve the two-dimensional Helmholtz equation for electromagnetic modeling. The theory behind this hybrid scheme is presented. Preliminary results for the two-dimensional problem show that substantial computing time and storage savings can be made.

The electromagnetic fields scattered by a three-dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E-field distortions below certain frequencies are essentially in-phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane-wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small-scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phase of all MT functions due to small-scale extraneous structure will be limited to high frequencies, so that one may ‘see through’ such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1 -D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometres, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half-spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper-strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

In the application of the broadband induced polarization method, it is necessary to know how a petrophysical resistivity spectrum is transformed into an apparent spectrum measured in the field. Investigated in the present work was the forming of an apparent spectrum in the case of a polarizable three-dimensional prism embedded in an unpolarizable half-space for gradient and dipole-dipole arrays. The computations were done numerically using the integral equation technique. The frequency dependence of the resistivity of the prism was depicted by means of the Cole–Cole dispersion model. With this simple model geometry, the phase spectra of apparent resistivity resemble quite closely in functional form the original petrophysical phase spectrum of the Cole–Cole dispersion model. The apparent spectra have shifted on the log-log scale downward, owing to geometric attenuation, and toward lower frequencies. The apparent Cole–Cole parameters have been inverted from the apparent spectra. The apparent charge-ability is generally noticeably smaller, owing to the geometric attenuation, than the chargeability of the original petrophysical spectrum. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The shift of the apparent phase spectrum toward lower frequencies partly compensates for the decrease in the apparent time constant caused by attenuation of the spectrum. The apparent time constant is thus close to the true time constant of the petrophysical spectrum. It is therefore possible in principle to obtain by direct inversion from an apparent spectrum measured in the field a reasonable estimate of the frequency dependence and time constant of the true spectrum of a polarizable body.

This paper reports on an investigation of the inversion of borehole normal resistivity data via ridge regression. Interpretation is afforded of individual thin beds and’ of complicated layered structures. A theoretical solution is given for a layered model containing an arbitrary number of layers in the forward problem. Two forward model results for resistive and conductive thin beds indicate that for high-resistivity contrasts, the departure between true and apparent resistivity may be more important than the effects caused by the variations in borehole diameter and mud resistivity. Four normal resistivity logs were chosen to test the inversion scheme. Two of the logs were theoretical logs with and without random noise added, and the remaining two were field examples. Theoretical model results and field examples indicate that the inverse method can be used to obtain the resistivity for each layer when the boundary position is known, but it also can be used to obtain the thickness and resistivity for each layer simultaneously.

The ideal rock model in electrical well logging for prospecting hydrocarbon consists of three cylindrical layers characterized by homogeneous resistivities. The second layer of model represents the zone of invasion, where under real circumstances the resistivity is not constant but changes with the distance from the borehole. This condition could be taken into consideration, but the solution of the electrical direct problem for such a case is very complicated. Any kind of invasion resistivity profile can be approximated by many cylindrical layers of homogeneous resistivities. A recursive formula is derived by which the many-layer problem can be solved simply. Numerical calculations were made to study the effect of the inhomogeneity of the invaded zone. Apparent resistivities of different Laterolog and normal arrangements were calculated for several models having linearly increasing resistivity values. These were evaluated by least-squares fitting to determine the equivalent electrical parameters of the usual model of three homogeneous layers. The results show that there is practically no error in determination of the true resistivity, but the depth of invasion may be significantly smaller than that of the linear resistivity profile.

This paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities. The bed boundary is assumed to be horizontal and the inhomogeneities to be axially symmetric. In such a geometry, an axially symmetric source will produce only axially symmetric waves. Since the borehole is an open structure, the mode spectrum consists of a discrete part as well as a continuum. The scattering of a continuum of waves by bed boundaries is difficult to treat. The approach used in the past in treating this class of problem has been approximate in nature, or highly numerical, such as the finite-element method. We present here a systematic way to approximate the continuum of modes by discrete modes. After discretization, the scattering problem can be treated simply. Since the approach is systematic, it allows derivation of the solution to any desired degree of accuracy in theory; but in practice, it is limited by the computational resources available. We also show that our approach is variational and satisfies both the reciprocity theorem and energy conservation.

The fundamental resistivity logging problem of a resistivity tool in the presence of both vertical and horizontal boundaries is solved with a hybrid method. The hybrid method combines the mode concept in wave-guide theory together with the finite-element method. In the mathematical formulation, the horizontal boundaries are used to separate the geometry of the problem into different regions. In each region, the waveguide modes are obtained through the solution of an equivalent variational problem. The solutions are calculated by a one-dimensional finite-element method. The vertical boundaries are taken into account in these calculations. The orthonormality of modes in each region allows a series representation of the potential in the regions. Boundary conditions at horizontal bed boundaries then couple the modes between different regions and enable the solutions for the potential to be expressed in terms of reflection and transmission matrices of modes. The source excitation determines the amplitudes of the modes. The results of the hybrid method are in excellent agreement with those of the integral transform solution. Numerical results of the apparent resistivity are illustrated as a function of formation properties. The effects of an invaded zone are also examined by considering radial inhomogeneous profiles in the formation. The results of the hybrid method are numerically efficient because it reduces the two-dimensional finite-element problem into a one-dimensional one. It also provides a physical interpretation of the solution in terms of modes.

Two-ship multichannel seismic profiles, using expanding spread and constant offset source–receiver configurations, were shot with explosive charges and a 16.4 I air gun to investigate the structure of the continental shelf off northwest Britain. A long-range (69 km) expanding spread profile reveals that the crystalline basement off northern Scotland is covered by sedimentary sections up to 2.5 km thick, and is divisible into two seismic units with velocities of 6.1 km/s and 6.6 km/s. Prominent supercritical Moho reflections indicate a crustal thickness of 26.7 km. Strong sedimentary and basement refractions, together with oblique reflections from the vicinity of the Moho, have been profiled at a constant air gun–receiver offset of 10 km across a sedimentary basin west of the Orkney Islands. On the Outer Hebridean shelf to the west of mainland Scotland, the metamorphic basement lies within 250 m of the sea floor, P- to S-wave conversion occurs at the basement surface; Vp/Vs gives a Poisson’s ratio of 0.27–0.31 at depths of 300–1000 m. Marked changes in mode conversion efficiency are observed on constant offset profiles and are attributed to variations in the velocity structure of an uppermost low-velocity (4.9 km/s) layer of weathered basement. The deeper crustal velocity appears uniform with depth, although there is some evidence of significant lateral velocity changes (6.28–6.61 km/s). In contrast to the shelf north of Scotland, reflections from within the basement and from near the base of the crust are recorded only sporadically on constant offset profiles. A strong event at 10.4 s two-way reflection time appears to have arisen from a seismic discontinuity within the upper mantle. The difference in seismic character of the basement on the two-ship profiles suggests significant variations in crustal structure within the Caledonian foreland of northern Britain.