Showing papers in "Geophysical Prospecting in 2001"

Improved amplitude preservation for prestack depth migration by inverse scattering theory

Abstract: A prestack reverse time-migration image is not properly scaled with increasing depth. The main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back-propagation of the measured data and the generation of the forward-modelled wavefields. This unscaled image can be enhanced by multiplying the inverse of the approximate Hessian appearing in the Gauss–Newton optimization technique. However, since the approximate Hessian is usually too expensive to compute for the general geological model, it can be used only for the simple background velocity model.We show that the pseudo-Hessian matrix can be used as a substitute for the approximate Hessian to enhance the faint images appearing at a later time in the 2D prestack reverse time-migration sections. We can construct the pseudo-Hessian matrix using the forward-modelled wavefields (which are used as virtual sources in the reverse time migration), by exploiting the uncorrelated structure of the forward-modelled wavefields and the impulse response function for the estimated diagonal of the approximate Hessian. Although it is also impossible to calculate directly the inverse of the pseudo-Hessian, when using the reciprocal of the pseudo-Hessian we can easily obtain the inverse of the pseudo-Hessian. As examples supporting our assertion, we present the results obtained by applying our method to 2D synthetic and real data collected on the Korean continental shelf.

Detection of potential fields source boundaries by enhanced horizontal derivative method

Abstract: A 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.

Constraints in 3D gravity inversion

Abstract: A three-dimensional (3D) inversion program is developed to interpret gravity data using a selection of constraints. This selection includes minimum distance, flatness, smoothness and compactness constraints, which can be combined using a Lagrangian formulation. A multigrid technique is also implemented to resolve separately large and short gravity wavelengths. The subsurface in the survey area is divided into rectangular prismatic blocks and the problem is solved by calculating the model parameters, i.e. the densities of each block. Weights are given to each block depending on depth, a priori information on density and the density range allowed for the region under investigation. The present computer code is tested on modelled data for a dipping dike and multiple bodies. Results combining different constraints and a weight depending on depth are shown for the dipping dike. The advantages and behaviour of each method are compared in the 3D reconstruction. Recovery of geometry (depth, size) and density distribution of the original model is dependent on the set of constraints used. From experimentation, the best combination of constraints for multiple bodies seems to be flatness and a minimum volume for the multiple bodies. The inversion method is tested on real gravity data from the Rouyn-Noranda (Quebec) mining camp. The 3D inversion model for the first 10 km is in agreement with the known major lithological contacts at the surface; it enables the determination of the geometry of plutons and intrusive rocks at depth.

Porosity and permeability prediction from wireline logs using artificial neural networks: a North Sea case study

Abstract: Estimations of porosity and permeability from well logs are important yet difficult tasks encountered in geophysical formation evaluation and reservoir engineering. Motivated by recent results of artificial neural network (ANN) modelling offshore eastern Canada, we have developed neural nets for converting well logs in the North Sea to porosity and permeability. We use two separate back-propagation ANNs (BP-ANNs) to model porosity and permeability. The porosity ANN is a simple three-layer network using sonic, density and resistivity logs for input. The permeability ANN is slightly more complex with four inputs (density, gamma ray, neutron porosity and sonic) and more neurons in the hidden layer to account for the increased complexity in the relationships. The networks, initially developed for basin-scale problems, perform sufficiently accurately to meet normal requirements in reservoir engineering when applied to Jurassic reservoirs in the Viking Graben area. The mean difference between the predicted porosity and helium porosity from core plugs is less than 0.01 fractional units. For the permeability network a mean difference of approximately 400 mD is mainly due to minor core-log depth mismatch in the heterogeneous parts of the reservoir and lack of adequate overburden corrections to the core permeability. A major advantage is that no a priori knowledge of the rock material and pore fluids is required. Real-time conversion based on measurements while drilling (MWD) is thus an obvious application.

Effective-medium theories for fluid-saturated materials with aligned cracks

Abstract: There is general agreement between different theories giving expressions for the overall properties of materials with dry, aligned cracks if the number density of cracks is small There is also very fair agreement for fluid-filled isolated cracks However, there are considerable differences between two separate theories for fluid-filled cracks with equant porosity Comparison with recently published experimental data on synthetic sandstones gives a good fit with theory for dry samples However, although the crack number density in the laboratory sample is such that first-order theory is unlikely to apply, expressions correct to second order (in the number density) provide a worse fit It also appears that the ratio of wavelength to crack size is not sufficiently great for any detailed comparison with effective-medium theories, which are valid only when this ratio is large The data show dispersion effects for dry cracks and scattering, neither of which will occur at sufficiently long wavelengths Data from the water-saturated samples indicate that the effect of equant porosity is significant, although the two theories differ strongly as to just how significant Once again, and in spite of the reservations mentioned above, a reasonable fit between theory and observation can be shown

Common-reflection-surface(CRS) stack for common offset.

Abstract: We provide a data-driven macro-model-independent stacking technique that migrates 2D prestack multicoverage data into a common-offset (CO) section. We call this new process the CO common-reflection-surface (CRS) stack. It can be viewed as the generalization of the zero-offset (ZO) CRS stack, by which 2D multicoverage data are stacked into a well-simulated ZO section. The CO CRS stack formula can be tailored to stack P-P, S-S reflections as well as P-S or S-P converted reflections. We point out some potential applications of the five kinematic data-derived attributes obtained by the CO CRS stack for each stack value. These include (i) the determination of the geometrical spreading factor for reflections, which plays an important role in the construction of the true-amplitude CO section, and (ii) the separation of the diffractions from reflection events. As a by-product of formulating the CO CRS stack formula, we have also derived a formula to perform a data-driven prestack time migration.

Inversion of DC resistivity data using neural networks

Abstract: The inversion of geoelectrical resistivity data is a difficult task due to its non-linear nature. In this work, the neural network (NN) approach is studied to solve both 1D and 2D resistivity inverse problems. The efficiency of a widespread, supervised training network, the back-propagation technique and its applicability to the resistivity problem, is investigated. Several NN paradigms have been tried on a basis of trial-and-error for two types of data set. In the 1D problem, the batch back-propagation paradigm was efficient while another paradigm, called resilient propagation, was used in the 2D problem. The network was trained with synthetic examples and tested on another set of synthetic data as well as on the field data. The neural network gave a result highly correlated with that of conventional serial algorithms. It proved to be a fast, accurate and objective method for depth and resistivity estimation of both 1D and 2D DC resistivity data. The main advantage of using NN for resistivity inversion is that once the network has been trained it can perform the inversion of any vertical electrical sounding data set very rapidly.

Implementing the fast marching eikonal solver: spherical versus Cartesian coordinates

Abstract: Spherical coordinates are a natural orthogonal system for describing wavefronts emanating from a point source. A regular grid distribution in the Cartesian-coordinate system tends to undersample the wavefront description near the source (at the highest wavefront curvature) and oversample it away from the source. Spherical coordinates, in general, provide a more balanced grid distribution for characterizing point-source wavefronts. Our numerical implementation confirms that the recently introduced fast marching algorithm is both a highly efficient and an unconditionally stable eikonal solver. However, its first-order approximation of traveltime derivatives can induce relatively large traveltime errors for waves propagating in a diagonal direction with respect to the coordinate system. Examples, including the IFP Marmousi and the SEG/EAGE 3D salt-dome models, show that a spherical-coordinate implementation of the method results in far fewer errors in traveltime calculation than the conventional Cartesian-coordinate implementation, and with practically no loss in computational advantages.

Detecting small-scale targets by the 2D inversion of two-sided three-electrode data: application to an archaeological survey

Abstract: The detecting capabilities of some electrical arrays for the estimation of position, sizeand depth of small-scale targets were examined in view of the results obtained from2D inversions of apparent-resistivity data. The two-sided three-electrode apparent-resistivity data are obtained by the application of left- and right-hand pole–dipolearrays that also permit the computation of four-electrode and dipole–dipoleapparent-resistivity values without actually measuring them. Synthetic apparent-resistivity data sets of the dipole–dipole, four-electrode and two-sided three-electrodearrays are calculated for models that simulate buried tombs. The results of two-dimensional inversions are compared with regard to the resolution in detecting theexact 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 archaeologicalsite 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 hasled to locating a part of the city wall and a buried small room. The validity of theinterpretation has been checked against the results of subsequent archaeologicalexcavations.INTRODUCTIONThe two-dimensional (2D) inversion of direct current (DC)sounding data has become a standard tool for the investiga-tion of targets buried at shallow and intermediate depths. Theapplications include archaeology, environmental and hydro-geological works, mining exploration and engineeringstudies. When using the traditional electrode arrays thedata acquisition is usually carried out by expanding electro-des along a measurement profile. The apparent-resistivitydata obtained from all soundings are then used as the input ofa 2D inversion algorithm. Pelton, Rijo and Swift (1978) andSasaki (1981) first introduced inversion algorithms applied tothe dipole–dipole and Schlumberger arrays, respectively.Later, Loke and Barker (1996) introduced a fast 2D inversionmethod for the Wenner and dipole–dipole electrode arrays.This algorithm is based on a quasi-Newton method whichcalculates an approximate value of partial derivatives of theapparent-resistivity data with respect to model parameters.The finite-difference technique is used for the computation ofthe model response.One of the remarkable developments in DC methods is theuse of modern measuring systems with multicore cableswhich allows automatic switching between electrodes. Forpractical field operations, the electrodes are located at equallyspaced measurement stations. For example, Morris, Ronningand Lile (1997) described a data acquisition system thatsimultaneously collects Schlumberger and two dipole–dipoledata. However, they did not indicate a quantitative inter-pretation tool. Acworth and Griffiths (1985) and Griffithsand Turnbull (1985) described Wenner tripotential apparent-resistivity measurements to reduce the number of ambiguitiesarising in the qualitative interpretation of apparent-resistivitypseudosections. The tripotential method produces threeapparent-resistivity measurements for each position of acollinear equispaced quadripole of electrodes. They used the

Three-dimensional imaging of subsurface structures using resistivity data

Abstract: We have developed a three-dimensional inverse scheme for carrying out DC resistivity surveys, incorporating complicated topography as well as arbitrary electrode arrays. The algorithm is based on the finite-element approximation to the forward problem, so that the effect of topographic variation on the resistivity data is effectively evaluated and incorporated in the inversion. Furthermore, we have enhanced the resolving power of the inversion using the active constraint balancing method. Numerical verifications show that a correct earth image can be derived even when complicated topographic variation exists. By inverting the real field data acquired at a site for an underground sewage disposal plant, we obtained a reasonable image of the subsurface structures, which correlates well with the surface geology and drill log data.

The effect of clay distribution on the elastic properties of sandstones

Abstract: The 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.

Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets

Abstract: Azimuthal 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 cos 2(o - o 2 ), where o is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. o 2 depends on both the normal compliance B N and the shear compliance B T of the fractures and may differ from zero if B N /B T varies significantly between fracture sets. If B N /B T is the same for all fractures, o 2 = 0 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 cos 4(o - o 4 ) and cos 6(o - o 6 ) are required to describe the azimuthal variation in AVO accurately. o 4 and o 6 also depend on B N /B T . For gas-filled open fractures B N /B T 1, but a lower value of B N /B T may result from the presence of a fluid with non-zero bulk modulus.

Hagedoorn's plus‐minus method: the beauty of simplicity

Abstract: This paper examines return migrants and new migrants to Montana: Who are they? Why do they move? Do return migrants move for different reasons than new migrants? Data from the 1994–1997 Montana Poll, a representative survey of Montana households, are used. A comparison of socio-economic differences of return and new migrants shows that the two migrant types are very similar in terms of education, income, and age. This stands in contrast to the findings of others who maintain that return migrants are negatively selected with respect to education. Logistic regressions were employed to identify the effect of age and place ties on reasons for moving. Return migrants and new migrants move to Montana for very similar reasons, with family being the most important primary reason for moving. Moving for lifestyle reasons, such as environmental quality and urban amenities, were found to systematically change with age. This could explain why people return to a place they left earlier in life. While other research on return migration compared return migrants and other migrants who left the same place of origin, this paper offers a comparison of return migrants and other migrants who seek out the same destination. Results from the Montana Poll suggest that the same destination attracts return migrants and new migrants with similar socio-economic characteristics who move there for very similar reasons.

Gravity probability tomography: a new tool for buried mass distribution imaging

Abstract: Following 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.

The 3D shear experiment over the Natih field in Oman: the effect of fracture‐filling fluids on shear propagation

Abstract: This is the final paper in a series on the 3D multicomponent seismic experiment in Oman. In this experiment a 3D data set was acquired using three-component geophones and with three source orientations. The data set will subsequently be referred to as the Natih 9C3D data set. We present, for the first time, evidence demonstrating that shear waves are sensitive to fluid type in fractured media. Two observations are examined from the Natih 9C3D data where regions of gas are characterized by slow shear-wave velocities. One is that the shear-wave splitting map of the Natih reservoir exhibits much larger splitting values over the gas cap on the reservoir. This increase in splitting results from a decrease in the slow shear-wave velocity which senses both the fractures and the fracture-filling fluid. Using a new effective-medium model, it was possible to generate a splitting map for the reservoir that is corrected for this fluid effect. Secondly, an anomaly was encountered on the shear-wave data directly above the reservoir. The thick Fiqa shale overburden exhibits a low shear-wave velocity anomaly that is accompanied by higher shear reflectivity and lower frequency content. No such effects are evident in the conventional P-wave data. This feature is interpreted as a gas chimney above the reservoir, a conclusion supported by both effective-medium modelling and the geology. With this new effective-medium model, we show that introduction of gas into vertically fractured rock appears to decrease the velocity of shear waves (S2), polarized perpendicular to the fracture orientation, whilst leaving the vertical compressional-wave velocity largely unaffected. This conclusion has direct implications for seismic methods in exploration, appraisal and development of fractured reservoirs and suggests that here we should be utilizing S-wave data, as well as the conventional P-wave data, as a direct hydrocarbon indicator.

Adaptation of prestack migration to multi-offset ground-penetrating radar (GPR) data

Abstract: In adapting the prestack migration technique used in seismic imaging to the inversion of ground-penetrating radar (GPR) from time- to depth-sections, we show that the theoretical integral formulation of the inversion can be applied to electromagnetic problems, albeit with three assumptions. The first two assumptions concern the electromagnetic characteristics of the medium, primarily that the medium must be perfectly resistive and non-dispersive, and the third concerns the antennae radiation pattern, which is taken to be 2D. The application of this adaptation of the inversion method is confirmed by migrating actual GPR measurements acquired on the test site of the Laboratoire Central des Ponts et Chaussees. The results show good agreement with the geometry of the structures in the medium and confirm that the possible departure from the assumption of a purely resistive medium has no visible effect on the information concerning the geometry of scattering and reflecting structures. The field experiments also show that prestack migration processing is sufficiently robust with regard to the assumption of a non-dispersive medium. The assumption of a 2D antennae radiation pattern, however, produces artefacts that could be significant for laterally heterogeneous media. Nevertheless, where the medium is not highly laterally heterogeneous, the migration gives a clear image of the scattering potential due to the geometry of structural contrasts in the medium; the scatterers are well focused from diffraction hyperbolae and well localized. Spatial geometry has limited dimensional accuracy and positions are located with a maximum error equal to the minimum wavelength of the signal bandpass. Objects smaller than one wavelength can nevertheless be detected and well focused if their dielectric contrasts are sufficiently high, as in the case of iron or water in gneiss gravels. Furthermore, the suitability of multi-offset protocols to estimate the electromagnetic propagating velocity and to decrease the non-coherent noise level of measurements is confirmed. Our velocity estimation is based on the semblance calculation of multi-offset migrated images, and we confirmed the relevance of this quantification method using numerical data. The signal-to-noise ratio is improved by summing multi-offset results after the addition of random noise on measurements. Thus the adaptation of prestack migration to multi-offset radar measurements significantly improves the resolution of the scattering potential of the medium. Limitations associated with the methods used here suggest that 3D algorithms should be applied to strongly laterally heterogeneous media and further studies concerning the waveform inversion are necessary to obtain information about the electric nature of the medium.

Seismic refraction, isotropic anisotropic seismic tomography on an ancient monument (Antonino and Faustina temple ad 141)

Abstract: This paper describes the results of using geophysical techniques to investigate three columns of the Pronaos of the Antonino and Faustina temple (AD 141) in Rome, Italy; the columns are of cipollino marble which shows alternate sequences of mica and calcite beds. We applied seismic refraction using traditional interpretation, and seismic transmission tomography. The comparison between the results of the refraction study and the 2D and 3D isotropic tomographic analyses suggested anisotropic characteristics for the marble, and this prompted us to perform a further tomographic experiment, taking into account these characteristics of the material. Assuming an elliptical model, the main directions of anisotropy were detected. Two velocity fields corresponding to the main directions of the anisotropy were measured and anomalies such as cracks and fractures were noted. The conjugate-gradient algorithm was used to invert the data. The results of the isotropic and anisotropic models were compared. The correlation between the methods highlighted the characteristics of the marble, i.e. anisotropy, depth of the weathering, fractures and small cracks. The results show that the material of the columns is in reasonable condition, with the exception of a surface area 6 cm to 15 cm deep that we estimate has been weathered for 2000 years, and that has been particularly affected by pollution in the last century.

Compressional-wave Q estimation from full-waveform sonic data

Abstract: There is significant evidence that the anelastic loss of seismic energy is linked to petrophysical properties such as porosity, permeability and clay content. Thus, reliable estimation of anelastic attenuation from seismic data can lead to improved methods for the prediction of petrophysical properties. This paper is concerned with methods for the estimation of attenuation at sonic frequencies (5-30 KHz) from in situ data. Two independent methods have been developed and tested for estimating compressional-wave attenuation from full-waveform sonic data. A well-established technique, the logarithm spectral ratio (LSR) method, is compared with a new technique, the instantaneous frequency (IF) method. The LSR method uses the whole spectrum of the seismic pulse whilst the IF method uses a carefully estimated value of instantaneous frequency which is representative of the centre frequency of the pulse. In the former case, attenuation estimation is based on the relative variation of amplitudes at different frequencies, whilst in the latter case it is based on the shift of the centre frequency of the pulse to lower values during anelastic wave propagation. The IF method does not assume frequency independence of Q which is a necessary assumption for the LSR method, and it provides a stable frequency log, the peak instantaneous frequency (PIF) log, which may be used as an indicator for attenuation under certain limitations. The development and implementation of the two methods is aimed at minimizing the effect of secondary arrivals, such as leaky modes, and involved a series of parameter tests. Testing of the two methods using full-waveform sonic data of variable quality, obtained from a gas-bearing sandstone reservoir, showed that the IF method is in general more stable and suitable for full-waveform sonic data compared with the LSR method. This was evident especially in data sets with high background noise levels and wave-interference effects. For good quality data, the two methods gave results that showed good agreement, whilst comparison with other log types further increased confidence in the results obtained. A significant decrease (approximately 5 KHz) in the PIF values was observed in the transition from an evaporite/shale sequence to the gas-bearing sandstone. Average Q values of 54 and 51 were obtained using good quality data from a test region within the gas-saturated sandstone reservoir, using the LSR and IF methods, respectively.

On removing the primary field from fixed‐wing time‐domain airborne electromagnetic data: some consequences for quantitative modelling, estimating bird position and detecting perfect conductors

Abstract: In the process of removing the primary field from fixed-wing time-domain airborne EM data, the response is decomposed into two parts, which are referred to here as the time-domain ‘in-phase’ and ‘quadrature’ components. The time-domain in-phase component is dominated by the primary field, which varies significantly as the transmitter–receiver separation changes. The time-domain quadrature component comes solely from the secondary response associated with currents induced in the ground and this is the component that has traditionally been used in the interpretation of data from fixed-wing towed-bird time-domain EM systems. In the off-time, the quadrature response is very similar to the total secondary response. However, there are large differences in the on-time and even some small differences in the off-time.One consequence of these differences is that when airborne EM data are to be interpreted using a synthetic mathematical model, the synthetic data calculated should also be the quadrature component. A second consequence relates to the time-domain in-phase component which is sometimes used to estimate the receiver-sensor (bird) position. The bird-position estimation process assumes there is no secondary field in the in-phase component. If the ground is resistive, the secondary contained in the in-phase component is small, so the bird-position estimate is accurate to about 30 cm, but in highly conductive areas the secondary contribution can be large and the position estimate can be out by as much as 5 m. A third consequence arises for highly conductive bodies, the response of which is predominantly in-phase. This means that any response from these types of body is lost in the component that has been removed in the primary-field extraction procedure. However, if the bird position is measured very accurately, the actual free-space primary field can be estimated. If this is then subtracted from the estimated primary (actually free-space primary plus secondary in-phase response), then the residual is the secondary in-phase response of the ground. Using this methodology, very conductive ore bodies could be detected. However, a sensitivity analysis shows that detection of a large vertically dipping very conductive body at 150 m depth would require that the bird position be measured to an accuracy of about 1.4 cm and the aircraft attitude to within about 0.01°. Such tolerances are very stringent and not easily attainable with current technology.

Finding the strike direction of fractures using GPR

Abstract: GPR reflection energy varies with antenna orientation relative to the strike and dip of the reflector. This directional dependence of GPR responses was investigated through numerical experiments and was used to estimate the azimuth of fractures and joints. Three antenna configurations were considered in this study: perpendicular-broadside (YY mode), parallel-broadside (XX mode) and cross-polarization (YX mode). The reflection energy in the cross-polarization mode shows a shape characteristic similar to the strike, regardless of the dip angle. Those in the other two modes show quite different amplitudes from the strike, depending on the dip angle. We have developed a strike-direction-finding scheme using data obtained from the three different modes for the same survey line. The azimuth angle of each reflector was displayed in colour on the GPR profile. This scheme was applied to a field survey at a granite quarry in southern Korea. The GPR profiles showed different images of the reflectors depending on the antenna configuration. The estimated azimuths of reflectors obtained using our scheme matched fairly well with those of known fractures and joints.

Depth migration of shot records in heterogeneous, transversely isotropic media using optimum explicit operators

Abstract: A space-frequency domain 2D depth-migration scheme is generalized for imaging in the presence of anisotropy. The anisotropy model used is that of a transversely isotropic (TI) medium with a symmetry axis that can be either vertical or tilted. In the proposed scheme the anisotropy is described in terms of Thomsen parameters; however, the scheme can accommodate a wide range of anisotropy rather than only weak anisotropy. Short spatial convolution operators are used to extrapolate the wavefields recursively in the space-frequency domain for both qP- and qSV-waves. The weighted least-squares method for designing isotropic optimum operators is extended to asymmetric optimum explicit extrapolation operators in the presence of TI media with a tilted symmetry axis. Additionally, an efficient weighted quadratic-programming design method is developed. The short spatial length of the derived operators makes it possible for the proposed scheme to handle lateral inhomogeneities. The performance of the operators, designed by combining the weighted least-squares and weighted quadratic-programming methods, is demonstrated by migration impulse responses of qP and qSV propagation modes for the weak and strong TI models with both vertical and tilted symmetry axes. Finally, a table driven shot-record depth-migration scheme is proposed, which is illustrated for finite-difference modelled shot records in TI media.

Vibroseis deconvolution: a comparison of cross-correlation and frequency-domain sweep deconvolution

Abstract: Ideally, traditional vibroseis processing produces a band-limited zero-phase Klauder wavelet through cross-correlation of the sweep with the recorded signal. An alternative wavelet processing method involves deconvolving the sweep from the recorded vibroseis trace. This deconvolution can be achieved through frequency-domain division. We compare and contrast the advantages and disadvantages of sweep deconvolution versus cross-correlation on synthetic and real data.

From the Hagedoorn imaging technique to Kirchhoff migration and inversion

Abstract: The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique – a ‘string construction’ or ‘ruler and compass’ method – for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave-equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle-dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two.

Removal of overburden velocity anomaly effects for depth conversion

Abstract: A 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 commonmidpoint (CMP) stacking using a linear regression of time delay, At, 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.

The seismic response to overpressure: a modelling study based on laboratory, well and seismic data

Abstract: We investigate the seismic detectability of an overpressured reservoir in the North Sea by computing synthetic seismograms for different pore-pressure conditions. The modelling procedure requires the construction of a geological model from seismic, well and laboratory data. Seismic inversion and AVO techniques are used to obtain the P-wave velocity with higher reliability than conventional velocity analysis. From laboratory experiments, we obtain the wave velocities of the reservoir units versus confining and pore pressures. Laboratory experiments yield an estimate of the relationship between wave velocities and effective pressure under in situ conditions. These measurements provide the basis for calibrating the pressure model. Overpressures are caused by different mechanisms. We do not consider processes such as gas generation and diagenesis, which imply changes in phase composition, but focus on the effects of pure pore-pressure variations. The results indicate that changes in pore pressure can be detected with seismic methods under circumstances such as those of moderately deep North Sea reservoirs.

Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators

Abstract: We present a numerical method of simulating seismic wave propagation on unstructured 2D grids. The algorithm is based on the velocity-stress formulation of the elastic wave equation and therefore uses a staggered grid approach. Unlike finite-element or spectral-element methods, which can also handle flexible unstructured grids, we use explicit differential operators for the calculation of spatial derivatives in each time step. As shown in previous work, three types of these operators are used, and their particular performance is analysed and compared with standard explicit finite-difference operators on regular quadratic and hexagonal grids. Our investigations are especially focused on the influence of grid irregularity, sampling rate (i.e. gridpoints per wavelength) and numerical anisotropy on the accuracy of numerical seismograms. The results obtained from the various methods are therefore compared with analytical solutions. The algorithm is then applied to a number of models that are difficult to handle using (quasi-)regular grid methods. Such alternative techniques may be useful in modelling the full wavefield of bodies with complex geometries (e.g. cylindrical bore-hole samples, 2D earth models) and, because of their local character, they are well suited for parallelization.

AVO investigations of shallow marine sediments

Abstract: Amplitude-variation-with-offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High-frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P- and S-wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40 degrees, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S-wave velocity on the reflection coefficient is small (especially for low S-wave velocities encountered at the sea-floor). Thus, it is difficult to extract the S-wave parameter from AVO trends. On the other hand, P-wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea-floor reflection in a common-midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential-quadratic programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P-wave velocity alpha = 1450 +/- 25 m/s, S-wave velocity beta = 90 +/- 35 m/s. density rho = 1220 +/- 45 kg/m(3), quality factor for P-wave Qp = 15 +/- 200, quality factor for S-wave Qs = 10 +/- 30. The inverted sediment physical properties for the boulder clay are: alpha = 1620 +/- 45 m/s, beta = 360 +/- 200 m/s, rho = 1380 +/- 85 kg/m(3), Qp = 790 +/- 660, Qs = 25 +/- 10.

On the effectiveness of 2D electrical inversion results: an agricultural case study

Abstract: Electrical resistivity tomography was used in Beauce (France) to assess the water extraction by corn plants (evapotranspiration). The acquired pseudosections show conductive anomalies under the plants. A 2D inversion of measurements led us to identify clear resistive features associated with the water losses under the corn-plant rows. New models have been calculated with two different 3D algorithms (finite-difference and moment-method) to take into account 3D structure of the ground and to confirm that periodic resistive features may generate shifted apparent-resistivity anomalies.

3D resistivity inversion using 2D measurements of the electric field

Abstract: Field 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.

Identification and classification of multiple reflections with self-organizing maps

Abstract: Artificial neural networks can be used effectively to identify and classify multiple events in a seismic data set. We use a specialized neural network, a self-organizing map (SOM), that tries to establish rules for the characterization of the physical problem. Selected seismic data attributes from CMP gathers are used as input patterns, such that the SOM arranges the data to form clusters in an abstract space. We show with synthetic and real data how the SOM can identify and classify primaries and multiples, and how it can classify the various types of multiple corresponding to a certain generating mechanism in the subsurface.