Geophysical Prospecting - Volume 57, Issue 4, 2009

The interpretation of potential and electromagnetic fields observed over 3D geological structures remains one of the most challenging problems of exploration geophysics. In this paper I present an overview of novel methods of inversion and imaging of gravity and electromagnetic data, which are based on new advances in the regularization theory related to the application of special stabilizing functionals, which allow the reconstruction of both smooth images of the underground geological structures and models with sharp geological boundaries. I demonstrate that sharp‐boundary geophysical inversion can improve the efficiency and resolution of the inverse problem solution. The methods are illustrated with synthetic and practical examples of the 3D inversion of potential and electromagnetic field data.

A complex aeromagnetic anomaly in Southern Apennines (Italy) is analysed and interpreted by a multiscale method based on the scaling function. We use multiscale methods allowing analysis of a potential field along ridges, which are lines defined by the position of the extrema of the field at the considered scales. The method developed and applied in this paper is based on the study of the scaling function of the total magnetic field. It allows recovering of source parameters such as depth and structural index. The studied area includes a Pleistocene volcanic structure (Mt. Vulture) whose intense dipolar anomaly is superimposed on a longer wavelength regional anomaly. The interpretation of ridges of the modulus of the analytic signal at different altitude ranges allows recognition of at least three distinct sources between about 5 km and 20 km depth. Their interpretation is discussed in light of borehole data and other geophysical constraints. A reasonable geological model for these sources indicates the presence of intrusions, probably linked to the past activity of Mt. Vulture.

We present a new method to estimate the direction of the magnetization vector of geological bodies based upon the correlation between the reduced‐to‐the‐pole field for tentative values of the magnetization direction and the total magnitude anomaly, obtained by a transform of the measured magnetic field. The reduced‐to‐the‐pole and the total magnitude anomaly are centred over the sources in the case of 2D anomalies or well‐centred in the case of compact 3D sources and have similar patterns for the same source. The method has several important advantages over similar transform‐correlation methods for estimation of the magnetization direction. It calculates only one transform for many tentative values of the magnetization direction. The method does not use derivatives of any order and relies on confident isolation of the target anomalies based on one of the compared transforms, the total magnitude anomaly. We studied the performance of the method on five 2.5D and compact 3D sources. We analysed possible inherent to the method errors, as well as errors due to interference from neighbouring sources. Finally, we estimated the magnetization‐vector direction of the main sources causing the magnetic field in the Burgas region and the adjoining southeast Bulgarian Black Sea shelf. The sources in the Black Sea shelf show prevalently reverse magnetization, while the sources on land have normal or reverse magnetization.

Evaluation of higher derivatives (gradients) of potential fields plays an important role in geophysical interpretation (qualitative and/or quantitative), as has been demonstrated in many approaches and methods. On the other hand, numerical evaluation of higher derivatives is an unstable process – it has the tendency to enlarge the noise content in the original data (to degrade the signal‐to‐noise ratio). One way to stabilize higher derivative evaluation is the utilization of the Tikhonov regularization. In the submitted contribution we present the derivation of the regularized derivative filter in the Fourier domain as a minimization task by means of using the classical calculus of variations. A very important part of the presented approach is the selection of the optimum regularization parameter – we are using the analysis of the C‐norm function (constructed from the difference between two adjacent solutions, obtained for different values of regularization parameter). We show the influence of regularized derivatives on the properties of the classical 3D Euler deconvolution algorithm and apply it to high‐sensitivity magnetometry data obtained from an unexploded ordnance detection survey. The solution obtained with regularized derivatives gives better focused depth‐estimates, which are closer to the real position of sources (verified by excavation of unexploded projectiles).

We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreauet al. in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal‐to‐noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.

The Euler deconvolution is the most popular technique used to interpret potential field data in terms of simple sources characterized by the value of the degree of homogeneity. A more recent technique, the continuous wavelet transform, allows the same kind of interpretation. The Euler deconvolution is usually applied to data at a constant level while the continuous wavelet transform is usually applied to the points belonging to lines (ridges) connecting the m‐order partial derivative modulus maxima of the upward‐continued field at different altitudes in the harmonic region. In this paper a new method is proposed that unifies the two techniques. The method consists of the application of Euler's equation to the ridges so that the equation assumes a reduced form. Along each ridge the ratio among the m‐order partial derivative of the field and its vertical partial derivative, for isolated source model, is a straight line whose slope and intercept allows the estimation of the source depth and degree of homogeneity. The method, strictly valid for single source model, has also been applied to the multisource case, where the presence of the interference among the field generated by each single source causes the path of the ratio to be no longer straight. The method in this case gives approximate solutions that are good estimations of the source depth and its degree of homogeneity only for a restricted range of altitudes, where the ratio is approximately linear and the source behaves as if it were isolated.

The way potential fields convey source information depends on the scale at which the field is analysed. In this sense a multiscale analysis is a useful method to study potential fields particularly when the main field contributions are caused by sources with different depths and extents. Our multiscale approach is built with a stable transformation, such as depth from extreme points. Its stability results from mixing, in a single operator, the wavenumber low‐pass behaviour of the upward continuation transformation of the field with the enhancement high‐pass properties of n‐order derivative transformations. So, the complex reciprocal interference of several field components may be efficiently faced at several scales of the analysis and the depth to the sources may be estimated together with the homogeneity degrees of the field. In order to estimate the source boundaries we use another multiscale method, the multiscale derivative analysis, which utilizes a generalized concept of horizontal derivative and produces a set of boundary maps at different scales. We show through synthetic examples and application to the gravity field of Southern Italy that this multiscale behaviour makes this technique quite different from other source boundary estimators.

The main result obtained by integrating multiscale derivative analysis with depth from extreme points is the retrieval of rather effective information of the field sources (horizontal boundaries, depth, structural index). This interpretative approach has been used along a specific transect for the analysis of the Bouguer anomaly field of Southern Apennines. It was set at such scales, so to emphasize either regional or local features along the transect. Two different classes of sources were individuated. The first one includes a broad, deep source with lateral size of 45∼50 km, at a depth of 13 km and having a 0.5 structural index. The second class includes several narrower sources located at shallowest depths, ranging from 3–6 km, with lateral size not larger than 5 km and structural indexes ranging from 1–1.5. Within a large‐scale geological framework, these results could help to outline the mean structural features at crustal depths.

The recently released gravity potential field development derived from the Gravity Recovery and Climate Experiment satellite allows an unprecedented opportunity to use the gravity field to make global comparisons of structures of geological interest. The spatial resolution of the gravity field is sufficiently good to map large‐scale or intracratonic and cratonic basins, as the areal extent of these basins is 0.5 × 10⁶ km² and greater. We present the gravity anomaly, Bouguer, geoid and terrain corrected geoid fields for a selection of nine large‐scale basins and show that the satellite‐derived field can be used to successfully identify distinctive structures of these basins, e.g., extinct rifts underlying the basins and generally the isostatic state. The studied basins are the Eastern Barents Sea, West Siberian, Tarim, Congo, Michigan, Amazon, Solimões, Parnaiba and Paranà basins. We complete the mapping of the gravity field with a description of the basins in terms of areal extension and depth, sedimentary age and presence and age of volcanism. Interpretation of the satellite gravity anomalies and considerations regarding the crustal thickness as known from seismic investigations, allows us to conclude that for the greater part of the basins there is evidence for high‐density material in the lower crust and/or upper mantle. This density anomaly is, at least partly, compensating for the low‐density sedimentary infill instead of the crustal thinning mechanism. For our selection of basins, crustal thickness variations and Moho topography cannot be considered as mechanisms of compensation of the sedimentary loading, which is a clear difference to well‐defined rift basins.

In this paper we show how marine controlled source electromagnetic data interpretation can be improved if the data are acquired with an expanded frequency spectrum. Especially in the case of targets located at a wide range of depths, both high‐ and low‐frequency data can provide useful information for improving the risk analysis associated with different prospects with variable size and depth. We discuss an application to a real data set acquired in deep water offshore Nigeria using two values of fundamental frequency: 0.05 Hz and 0.25 Hz. Both frequencies, together with higher frequency harmonics, have been used for multi‐frequency and multi‐dimensional modelling and inversion with excellent results.

At the end of the interpretation work, areas with different electric and magnetic anomalies were mapped and quantitatively interpreted in terms of resistivity distribution in the 3D space. Relatively high‐frequency data (0.25 Hz and the first two harmonics) were useful for constraining the shallowest part of the resistivity models, including the presence of thin resistive layers, such as the gas sand recognized in correspondence of the well previously drilled in the NW portion of the block.

Low‐frequency data (0.05 Hz) were useful for constraining the deepest portion of the models (from 2 km to 4 km below sea floor) and for characterizing the resistivity of the background.

From an exploration point of view, the whole workflow based on multi‐frequency data analysis of this electromagnetic data set was very useful for further de‐risking the different prospects previously individuated in the area using seismic information.

A thorough investigation of the role that the source velocity has in the spatial and temporal variation of the secondary electromagnetic energy scattered by the Earth is necessary because marine controlled‐source electromagnetic geophysical surveys employ moving sources. A first step towards this goal is the analysis, for this type of survey, of the difference of the measured value of the secondary electromagnetic energy between two systems: one with a moving source and the other with a fixed source. The model that suffices to stress this kinematic aspect is a vertical magnetic dipole moving at a constant speed along a horizontal line in a homogeneous medium separated from two homogeneous half‐spaces by horizontal boundaries both above and below the dipole. The results show that both the velocity and the relative displacement between the source and the medium may cause a measurable variation relative to the static condition. Therefore, it may be necessary to take them into account in geophysical interpretation and to adapt the concepts of time and frequency domain for electromagnetic systems with moving sources.

Data from a recently acquired sea‐bed logging deep‐water survey are analysed for resistive bodies at depths below mudline shallower than about 300 m. A model consistent with known methane hydrate properties is found to explain near‐offset structures over an offset scale of a few hundred metres observed in the data. The lateral near‐seabed resolution of the sea‐bed logging method was determined to less than 100 m for source frequencies of up to 10 Hz. The importance of accurate hydrate maps to improve data processing is demonstrated by placing synthetic reservoirs below hydrates and observing their effects on reference model processing. The phase is shown to be less perturbed by shallow resistors than the amplitude, which is an important quality control of standard anomaly maps. While patchy shallow resistors can generally be mapped with simple normalized magnitude‐versus‐offset and phase‐versus‐offset difference analyses, large area distributions of hydrates over kilometres are hard to distinguish from deeper structures using controlled‐source electromagnetic data only, short of conducting a full 3D inversion of a sufficiently large survey. Beyond, the study confirms the applicability of controlled‐source electromagnetic techniques in general to map shallow resistive structures for drilling hazards and possible future exploration of methane hydrates as an energy source.

The past few years have witnessed significant advances and unparalleled interest in gravity gradiometer instrument technology as well as new deployment scenarios for various applications. Gravity gradiometry is now routinely considered as a viable component for resource exploration activities as well as being deployed for global information gathering. Since the introduction of the torsion balance in the 1890s, it has been recognized that gravity gradient information is valuable – yet difficult and time‐consuming to obtain. The recent acceptance and routine use of airborne gravity gradiometry for exploration has inspired many new technology developments. This paper summarizes advances in gravity gradient sensor development and also looks at deployment scenarios and gradiometer systems that have been successfully fielded. With projected improved system performance on the horizon, new challenges will also come to the forefront. Included in these challenges are aspects of instrument and system intrinsic noise, vehicle dynamic noise, terrain noise, geologic noise and other noise sources. Each of these aspects is briefly reviewed herein and recommendations for improvements presented.

Airborne gravimetry is an important method for measuring gravity over large unsurveyed areas. This technology has been widely applied in Canada, Antarctica and Greenland to map the gravity fields of these regions and in recent years, in the oil industry. In 2005, two tests in the Italian area were performed by ENI in cooperation with the Politecnico di Milano and the Danish National Space Center. To the knowledge of the authors, these were the first experiments of this kind in Italy and were performed over the Ionian coasts of Calabria and the Maiella Mountains. The Calabria test field is characterized by strong gravity variations due to the geophysical and topographic structure of the area. The ground gravity coverage is also quite dense. It was thus possible to compare airborne gravity with the ground observed values in order to check the precision of the airborne gravimetry. The second campaign was performed in an unsurveyed area centred on the Maiella Mountains, thus filling the data gap of this zone. Comparisons with existing ground data were also carried out in this area.

After smoothing, the collected data have an accuracy of 2–3 mgal, as derived by cross‐over analysis. Moreover, the collocation method applied to compare and merge ground‐based and airborne data proved to be efficient and reliable. The standard deviation of the discrepancies between airborne data and collocation upward continued gravity is, in both cases, less than 8 mgal. In the Maiella test, the gravity field obtained by merging airborne and ground data using collocation also provides a more detailed description of the high‐frequency pattern of the geopotential field in this area.

Previous studies using commercial airborne electromagnetic equipment that is not optimized for marine surveying have demonstrated the use of airborne electromagnetic methods for measuring water depth and estimating sediment thickness. A new prototype helicopter time‐domain airborne electromagnetic system, SeaTEM(0), is now under development for bathymetric surveying. The first sea trial of the SeaTEM(0) system took place over Broken Bay, New South Wales, Australia, in shallow water up to ∼30 m in depth. Broken Bay was chosen because the separate paleodrainage systems for the Hawkesbury River, Brisbane Water and Pittwater, which join in Broken Bay give rise to paleovalleys infilled with unconsolidated sediments, ranging in thickness between 0 m (bedrock outcrop) and ∼200 m. The survey area also included a tombolo with a beach either side, which provided the opportunity to measure water depth through a surf zone. Sediment thickness and water depth is predicted from stitched layered‐earth inversion of data based on a simplified two‐layer model that represents seawater and sediment overlying a resistive half‐space basement (bedrock). The resulting bathymetric profiles show agreement typically to within ∼±1 m and ∼±0.5 m with known water depths in areas less than 20 and 6 m deep respectively. The inverted depth profile of the second (sediment) layer is noisy; however, the profiles reveal coarse topographic features of paleovalleys to depth limits of ∼60 to 80 m below sea level in 20 to 30 m water depth, as well as resolving bedrock ridges and exposed reefs in shallow waters.

We study the feasibility of the application of an indirect EM geothermometer, developed recently, to the temperature extrapolation in depth using magnetotelluric data collected in the seismically active northern Tien Shan faulted area (Bishkek Geodynamic Test Site, Kyrgyzstan) and Hengill geothermal zone (Iceland). The approach used is based on the artificial neural network technique, which does not imply the prior knowledge of the electrical conductivity mechanisms on the one hand and provides temperature estimates based on the analysis of the implicit conductivity‐temperature relations, on the other.

The samples for neuronet teaching consisted in the well temperature records and electrical conductivity values determined for the same depths from the magnetotelluric data measured in the vicinities of eight boreholes in each testing area. The testing of the taught neuronets was carried out using the temperature records not involved in the teaching process. The results indicate that the temperature extrapolation accuracy essentially depends on the ratio between the well length and the extrapolation depth. In particular, in extrapolation to a depth twice as large as the well depth the relative error is 5–6% and in case of threefold excess, the error is around 20%. This result makes it possible to increase significantly the depth of indirect temperature estimation in the Earth's interior (in particular, for geothermal exploration) based on the available temperature logs.

The practical application of an indirect electromagnetic geothermometer could provide the following facilities: 1) more exact temperature estimation in the extrapolation mode; 2) remote temperature estimates in the boreholes in areas characterized by extreme conditions for conventional geothermometers.

We discuss the correlation between the depth extent of magnetic sources, the Curie temperature depth and crustal structures on the mid‐Norwegian margin. Spectral methods can be used to estimate the depth extent of magnetic sources, even if the bottom is located in the lower crust, however, only with limited resolution. The bottom of the magnetic surfaces is often regarded to represent the depth to the Curie isotherm. However, comparison with a 3D model based on the interpretation of potential field and seismic reflection data and thermal modelling shows that the depth extent of the magnetic sources is merely controlled by the overall geometry of the crystalline crust and not the temperature distribution. The observed changes in the magnetic field between the inner and outer part of the mid‐Norwegian margin appears not to reflect, as previously assumed, the depth to the Curie temperature but the geometry of the basement and lower crust. Our 3D model of the mid‐Norwegian margin reveals a basement configuration that involves a basement with different petrophysical properties, which can be connected with lithological basement units of onshore Norway.

The founder of the Russian school of direct interpretation of potential fields (with minimal prior geological‐geophysical information) was V.M. Berezkin, who introduced the operator of total normalized gradient for the 2D interpretation of profile gravity data sets. This operator was successfully applied in searches of hydrocarbon reservoirs. The further development of this approach (the so‐called quasi‐singular points method) has allowed solution also to various structural problems, using mathematical criteria for the transition from extremes of total normalized gradient fields to coordinates of anomalous sources. The main numerical evaluation strategy is based on stabilized downward continuation of field derivatives and specific use of the filtration properties of Fourier series approximation. The characteristic properties of the quasi‐singular points method are: 1) presentation of a more general total normalized gradient function through additional parameters (derivative order m, form of smoothing function Q, number of Fourier coefficients N* with maximal N), optimum values being chosen during a peak‐spectrum analysis of the interpreted function; 2) calculation of the set of total normalized gradient fields for various values of N*/N, representing coordinate systems {x,N*/N} as an ‘axes tree’ of extrema, where each 2D total normalized gradient field is representationally compressed in a 1D line, permitting a) immediate overview of the positions of the axes in all variants of the calculated fields and b) reduction of the retained information, as required in subsequent interpretation; 3) development of two criteria for transition from extrema of total normalized gradient fields to the coordinates of anomaly sources. The quasi‐singular points method is intended for tracing limiting gently‐sloping boundaries, if their micro‐relief features are sources of the interpreted anomaly but sub‐vertical contacts may also be traced. The method has been tested in delineating various geological structures. One of the most challenging, successfully achieved, was tracing of the Moho discontinuity and study of the upper mantle, using only Bouguer anomaly data along interpretation profiles. This is attested in an example of two regional profiles intersecting the European part of Russia. The central part of one of them coincides with the results from a deep seismic profile.

The differential similarity transform of a magnetic anomaly is a linear combination of its intensity and gradient components. This transform is sensitive to the distance between a chosen central point of similarity and the source and depends on the degree of homogeneity of the field. Taking advantage of this property, a new field inversion method resulting in the evaluation of source position and shape type is proposed and implemented. The field gradient components are measured directly in magnetic gradiometry, or they can be calculated from the measured field data. Regional and local linear backgrounds are accounted for by the method. The method can be applied on either regularly or irregularly‐spaced data sets, on even or uneven surfaces of observation. The solving of the systems of equations is not necessary. A semi‐automated inversion for both location and shape of the sources is implemented. Model and field tests illustrate the effectiveness of the proposed inversion technique for depth and shape estimates.

Detailed gravity measurements integrated with geological data were computed to constrain the mechanisms that were active during the emplacement of the Triassic evaporite‐bearing folds of Jebel Cheid from the salt‐dome zone in the Atlassic region. The gravity analysis consists in mapping the contrasting gravity responses: complete Bouguer anomaly, residual anomaly and derivative maps; the main results display a positive amplitude gravity anomaly as the response of Triassic evaporite bodies and important NE–SW‐trending features at the boundaries between the Triassic outcrops and their enveloping strata. In contrast with gravity calculations of a salt dome structure usually resulting in negative gravity anomaly models, the Jebel Cheid clearly expresses a positive gravity anomaly; furthermore, this result is supported by synthetic gravity interpretation.