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 Volume 49, Issue 1, 2001
Geophysical Prospecting  Volume 49, Issue 1, 2001
Volume 49, Issue 1, 2001

Gravity probability tomography: a new tool for buried mass distribution imaging
Authors Paolo Mauriello and Domenico PatellaFollowing the probability tomography principles previously introduced to image the sources of electric and electromagnetic anomalies, we demonstrate that a similar approach can be used to analyse gravity data. First, we give a coherent derivation of the Bouguer anomaly concept as a Newtonian‐type integral for an arbitrary mass distribution buried below a non‐flat topography. A discretized solution of this integral is then derived as a sum of elementary contributions, which are cross‐correlated with the gravity data function in the expression for the total power associated with the Bouguer anomaly. To image the mass distribution underground we introduce a mass contrast occurrence probability function using the cross‐correlation product of the observed Bouguer anomaly and the synthetic field due to an elementary mass contrast source. The tomographic procedure consists of scanning the subsurface with the elementary source and calculating the occurrence probability function at the nodes of a regular grid. The complete set of grid values is used to highlight the zones of highest probability of mass contrast concentrations. Some synthetic and field examples demonstrate the reliability and resolution of the new gravity tomographic approach.

Detecting small‐scale targets by the 2D inversion of two‐sided three‐electrode data: application to an archaeological survey
Authors M. Emin Candansayar and Ahmet T. BaşokurThe detecting capabilities of some electrical arrays for the estimation of position, size and depth of small‐scale targets were examined in view of the results obtained from 2D inversions of apparent‐resistivity data. The two‐sided three‐electrode apparent‐resistivity data are obtained by the application of left‐ and right‐hand pole–dipole arrays that also permit the computation of four‐electrode and dipole–dipole apparent‐resistivity values without actually measuring them. Synthetic apparent‐resistivity data sets of the dipole–dipole, four‐electrode and two‐sided three‐electrode arrays are calculated for models that simulate buried tombs. The results of two‐dimensional inversions are compared with regard to the resolution in detecting the exact location, size and depth of the target, showing some advantage for the two‐sided three‐electrode array. A field application was carried out in the archaeological site known as Alaca Hoyuk, a religious temple area of the Hittite period. The two‐dimensional inversion of the two‐sided three‐electrode apparent‐resistivity data has led to locating a part of the city wall and a buried small room. The validity of the interpretation has been checked against the results of subsequent archaeological excavations.

3D resistivity inversion using 2D measurements of the electric field
Authors P.D. Jackson, S.J. Earl and G.J. ReeceField and ‘noisy’ synthetic measurements of electric‐field components have been inverted into 3D resistivities by smoothness‐constrained inversion. Values of electrical field can incorporate changes in polarity of the measured potential differences seen when 2D electrode arrays are used with heterogeneous ‘geology’, without utilizing negative apparent resistivities or singular geometrical factors. Using both the X‐ and Y‐components of the electric field as measurements resulted in faster convergence of the smoothness‐constrained inversion compared with using one component alone. Geological structure and resistivity were reconstructed as well as, or better than, comparable published examples based on traditional measurement types. A 2D electrode grid (20 × 10), incorporating 12 current‐source electrodes, was used for both the practical and numerical experiments; this resulted in 366 measurements being made for each current‐electrode configuration. Consequently, when using this array for practical field surveys, 366 measurements could be acquired simultaneously, making the upper limit on the speed of acquisition an order of magnitude faster than a comparable conventional pole–dipole survey. Other practical advantages accrue from the closely spaced potential dipoles being insensitive to common‐mode noise (e.g. telluric) and only 7% of the electrodes (i.e. those used as current sources) being susceptible to recently reported electrode charge‐up effects.

Detection of potential fields source boundaries by enhanced horizontal derivative method
More LessA high‐resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced‐to‐the‐pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries.
The EHD method is highly flexible, and different conditions of signal‐to‐noise ratios and depths‐to‐source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high‐order vertical derivatives is also suggested. This involves both frequency‐ and space‐domain transformations and gives more stable results than the usual Fourier method.
The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep‐seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high‐resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum.
Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method.

The AVA (amplitude‐versus‐angle) signature of small‐scale reflector topography
Authors Rosemary K. Quinn, Roger A. Clark and Jürgen W. NeubergRoutine amplitude‐versus‐offset or amplitude‐versus‐angle (AVA) analysis is founded on the predicted reflectivity of a planar boundary between isotropic homogeneous half‐spaces, yet many real boundaries of interest to hydrocarbon exploration may violate these assumptions. Here, we evaluate consequences of boundary roughness, i.e. small‐scale, sub‐resolution topography, on the reflecting boundary, to find whether sub‐resolution topography can deceive routine AVA analysis and produce misleading hydrocarbon indicators. We use noise‐free synthetic CMP and stacked‐section seismograms, generated with a Kirchhoff‐integral method, for offsets up to 4000 m. The reflecting boundary was at 2000 m depth below a single overburden layer, and comprised isolated mounds or channels (sinusoidal cross‐section, 5–40 m high and 100–750 m wide), and more complex roughness (simulated with seven 1.5–2 km long bathymetric profiles across modern‐day river‐beds, with dune and bar features up to approximately 20 m or 20 ms TWT vertical relief, and 10–100 m or more lateral extent). Flat‐boundary responses were taken as the ‘reference’ against which to compare waveforms and amplitudes through semblance analysis, AVA intercept A and slope B cross‐plots, and inferred Poisson's ratios. Physical properties of the media were based on shales and brine‐ or oil‐sands from an offshore UK oilfield.
For the CMP centred on the topographic feature, isolated mounds and channels produced correlated excursions of A and B from the flat‐boundary response (by approximately 35–200%), simulating the familiar ‘background trend’ but sometimes oblique to it. Inferred Poisson's ratios were around 0.3, but for some channels often fell as low as 0.2, potentially interpretable as gas sand. For complex boundary topographies on a shale/brine‐sand model, AVA parameters were extracted for 29 CMPs, 100 m apart along each of seven profiles. On a cross‐plot, they spanned the flat‐boundary response on a linear trend B = (0.01 ± 0.02) – (1.72 ± 0.09)A, similar to reported real data and a realistic ‘mudrock trend’ but with outliers both above and below it that could be interpreted as ‘real’ weak anomalies. Poisson's ratios were 0.30 ± 0.01, between the expected values for brine‐ and oil‐sand. This suggests that boundary roughness may contribute to observed trends on cross‐plots and possibly small, but potentially laterally extensive, false AVA anomalies may also be induced.

Successive cracking steps of a limestone highlighted by ultrasonic wave propagation
Authors J.F. Couvreur, A. Vervoort, M.S. King, E. Lousberg and J.F. ThimusA number of laboratory tests (uniaxial, triaxial and hydrostatic) have been conducted on a dry porous limestone. A conceptual model is proposed to correlate deformation and damage fields (including acoustic emission activity) with the variation of ultrasonic velocities, quality factors and energies as measures of attenuation. This correlation is presented in a stress deviator versus confining pressure diagram. In this way, the successive steps occurring in the damage process of this rock are well described. In particular, the quality factor of S‐waves distinguishes clearly the onset of the initially stable cracking, while the velocity of S‐waves and strain measurements are sensitive to dilatancy which appears later in the damage process of the limestone studied.

Removal of overburden velocity anomaly effects for depth conversion
Authors T. Armstrong, J. McAteer and P. ConnollyA method of compensating for the presence of discrete overburden velocity anomalies during depth conversion of time horizons interpreted on conventional, post‐stack time‐migrated seismic data is presented. Positive and negative time delays are estimated either from the push‐down or pull‐up of reflectors directly beneath the anomalies or from interpreted time thickness of the anomalous body and interval velocities estimated from well data. The critical steps are pre‐stack simulation of seismic acquisition across the velocity anomalies, incorporating the effects of a Fresnel volume which changes its width as a function of depth, and simulation of common‐midpoint (CMP) stacking using a linear regression of time delay, Δt, versus offset‐squared, X^{2}. The time‐correction method predicts the time distortion for any target horizon and the distortion is removed as a correction in time. Depth conversion is then performed using a background velocity function. The final average velocity map is calculated from the resulting depth structure and the raw times at the target horizon. The method is implemented by manipulating time grids within an industry‐standard mapping package. The final average velocity map shows steep lateral velocity gradients which are constrained by the interpreted boundaries of the velocity anomalies.

Azimuth‐dependent AVO in reservoirs containing non‐orthogonal fracture sets
Authors Colin M. Sayers and Simon DeanAzimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. The symmetry of a rock with horizontal bedding that contains two or more non‐orthogonal sets of vertical fractures may be approximated as monoclinic with a horizontal plane of mirror symmetry. For offsets that are small compared with the depth of the reflector, the azimuthal variation in P‐wave AVO gradient for such a medium varies with azimuth as where φ is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. φ2 depends on both the normal compliance BN and the shear compliance BT of the fractures and may differ from zero if BNBT varies significantly between fracture sets. If BNBT is the same for all fractures, and the principal axes of the azimuthal variation in P‐wave AVO for fixed offset are determined by the polarization directions of a vertically propagating shear wave. At larger offsets, terms in and are required to describe the azimuthal variation in AVO accurately. φ4 and φ6 also depend on BNBT. For gas‐filled open fractures but a lower value of BNBT may result from the presence of a fluid with non‐zero bulk modulus.

Electromagnetic profiling interpretation across vertical faults and dikes
Authors Edson E.S. Sampaio and Carlos A. DiasWhen a vertical fault or dike scatters a normally incident TE‐mode plane wave, the horizontal components of the electric and the magnetic fields vary along the direction perpendicular to the strike. This scattering is also responsible for the formation of a vertical component of the magnetic field, which also varies along the direction perpendicular to the strike. Analysis of the lateral variations of the field components permits the identification of the type of geological structure, either fault or dike, as well as an estimate of the position of the geological contacts and the electrical conductivity of each medium. Previous exact analytical solutions have shown that two Fourier cosine integrals can express each field component. A series of functions specified for each model represent the kernel of each integral. From the field components obtained from the first non‐zero term of each series, we calculated the following functions: the dip angle and the ellipticity of the vertical polarization ellipse in a plane perpendicular to the strike of the structure, and the azimuth and the ellipticity of the horizontal ellipse. We established master‐curves of these functions for the interpretation of vertical faults and dikes for the polarization ellipsoid, for instance VLF or audio‐frequency methods. This representation has as variable the induction number , and as parameters σ2/σ1 and , where a denotes the half‐thickness of the dike. The interpretation procedure using curve fitting is possible because the induction number is represented on a logarithmic scale. This procedure represents an important step before automatic interpretation is carried out. Two case histories using field data illustrate the effectiveness of the procedure and the type of quantitative interpretation obtained from it.

Preliminary laboratory investigations into the attenuation of compressional and shear waves on near‐surface marine sediments
Authors Arthur Ayres and Friedrich TheilenThe attenuation of compressional and shear waves (Qp and Qs) has been studied by several authors but most of these investigations were performed on deep buried reservoir sandstones in order to distinguish between gas and condensate reservoirs and water‐saturated sandstones. We present a preliminary investigation into the use of seismic wave attenuation as a measure of the geotechnical parameters of the near‐surface marine sediments, a little‐studied geological setting. A 6.9 m‐long gravity core was taken from the continental slope of the Barents Sea at a water depth of 2227 m. The core was primarily composed of brown to olive‐grey clayey mud, having a high content of foraminifers and being locally bioturbated. The values of Qp and Qs were determined using the rise‐time method at 19 and 18 different points of the core, respectively, and they were correlated with geotechnical parameters such as wet bulk density, porosity, water content, shear strength and C/P ratio (the ratio of shear strength to overburden pressure). The calculated correlation coefficients for all correlations ranged from −0.39 to 0.41, suggesting that the attenuation characteristics of seismic waves could not be used to derive geotechnical parameters of marine sediments. However, with such a small data set it is difficult to determine clearly whether attenuation is primarily a frequency‐dependent parameter and consequently not related to sediment properties, or whether the limited number of data points is the main factor responsible for the low correlation coefficients observed. Moreover, several different methods are available for the computation of the quality factor Q, and the rise‐time method may not be the most appropriate means of determining the attenuation on near‐surface marine sediments.

The effect of clay distribution on the elastic properties of sandstones
Authors Mark S. Sams and Martijn AndreaThe shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.

Self‐potential anomalies in Cerro de Pasco and Hualgayoc areas (Peru) revisited
Authors D.S. Vagshal and S.D. BelyaevSelf‐potential anomalies with unexplained high values have been observed in various places. Such anomalies were reported in Peru more than 30 years ago. An explanation is proposed based on the electrokinetic effect obtained when a topographic high occurs above a rock layer through which water filtrates and which itself lies over a highly resistive layer. In such a case a fairly high self‐potential may occur. Conversely, when one of these conditions is not met, the self‐potential anomaly at the earth's surface resulting from the electrokinetic effect is strongly attenuated.

Short note: Applications of third‐order statistics for the automatic time picking of seismic events
Authors Karthik Srinivasan and Luc T. IkelleWe present a new automatic time‐picking method based on third‐order statistics, namely bicoherence correlation. Contrary to conventional methods, which are based on second‐order statistics (i.e. cross‐correlation or neural‐network trainings), our method is less sensitive to coloured noise as well as the bandwidth of the signal. Bicoherence correlation can also be used for autotracking events in seismic data for an interpretation.

Short note: Source geometry identification by simultaneous use of structural index and shape factor
More LessA cross‐plot of the shape factors and the structural indices, determined from gravity anomalies over various idealized sources, namely horizontal/vertical lines and vertical ribbons with various strike lengths and depth extents, forms a closed loop. Different segments of this loop, termed the source geometry identification loop (SGIL), correspond to different source geometries. Combined use of the structural index and the shape factor determined from an isolated gravity anomaly reduces the ambiguity in characterizing the source geometry. A simulated example and three field examples, namely a Cuban chromite anomaly, an Indian example over manganese ore and a sulphide ore from Quebec, have been analysed by the proposed method in order to identify their respective source geometries.
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