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Dispersion is an important effect contributing to attenuating ground-penetrating radar (GPR) signals and must be incorporated in wave propagation. The constant-[Formula: see text] model (quality factor [Formula: see text]) is valid in rocks for typical GPR frequency ranges. In time-domain wave modeling, to simulate a constant-[Formula: see text] medium, using multiple Debye poles, the number of poles and their parameters must be previously estimated to honor target values for [Formula: see text] and velocity in the demanded frequency band. For electromagnetic waves, this problem is usually formulated as a highly nonlinear optimization problem presenting several solutions, which is solved using global optimization methods. An efficient linear approach to estimate multiple Debye poles to simulate constant-[Formula: see text] media for GPR data is presented. The resulting inverse problem is easy to solve because the number of poles is relatively small. The approach allows for a novel rescaled solution that depends only on the frequency band and number of poles. Solutions satisfying specific target values for velocity and [Formula: see text] are obtained from the rescaled solution by multiplying this solution by a proportionality factor that depends only on the target values. Choosing the number of poles is done so that velocity [Formula: see text] and [Formula: see text] curves, as a function of frequency [Formula: see text], are approximately invariant in the specified frequency band. Using the criterion that [Formula: see text] and [Formula: see text] curves must present maximum percentage deviations from the respective target values smaller than 5%, we find that, for the 200 MHz antenna, whose useful frequency band is 50–800 MHz, only three poles are sufficient. The theory is validated by modeling dispersion effects using synthetic models. The importance of introducing dispersion effects is illustrated by presenting a trial-and-error modeling approach to approximately reproduce a 200 MHz radargram acquired in fractured and karstified carbonate rocks.

Severe limitations of the standard Euler deconvolution to outline source shapes have been pointed out. However, Euler deconvolution has been widely employed on field data to outline interfaces, as faults and thrust zones. We investigate the limitations of the 3D Euler deconvolution–derived estimates of source dip and volume with the use of reduced‐to‐the‐pole synthetic and field anomalies. The synthetic anomalies are generated by two types of source bodies: (1) uniformly magnetized prisms, presenting either smooth or rough interfaces, and (2) bodies presenting smooth delimiting interfaces but strong internal variation of magnetization intensity. The dip of the first type of body might be estimated from the Euler deconvolution solution cluster if the ratio between the depth to the top and vertical extent is relatively high (>1/4). For the second type of body, besides dip, the source volume can be approximately delimited from the solution cluster envelope, regardless of the referred ratio. We apply Euler deconvolution to two field anomalies which are caused by a curved‐shape thrust zone and by a banded iron formation. These anomalies are chosen because they share characteristics with the two types of synthetic bodies. For the thrust zone, the obtained Euler deconvolution solutions show spatial distribution allowing to estimate a source dip that is consistent with the surface geology data, even if the above‐mentioned ratio is much less than 1/4. Thus, there are other factors, such as a heterogeneous magnetization, which might be controlling the vertical spreading of the Euler deconvolution solutions in the thrust zone. On the other hand, for the iron‐ore formation, the solution cluster spreads out occupying a volume, in accordance with the results obtained with the synthetic sources having internal variation of magnetization intensity. As conclusion, although Euler deconvolution–derived solutions cannot offer accurate estimates of source shapes, they might provide a sufficient degree of reliability in the initial estimates of the source dip and volume, which may be useful in a later phase of more accurate modelling.

Obtaining high‐quality ground penetrating radar (GPR) images in karst is difficult because materials resulting from the weathering of carbonate rocks might be electrically conductive. As a consequence, penetration depth and signal resolution might be greatly reduced due to attenuation. In addition, fractures and faults might cause a significant amount of electromagnetic wave scattering. We present a 2D data processing flow which allows improving the quality of GPR images in carbonate karst. The processing flow is composed of the following steps: obtaining a zero‐offset section by removing the direct wave, low‐frequency noise removal, geometrical spreading and exponential gain compensation, spectral balancing, Kirchhoff migration, bandpass filtering, amplitude‐volume enhancement, and topographic correction. For a 200‐MHz dataset, we present in detail each step of the processing flow, exemplifying how to parameterize every step. Spectral balancing is of key importance because it can approximately replenish the high‐frequency content lost due to propagation effects. In this step, we recommend to shift the centroid frequency as much as possible to high‐frequency values, even exceeding the nominal value of the antenna center frequency, but still looking for a band‐limited spectrum as the goal. Despite the difficulty of migrating GPR data, we show that migration (even assuming a constant velocity) might enhance the lateral continuity of the reflection events and allows identification of discontinuities such as faults and fractures. If imaged in a better way, these structures can have special importance as they are often the boundaries of dissolution features. Obtaining images based on amplitude‐volume enhancement techniques allows to better visualize karst voids and deep‐rooted discontinuities because these features are often associated with low‐amplitude zones, which are highlighted in such images. Due to this processing flow, stratigraphic, structural and dissolution features can be enhanced, allowing the interpreter to establish spatial and genetic associations among these elements to obtain a better understanding of the karst formation process.

Most of the approaches designed to avoid cycle skipping in full-waveform inversion (FWI) involve calculating a sequence of inversions in a multiscale fashion. We have adopted an alternative strategy, which is inverting a sequence of different misfit functions in the time domain. This is an implicit multiscale approach in the sense that the used misfit functions are sensitive to different wavelengths, but all of the inversion steps use the same modeling algorithm and the same model grid. In the first and third inversion steps, the transmitted (early arrivals) and reflected (late arrivals) components of the wavefield envelopes are respectively fitted. The second step promotes a smooth transition between the first and third steps, by using the envelope of the complete waveform. Because fitting just the envelope of the reflected waves has a minor effect on the misfit function of the whole data set, the phases of the reflected waves are mostly fitted in the fourth step, which is based on the waveform misfit function preserving only the late arrivals. The third and fourth steps are of crucial importance to fit the reflected events. We test the sequential inversion approach with the Marmousi model using data sets with different frequencies, obtaining better estimates of the velocity field than those obtained with the classic FWI. The solutions obtained with classic FWI and sequential inversion approach degrade with a progressively higher peak frequency data set, but the classic FWI solution degrades more rapidly.

We have developed an inversion approach based on particle swarm optimization (PSO) for 2D direct current resistivity data. Once the PSO algorithm is implemented, cost-function changes on constraints and misfit criteria can be easily performed and an approximate invariance of the Lagrange multipliers is obtained if each term of the cost function is properly normalized. More importantly, the interpreter can divide the mesh into partitions and apply a different constraint or combination of constraints in each partition. We explore several restrictions on the log-resistivity variation, either in single or in joint versions, including spatial continuity constraints in the [Formula: see text]-and [Formula: see text]-norms, total variation, sparsity constraints using the discrete cosine transform and Daubechies bases, and minimum moment of inertia constraints to impose concentration of resistive or conductive materials along target axes. In the latter case, the earth surface might be used also as a target axis. In addition, the final state of the PSO algorithm, once a stopping condition has been reached, contains not only the best solution but also a cluster of good suboptimal solutions that can be used for uncertainty analysis. As a result, the interpreter has the flexibility to perform an interpretation process based on a feedback trial-and-error inversion approach, in a similar manner that he/she has when using a friendly forward modeling software. The interpreter can then drive the tentative solutions obtained along the inversion process to incorporate their conceptions about the geologic environment, besides appraising misfit and stability of the solutions. We evaluate synthetic and field data examples. In the first case, we determine how the interpreter can drive the inversion process in a karst environment to image dissolution features. In the second case, we explore a similar situation aiming to optimize borehole locations in fracture zones in crystalline rocks.

Structural inheritance control of oceanic fracture zone formation by a large basement shear zone during continental breakup is still a matter of debate. In this research, we investigated the reactivation of Precambrian shear zones and their role in the formation of the Ascension and Fernando Poo fracture zones during the evolution of the South Atlantic Ocean. We used aeromagnetic and multichannel 2D seismic reflection data associated with previous geological and geophysical data to analyze how the Precambrian shear zones may have influenced the formation of oceanic fracture zones. Our results suggest that the fracture zones are extensions of the shear zones in the transition between continental and oceanic crust. The Sao Miguel do Aleixo and Pernambuco shear zones were reactivated during the Pangea breakup and acted as zones of weakness controlling the location of the Ascension and Fernando Poo fracture zones during the process of oceanic crust spreading. Our model suggests that the formation of these fracture zones influenced by the shear zones occurred in the early stages of ocean opening. It indicates that the fracture zones that formed in the late opening stages were related to the thermal subsidence stage, as suggested in previous studies.

In passive continental margins, the brittle reactivation of shear zones and their role in the deformation and deposition of sedimentary basins are still a matter of debate. In this research, we investigated the role of the brittle reactivation of Precambrian shear zones in the nucleation of rift and postrift faults in the onshore portion of the Sergipe-Alagoas and Pernambuco basins in northeastern Brazil. We combine and interpret a dataset of aeromagnetic and topographic data, associated with reflection seismic and borehole data, to analyze the evolution of a portion of the Atlantic continental margin of Brazil. Our results indicate that in the crystalline basement, the magnetic lineaments are correlated with ductile structures as shear zones, and the continuity of these lineaments in the Sergipe-Alagoas and Pernambuco basins is interpreted as the shear zones below the sedimentary cover of these basins. We document the following phases of the brittle reactivation of basement shear zones: (1) the opening of the South Atlantic Ocean in the Early Cretaceous under an extensional stress regime and (2) tectonic inversion induced by the Mid-Atlantic Ridge push and the Andean Cordillera rise in the Neogene-Quaternary under a predominantly strike-slip stress regime. During the rift phase, the brittle reactivation of the shear zones controlled the locations and architectures of the rifts. These structures acted as zones of weakness and were reactivated as normal faults. The brittle reactivation of shear zones was still active during the postrift phase and was responsible for the development of compressional structures. The reverse faulting and related folding pattern indicate tectonic inversion in the Late Cretaceous-Cenozoic. The structures formed during the postrift phase under a strike-slip regime are consistent with the present-day stress field, indicating that tectonic inversion is an active phase of the Brazilian margin.

One-dimensional forward modeling in direct current (DC) resistivity is actually computationally inexpensive, allowing the use of global optimization methods (GOMs) to solve 1.5D inverse problems with flexibility in constraint incorporation. GOMs can support computational environments for quantitative interpretation in which the comparison of solutions incorporating different constraints is a way to infer characteristics of the actual subsurface resistivity distribution. To this end, the chosen GOM must be robust to changes in the cost function and also be computationally efficient. The performance of the classic versions of the simulated annealing (SA), genetic algorithm (GA), and particle swarm optimization (PSO) methods for solving the 1.5D DC resistivity inverse problem is here compared using synthetic and field data. The main results are as follows: (1) All methods reproduce synthetic models quite well, (2) PSO and GA are comparatively more robust to changes in the cost function than SA, (3) PSO first and GA second present the best computational performances, requiring less forwarding modeling than SA, and (4) GA gives higher performance than PSO and SA with respect to the final attained value of the cost function and its standard deviation. From our experience, to put them into effective operation, the methods can be classified from easy to difficult in the order PSO, GA, and SA as a consequence of robustness to changes in the cost function and of the underlying simplicity of the associated equations. To exemplify a quantitative interpretation using GOMs, we compare solutions with least-absolute and least-squares norms of the discrepancies derived from the lateral continuity constraints of the log-resistivity and layer depth as a manner of detecting faults. GOMs additionally provide the important benefit of furnishing not only the best solution but also a set of suboptimal quasisolutions from which uncertainty analyses can be performed.

The Borborema Province BP (NE Brazil) consists of a complex rock mosaic composed mainly by Proterozoic metasedimentary belts that amalgamate Archean-to-Paleoproterozoic gneiss-migmatite complexes. It is a key region to understand the West Gondwana amalgamation, during the Pan-African/Brasiliano orogeny because it is an important portion of the orogen located between the Sao Francisco-Congo and West African cratons. We present the deep-rooted crustal framework of the BP interpreting the lateral contrasts of density and magnetization using the first available regional coverage of gravity and aeromagnetic data. The external boundaries of the BP having deep-rooted crustal significance are the Transbrasiliano shear zone, to the west, and the limit with the Sao Francisco craton, to the south. The latter limit is marked by a gravity anomaly which is the typical gravity signature of collisional sutures. Inside the BP crustal block, the Pernambuco, Patos, and Jaguaribe shear zones are identified as the major structures, based on termination and/or truncation criteria of geophysical anomalies. The three shear zones correspond to geophysical lineaments which conform with the Transbrasiliano shear zone, forming a single splay that opens to the northeast/east direction. The external boundaries and major shear zones divide the BP crustal block into four internal major domains of contrasting geophysical characteristics, namely the Southern, Transversal Zone, Rio Grande do Norte, and Ceara geophysical domains in analogy with the division based on surface geology. However, compared with the delimitations based on surface geology, there are three differences: the Medio Coreau belt is not positioned over the BP crustal block, a portion of the Parnaiba basin baseament should be included in the BP crustal block, and the basement beneath the folded-and-thrusted metasedimentary rocks of the Casa Nova Group (which form the nappes of the Riacho do Pontal belt) is part of the Sao Francisco craton crustal block. A subdivision of each major domain is also presented. Of special relevance is a pattern of alternate-polarity, quasi-parallel aligned geophysical anomalies present in the Transversal Zone domain, suggesting a clear alternation of high-density/high-susceptibility with low-density/low-susceptibility deep-rooted crustal subdomains. This geophysical pattern is compatible with a tectonic model of terrane collage.

Additional information regarding the continuity and resolution of selected seismic reflectors in reverse time migration (RTM) images can be beneficial for seismic interpretation. We have developed and evaluated new imaging conditions for RTM based on the phase coherence between the forward- and backward-propagated wavefields. These imaging conditions make use of the instantaneous phase and envelope of the analytical signals of the source and receiver wavefields, in addition to their real parts. Once the analytical wavefields are available, these imaging conditions can be calculated simultaneously with conventional conditions at little or no extra cost. The availability of these fields at each image point enables several alternative ways to define imaging conditions. We explore, in addition to pure phase crosscorrelation (PC), two approaches of amplitude-weighted PC. Our numerical experiments, imaging synthetic and field data sets, indicate that these new imaging conditions provide additional images that can highlight some weak reflectors by locally improving the resolution of RTM images. In our examples, this happens particularly in the deep portions of the seismic images. In addition, reflection events produced at discontinuities are enhanced as sharp signals, suggesting that the proposed imaging conditions can help to delineate stratigraphic and structural features that are harder to see in conventional images. These properties of the PC imaging conditions make them an interesting tool to provide additional information that can aid seismic interpretation in complex structural settings. © 2018 Society of Exploration Geophysicists., We thank CNPq for the financial support through the Instituto Nacional de Ciências e Tecnologia em Geofísica do Petróleo (INCT-GP). J. C. Costa, W. E. Medeiros, and J. Schleicher also thank CNPq for the research fellowships and associated grants. M. Schimmel thanks the Science without Borders Program for his PVE grant and Misterios project (CGL2013-48601-C2-1-R).

We investigate the role of reactivation of Precambrian basement fabric in the tectono-sedimentary and geomorphological evolution of the Paraiba Basin, continental margin of northeastern Brazil, during the Cretaceous, Neogene, and Quaternary. This basin represents part of the last bridge between South America and Africa before the last breakup stage of the South Atlantic rifting in the early Cretaceous. The Paraiba Basin infill is composed of siliciclastic and carbonate Cretaceous units, as well as aeolian, fluvial and marine Quaternary units. We used shuttle radar imagery, aeromagnetic, wellbore and field data. The reduced-to-the-pole magnetic map (RTP) indicates the continuity of the steeply dipping Precambrian basement shear zones beneath the Paraiba Basin. The combined analysis of surface and subsurface data shows that NE–SW and E–W-striking shear zones were subjected to brittle reactivation in the Aptian–Middle Albian during the basin opening and again in the Neogene–Quaternary, forming a system of horsts and grabens along the basin; some of these structures such as the E–W-oriented Pernambuco shear zone present modern-day seismicity. N–S- and mainly NW–SE-striking transfer faults cut across Aptian–Middle Albian to Neogene–Quaternary strata. These four main fault directions control main river channels and alluvial valleys up to 2 km wide. Topographic breaks up to 50 m were created by late reactivation of rift faults, which mark the boundary between horsts and grabens along the basin. In addition, structural data evidence syn-tectonic faulting with vertical offsets up to 80 m in the Cretaceous and up to 70 m in the Neogene–Quaternary. We conclude that shear zones across the study area are long-lived structures that have behaved as weakness zones. Their neotectonic brittle reactivation has controlled sediment deposition and landform development, which continued through the Neogene–Quaternary.

Global, full-fit plate reconstruction models predict a significant presence of oceanic floor in Northeast Brazil and West Africa during Albian time, while rifting was under earlier stages in the Pernambuco and Paraiba basins. We call it the Albian breakaway gap. Sedimentary, biostratigraphic and geochronological data from the Pernambuco and Paraiba basins challenge the timing of sea floor spreading in this region. In the onshore Pernambuco Basin, there are abundant outcrops of syn-rift continental siliciclastic rocks of Aptian–Albian age interbedded with intrusive and extrusive magmatic rocks (dated ca. 102 ± 2 Ma). Salt has been recognized on seismic data within the Pernambuco Basin, but there is no record or seismic indication of salt within the Paraiba Basin. Three interpreted seismic transects provide important clues about the type of intraplate margin developed in this region. Syn and post-rift magmatism within the onshore and offshore segments of the Pernambuco Basin indicate significant melt production during (and after) the main stretching phase. On the other hand, the abruptly-necked Paraiba Basin displays seismic evidence of seaward dipping reflectors, side by side with rift sediments, suggesting the development of an Albian volcanic intraplate margin. In addition, gravity and magnetic data, on the Brazilian side, suggest a wide transition from continental to pure oceanic crust in the Pernambuco and Paraiba basins, as well as at their African counterparts: Douala, Rio Del Rey, and Lower Benue, where either oceanic crust or proto-oceanic wide crust has been recognized. Instead of pure oceanic crust, as predicted by globally balanced plate motion reconstructions, the continent-ocean transitional domain was composed in part by stretched continental crust and partially by a wide embryonic or proto-oceanic crust. In fact, a continuous and regional mid ocean ridge was only defined at the end of Albian/early Cenomanian when the South America plate was completely separated from the African plate.

We have developed a new method for the approximate mapping of subsurface resistivity based on a geostatistical approach. We have used the characteristic points (CPs) of a resistivity sounding, which are their inflection and extreme (maximum and minimum) points. The methodology consists of five stages: (1) smoothing the geoelectric soundings to assure stability in the presence of measurement errors, (2) identifying the CPs in the smoothed versions of the geoelectric soundings, (3) obtaining subsurface sparse point resistivity estimates for the subsurface resistivity from the CPs, using empirical relationships between electrode spacing and penetration depth, (4) calculating semivariograms using the subsurface sparse point resistivity estimates, and fitting them with semivariogram models, and, finally, (5) estimating the subsurface resistivity distribution by kriging interpolation of the sparse point estimates. No explicit assumption is made about the true subsurface resistivity and, as result, the method can be applied to models of any dimension, given that the empirical rule for the penetration depth is approximately valid. Computationally, the method is very fast because no numerical modeling (either direct or inverse) is demanded and the most intensive computer operation is just a kriging interpolation. Given its independence of the model dimension and stability in the presence of measurement errors, the method can be readily implemented as a fast automatic method of interpretation. As result, the best scenario to apply the method is the initial treatment of large data sets. The methodology was developed, with synthetic and field data, using direct current (DC) resistivity soundings obtained with the Schlumberger array. The proposed method might be generalized for other DC-resistivity arrays and electromagnetic techniques based on resistivity soundings.

The key aspect limiting resolution in crosswell traveltime tomography is illumination, a well-known result but not well-exemplified. We have revisited resolution in the 2D case using a simple geometric approach based on the angular aperture distribution and the Radon transform properties. We have analytically found that if an isolated interface had dips contained in the angular aperture limits, it could be reconstructed using just one particular projection. By inversion of synthetic data, we found that a slowness field could be approximately reconstructed from a set of projections if the interfaces delimiting the slowness field had dips contained in the available angular apertures. On the one hand, isolated artifacts might be present when the dip is near the illumination limit. On the other hand, in the inverse sense, if an interface is interpretable from a tomogram, there is no guarantee that it corresponds to a true interface. Similarly, if a body is present in the interwell region, it is diffusely imaged, but its interfaces, particularly vertical edges, cannot be resolved and additional artifacts might be present. Again, in the inverse sense, there is no guarantee that an isolated anomaly corresponds to a true anomalous body, because this anomaly could be an artifact. These results are typical of ill-posed inverse problems: an absence of a guarantee of correspondence to the true distribution. The limitations due to illumination may not be solved by the use of constraints. Crosswell tomograms derived with the use of sparsity constraints, using the discrete cosine transform and Daubechies bases, essentially reproduce the same features seen in tomograms obtained with the smoothness constraint. Interpretation must be done taking into consideration a priori information and the particular limitations due to illumination, as we have determined with a real data case.

The Neoproterozoic Serido belt located in the Borborema Province, NE Brazil, was deformed and metamorphosed in the Pan-African/Brasiliano orogeny. The basement rocks of the belt were submitted to intense partial melting to form dome-like structures as documented in the Santa Luzia anatetic dome. The aeromagnetic map of the Serido belt shows a long-wavelength anomaly with elongated sigmoidal shape, whose limits coincide with shear zones. Comparison with gravity data shows that both anomalies share common sources, which are felsic rocks more magnetic and less dense than the surrounding crust. Correlation with geology shows that the geophysical anomalies are associated with magnetite-rich migmatites and granites. We modelled the geophysical datasets using magnetic susceptibility and density values from measurements in cores of a stratigraphic borehole. The results are consistent with a migmatite-dome system formed in the south-central part of the belt. This large-scale crustal structure is composed of elongated internal domes, which were geophysically modelled as four anomalous bodies, that resulted from partial melting of rocks mostly of the basement. The anomalies define an elongated migmatite-dome system with the main axis in the NNE-SSW direction that progressively bends to E-W approaching to the Patos shear zone, thus indicating that this shear zone had a key role in shaping the domic structure. The migmatitic domes of the Serido belt compose a fault-related dome system, formed in association with the broad strike-slip shear zone array of the Patos-Serido system, which evolved through the crustal extrusion resulting from the continental collisions that amalgamated West Gondwana in the Ediacaran.

The increasing importance of carbonate rocks as aquifers, oil reservoirs, and for urban problems is demanding detailed characterization of karst systems, a demand that can be partially satisfied with GPR imaging. However, the goal of imaging and interpreting karstified carbonate rocks is notoriously difficult due to the complex nature of the geometry of the dissolution and the GPR intrinsic limitations. One way forward is the direct comparison of GPR images with similar outcropping rocks. A joint study involving a 200 MHz GPR survey, unmanned aerial vehicle imagery (UAV), and outcrop characterization is presented aiming to improve the interpretation of sedimentary structures, fractures and karst structures in GPR images. The study area is a 500 m wide and 1000 m long carbonate outcrop of the Jandaira Formation in Potiguar basin, Brazil, where sedimentary, fracture, and karst features can be directly investigated in both vertical and horizontal plan views. The key elements to interpret GPR images of karstified carbonate rocks are: (1) primary sedimentary structures appear in radargrams as unaltered imaged strata but care must be taken to interpret complex primary sedimentary features, such as those associated with bioturbation; (2) subvertical fractures might appear as consistent discontinuities in the imaged strata, forming complex structures such as negative flowers along strike–slip faults; (3) dissolution may create voids along subhorizontal layers, which appear in radargrams as relatively long amplitude shadow zones; and (4) dissolution may also create voids along subvertical fractures, appearing in radargrams as amplitude shadow zones with relatively large vertical dimensions, which are bounded by fractures.

Neogene and late Quaternary sedimentary deposits corresponding respectively to the Barreiras Formation and Post-Barreiras Sediments are abundant along the Brazilian coast. Such deposits are valuable for reconstructing sea level fluctuations and recording tectonic reactivation along the passive margin of South America. Despite this relevance, much effort remains to be invested in discriminating these units in their various areas of occurrence. The main objective of this work is to develop and test a new methodology for semi-automated mapping of Neogene and late Quaternary sedimentary deposits in northeastern Brazil integrating geophysical and remote sensing data. The central onshore Paraiba Basin was selected due to the recent availability of a detailed map based on the integration of surface and subsurface geological data. We used airborne gamma-ray spectrometry (i.e., potassium-K and thorium-Th concentration) and morphometric data (i.e., relief–dissection, slope and elevation) extracted from the digital elevation model (DEM) generated by the Shuttle Radar Topography Mission (SRTM). The procedures included: (a) data integration using geographic information systems (GIS); (b) exploratory statistical analyses, including the definition of parameters and thresholds for class discrimination for a set of sample plots; and (c) development and application of a decision-tree classification. Data validation was based on: (i) statistical analysis of geochemical and airborne gamma-ray spectrometry data consisting of K and Th concentrations; and (ii) map validation with the support of a confusion matrix, overall accuracy, as well as quantity disagreement and allocation disagreement for accuracy assessment based on field points. The concentration of K successfully separated the sedimentary units of the basin from Precambrian basement rocks. The relief–dissection morphometric variable allowed the discrimination between the Barreiras Formation and the Post-Barreiras Sediments. In addition, two units of the latter (i.e., PB1 and PB2) previously mapped in the field were promptly separated based on Th concentration. A regression analysis indicated that the relationship between geophysical and geochemical values obtained for the PB1, PB2 and Barreiras Formation is significant ( R -squared = 0.91; p -value

We evaluate the performances of the Krischer-Esdorn (KE), Hashin-Shtrikman (HS), classic Maxwell (CM), Maxwell-Wiener (MW), and geometric mean (GM) models in reproducing 1,105 measurements of thermal conductivity of crystalline rocks collected in Borborema Province (NE-Brazil). Percent volumes of quartz, K-feldspar, plagioclase, andmafic minerals were also measured. Rock samples were divided into the IOG (igneous and ortho-derived) and MET (metasedimentary) groups. IOG-group (939 samples) covered most the lithologies of the Streckeisen diagram and MET-group (166 samples) covered low-to-medium metamorphic grade lithologies. Reproducing rock conductivities was treated as an inverse problem, where conductivity measurements and constituent mineral volumes are the known quantities while the constituent mineral effective conductivities and model parameters are the unknowns. To identify the model better reproducing the measurements, model performances were compared by using the percentage of number of samples whose estimated conductivities are close to the measured conductivities within the tolerance level of 15%. For all models, the performances are relatively inferior for the MET-group. In the IOG-group, the KE- and HS-model performances are relatively superior. In the MET-group, model performances are very contrasting but the KE-model is again superior. The KE-model thus presents the best performance in reproducing thermal conductivities of crystalline rocks. Keywords: thermal conductivity, rock models, crystalline rocks, Borborema Province. RESUMO. Avaliamos o desempenho dos modelos Krischer-Esdorn (KE), Hashin-Shtrikman (HS), Maxwell classico (CM), Maxwell-Wiener (MW), e media geometrica (GM) em reproduzir 1.105 medidas de condutividade termica de rochas cristalinas da Provincia Borborema (NE-Brasil). Os percentuais de volume de quartzo, K-feldspato, plagioclasio e minerais maficos foram tambem medidos. As amostras foram divididas nos grupos IOG (igneas e ortoderivadas) e MET (metassedimentares). O grupo IOG (939 amostras) cobre as litologias principais do diagrama de Streckeisen e o grupo MET (166 amostras) contem rochas de baixo a medio graus de metamorfismo. Estimar condutividade de rochas foi tratado como um problema inverso, em que medidas de condutividade e percentuais de volume de minerais sao conhecidos enquanto condutividades efetivas de minerais e parâmetros de modelo sao incognitas. O desempenho foi avaliado comparando-se a percentagem do numero de amostras cujas estimativas de condutividade reproduzem as medidas dentro da tolerância de 15%. Para todos os modelos, os desempenhos sao relativamente piores no grupo MET. No grupo IOG, os modelos KE e HS apresentaram os melhores desempenhos. No grupo MET, os desempenhos sao contrastantes, mas o modelo KE apresenta melhor desempenho. Assim, o modelo KE apresenta o melhor desempenho em reproduzir as medidas de condutividade termica de rochas cristalinas. Palavras-chave: condutividade termica, modelos de rocha, rochas cristalinas, Provincia Borborema.

Improving the attributes of Reverse Time Migration (RTM) images can be beneficial for seismic interpretation. We present and evaluate new image conditions for RTM taking also into account the phase coherence between the forward and backward propagated wavefields. To compute the new image conditions we need to propagate the source and receivers analytical signals; as consequence, we have at each image point source and receivers amplitude and phase fields, besides the real wavefields. These fields provide several alternatives to define imaging conditions. Here we explore one of the possibilities that is to weight the usual cross-correlation term with a power n of the phase cross-correlation. Our numerical experiments, imaging the Marmousi data, show that tunning the phase cross-correlation exponent parameter n in the imaging condition can produce sharp images across layer boundaries, suggesting that phase cross-correlation in RTM helps to enhance signals, reduce backscatering artfacts and highlight subtle stratigraphic and structural features. The properties of the phase cross-correlation imaging conditions can be advantageous for seismic interpretation in complex structural settings.

In the Borborema Province (BP) – northeastern Brazil – two important Cenozoic events occurred at the surface: the Macau magmatism and the Borborema Plateau epeirogenesis. To obtain appropriated-scale geophysical data to explain the deep origins of these two events, different gravimetric/elevation databases were integrated with new surveys. Bouguer admittance estimates reveal that isostatic condition of the BP, especially in the Borborema Plateau, can be explained using elastic models to the lithosphere only if surface and buried loadings are combined. If the buried load is applied in the base of the crust, the ratio between buried and surface weights is circa 15 for a lithosphere with effective elastic thickness around 15 km and crust thickness around 33 km. From an interpretative viewpoint of the buried load, it is assumed that the lower crust under the Borborema Plateau might have an anomalous high value of density. Magmatic underplating might explain this fact as well as the observed surface magmatism and epeirogenesis. Crustal thickening of about 4 km under the Borborema Plateau and intracrustal seismic velocity discontinuity with high Vp/Vs ratio are geophysical facts consistent with magmatic underplating. However, the surface magmatism presents low volume and mainly alkaline composition – facts that are not entirely consistent with the hypothesis of magmatic underplating. Regardless the validity of this hypothesis, Cenozoic-to-present events in BP might be somewhat associated with imbalances in lithosphere-asthenospheric mantle and/or crust-lithospheric mantle systems. The existence of free-air anomalies showing no null integral over area and of an expressive positive geoid anomaly are geophysical evidences of these imbalances. Possibly, the Borborema Plateau is still suffering epeirogenesis. Post-depositional deformation found in Barreiras Formation strata, Late Quaternay fault reactivations, and AFT thermochronology analysis suggesting the existence of a cooling stage between 20 and 0 Ma might be geologic evidences of the continued action of epeirogenesis until the present. In addition, the relatively high level of the present intraplate seismicity recorded in several regions of the BP is another unequivocal geophysical evidence that the crust of the province is still submitted to accommodation processes.

SUMMARY Hypocentre location is an ill-posed inverse problem even assuming that the velocity model is known, because different sets of hypocentre locations may satisfy the fitting criterion. We present a regularized hypocentre inversion in which the constraints of spatial proximity of the hypocentres to target planes are used. This constraint introduces the geological bias that earthquakes might occur along fault planes. Here, the target planes may be either (1) planes specified by the interpreter or (2) planes fitting groups of events. We assume also that initial estimates of hypocentres and origin times are available. Then, the initial hypocentre estimates, origin times and target planes are used as input to an inversion problem to relocate the hypocentres so that the maximum-possible clustering of events along the given planes is attained, matching the observed traveltimes. We use L1 norm for data fitting, L2 norm for the plane proximity criterion and a polytope algorithm to minimize the functional. Results from synthetic and real data indicate that the plane proximity constraint allows for hypocentre relocation presenting a high degree of clustering along planes. The real-data example is an intraplate earthquake sequence in NE Brazil. Our methodology defined the geometry and strike of fault segments close to known geology and focal mechanism data. In addition, the new method indicates that the fault is characterized by a splay geometry in its southern end and that more than three fault segments are necessary to explain the hypocentre distribution.

The performances of the spectral ratio (SR), frequency centroid shift (FCS), and frequency peak shift (FPS) methods to estimate the effective quality factor Q are compared. These methods do not demand true amplitude data and their implementations were done following an “as simple as possible” approach to highlight their intrinsic potentials and limitations. We use synthetic zero-offset seismic data generated with a simple layer-cake isotropic model. The methods can be ranked from simple to complex in terms of automation as: FPS, FCS and SR. This is a consequence of: (i) peak identification consists basically of a sorting procedure, (ii) centroid estimation involves basically the evaluation of two well-behaved integrals, and (iii) implementation of the SR method involves at least choosing a usable frequency bandwidth and fitting a gradient. The methods can be ranked from robust to sensitive in the presence of noise content in the sequence SR, FCS, and FPS. This is consequence of: (i) the gradient estimate associated to the SR method averages out the noise content in the entire usable frequency bandwidth, (ii) in the presence of moderate-to-high noise level, the centroid estimation is biassed towards overestimating Q due to noise contribution in the tail of the amplitude spectrum, and (iii) peak identification is unstable due to local noise fluctuation in the amplitude spectrum around the peak frequency. Regarding the stability of the estimates relative to the attenuation amount, SR and FCS methods show similar behaviours, whereas FPS method presents an inferior performance. This fact is an indirect consequence of the sensitivity of FPS method to the noise content because the higher is the attenuation the lower is the signal-to-noise ratio. Finally, regarding the robustness of the methods to the presence of dipping layers, only SR and FCS methods provide good estimates, at least to typical dips in non-faulted sedimentary layers, with the estimates obtained with SR method being more accurate that those obtained with FCS method. Except in relation to the automation complexity, which is less important than the performances of the methods, SR method was superior or showed similar performance to FCS method in all scenarios we tried.

It is assumed that deformation bands may compartmentalize aquifers or hydrocarbon reservoirs because these low-permeability structures may behave as barriers to fluid flow. To address the question whether there is, at a reservoir scale, hydraulic connectivity across a damage zone dominated by cataclastic deformation bands, we present results of two pumping tests carried out in a fluvial-deltaic phreatic sandstone aquifer from the Ilhas Group at Tucano Basin (NE Brazil) where intense concentration of deformation bands occurs. Both test sites are associated with macroscopic damage zones that are approximately 1 km in length and 15 m thick. In situ permeability measurements show values of 2000 mD for host rock and 0.1 mD for deformation bands. GPR profiles reveal good continuity of the primary sedimentary structures with almost no deformation band vertical offsets (less than 10 cm). The well locations for the pumping tests were chosen so that the damage zone is located between pumping and monitoring wells. Pumping tests in both cases revealed hydraulic connectivity across the damage zone since the observed stationary drawdown at monitoring wells was a considerable fraction of the drawdown observed in the pumped well. In one experiment using eight monitoring wells the drawdown cone is evolving through the damage zone instead of contouring it. Local deviations in the natural groundwater flow allow to say that the damage zone dimensions are quite large both in horizontal and vertical directions compared to the distances among the wells. The interpretation of all experimental results is that deformation bands do not fully compartmentalize the aquifer. Generalization of this result to hydrocarbon reservoirs has to take into account capillary effects which are not present in the studied case.

Laboralory and field experimenls were carried oul in order lo invesligale lhe causes of GPR refleclions inside non-consolidaled sand samples. In lhe sand samples, the content of water, heavy minerais grain size were varied and the velocity of propagation of GPR pulses were measured using antennas of 400 MHz and 900 MHz. In alaboratory experiment, it was verified the increase of the dielectric constant due to the increase in water content. Wyllie & Gregory (1953) and Topp et al. (1980) models furnish good previsions of experimental data, specially lhe first one when it is considered the enlire data set (two frequencies). However, it was verified that the velocity estimates are systematically greater for the higher frequency (900 MHz), afact which is not predicted by both models. For dry sand samples, it was verified arelatively minor increase of the dielectric constant with the increase in heavy minerais. Also for dry sand samples, no dependence of the dielectric constant was observed with grain size variation. On the other hand, for afield in situ experiment, where samples of sand were taken to perform grain size characterization, it was verified that the grain size might has an indirect influence on the dielectric constant because it may control water adsorption.

The history match procedure in an oil reservoir is of paramount importance because good estimates of the reservoir parameters may lead to a better forecast of the production. The reservoir is said to be ‘matched’ when the discrepancies between the model predictions and the observations of the real reservoir are below a certain tolerance. The determination of the model parameters via history matching requires the minimisation of an objective function in a parameter space that may be populated by many local minima. In other words, more than one set of reservoir model parameters fits the observation. Moreover, even a solution associated to a given minimum may be unstable. In order to reduce the ambiguity, it is necessary to incorporate constraints in the reservoir parameters to be estimated. Here, we use the smoothness constraint to regularise this inverse problem using as an example a modified version of the PUNQ model. The PUNQ model is suitable for applying this constraint because the sediments were depos...

The history matching (HM) hydrocarbon reservoir inverse problem is ill-posed because its solution may be non-unique or unstable. Variability of acceptable solutions around local minima may be very large. Nonetheless, it is a common practice in HM to find a unique reservoir model, although there is no guarantee that this model represents the geology. Qualitative geological information is generally not considered because of difficulties to express them mathematically. Here, we incorporate ‘smoothness’ in the spatial variation of physical properties as an example of a geological qualitative constraint that can be mathematically incorporated in an objective function also honouring the data. The constraint is valid if lateral continuity exists (e.g. fluvial-deltaic siliciclastic reservoirs). We mean smoothness by conditioning the permeability and/or porosity difference between adjacent grid blocks to be small. We use a synthetic 2D water–oil model and a solution search technique allowing characterising both th...

Sealing faults may have a major impact on reservoir compartmentalization and play a key role in advanced oil recovery strategies. Because of the different approaches and scales used to characterize faults, a considerable gap remains between engineers’ and geologists’ conceptions of faulted reservoirs. The fundamental difficulty in integrating these views lies in constructing realistic reservoir-scale models incorporating relevant fault properties on several scales, so that fault connectivity and its impact on fluid flow can be simulated and quantified properly. This paper is a step towards examining quantitatively the impact of fault connectivity on fluid flow at a reservoir scale. A stochastic reservoir model incorporating sealing faults was constructed. The number of faults in the model were gradually increased and several fluid flow simulations performed in order to verify the impact of fault density and fault connectivity on the spatial pressure variation. Despite being synthetic, the model incorporates some properties of an actual carbonate reservoir, the Xareu oil field (XOF) in the Ceara Basin, NE Brazil. In the XOF, thin ( 50 m) shale bed. Sealing effects may be caused by the faults because they usually have a normal slip component, so that the thick shale layer becomes juxtaposed against the thin carbonate layers, behaving as barriers to fluid flow in the carbonate layers. It appears that there is no reservoir compartmentalization in the carbonate layers because there is overall pressure depletion in XOF – all the new wells drilled in the carbonate layers, before starting production, showed formation pressure values smaller than the formation pressure measured in the first wells drilled in the field. Nevertheless, it was not understood how such communication throughout the entire reservoir (approx. 19 km 2 ) could occur, given the presence of laterally extensive faults, with up to 5 km in strike and maximum vertical displacement greater than the reservoir thickness. In the synthetic model, fault population follows a displacement-length property derived from seismic data. Sub-seismic faults were also incorporated in the model using a downscaling law. The location, direction and length of each fault were also generated stochastically. In order to quantify the ‘degree of faulting’, two criteria were used: fault density (the fraction9s ‘total fault length per occurrence area’; f 1 ) and fault connectivity (the fraction9s ‘number of fault intercepts per occurrence area’; f 2 ). By comparing f 1 and f 2 for the real and simulated versions of the XOF carbonate reservoir it is concluded that the carbonate layers remain interconnected so that compartmentalization does not exist. From a methodological viewpoint, the most important aspect of the modelling is the change of focus regarding sealing. At least for the purposes of investigating interconnection, the adequate focus is on the ‘percolation core’ of the reservoir (its hydraulically connected and undamaged parts) and not on the faults themselves, regardless of their sealing nature.

It is presented a new method for the approximate mapping of the subsurface resistivity based on a geostatistical approach. It are used the characteristic points (CPs) of a resistivity sounding, which are their inflection and extreme (maximum and minimum) points. The methodology consists of four stages: i) smoothing the geoelectric soundings to assure robusteness to measurement errors, ii) determining the CPs from the smoothed versions of the geoelectric soundings, and obtaining from the CPs point estimates for the subsurface resistivity using empirical relations between electrode spacing and depth, iii) calculating semivariograms associated to the point estimates, and fitting them to a semivariogram model, and finally iv) estimating the subsurface resistivity distribution by kriging interpolation of the point estimates. The method’s performance is demonstrated with real 2D Schlumberger array data.

We present an analytical approach to jointly estimate the correlation window length and number of correlograms to stack in ambient noise correlation studies to statistically ensure that noise cross-terms cancel out to within a chosen threshold. These estimates provide the minimum amount of data necessary to extract coherent signals in ambient noise studies using noise sequences filtered in a given frequency bandwidth. The inputs for the estimation process are (1) the variance of the cross-correlation energy density calculated over an elementary time length equal to the largest period present in the filtered data and (2) the threshold below which the noise cross-terms will be in the final stacked correlograms. The presented theory explains how to adjust the required correlation window length and number of stacks when changing from one frequency bandwidth to another. In addition, this theory provides a simple way to monitor stationarity in the noise. The validity of the deduced expressions have been confirmed with numerical cross-correlation tests using both synthetic and field data.

An integrated study based on ground penetrating radar (GPR) profiles, vibracore descriptions, water-well logs, and radiocarbon dating in a coastal deposit located in the northern region of Rio Grande do Norte State, northeastern Brazil, allowed us to identify Holocene transgressive and regressive barriers. The construction process for the studied coastal barrier is different from that proposed for the Holocene coastal plains along the eastern Brazilian coast, where the hydraulic barrier set up by large rivers for sediments transported by longshore currents has caused a strongly positive longshore sediment imbalance. In the study area, interpretation of the GPR images, within the constraints of vibracores data, allowed us to interpret five radar facies and four radar boundary sequences for these coastal deposits, which were built up during the Holocene coastal evolution of the region. As a result, the geometry of the coastal barrier was reconstructed. Based on barrier geometry, sediment ages, stratigraphic records, and sedimentation patterns, we propose a barrier evolutionary model for the Holocene for the study region. During the Holocene highstand, a transgressive barrier was deposited and a lagoon extended landward. During the sea-level fall soon after the Holocene highstand, the deposition of a regressive barrier (forced regression) started. This deposition was induced by the coastal geometry and high amounts of eolian sediments supplied by east-northeast winds. Also during this period of sea-level fall, the beach face became wider, and thus more subjected to wind action, facilitating the deposition of the first eolian deposits. These sediments were transported to the nearly formed embayment, providing a surplus for the construction of the regressive barrier. During the regressive phase, tidal channels closed and the lagoon became isolated from the open sea. The geometry of both the regressive and transgressive barriers as well as the stratigraphic relation between the sedimentary deposits suggest that the Holocene highstand in this region was not more than 1.4 m above present-day mean sea level.

As the GPR pulse propagates in the geologic medium, it suffers attenuation as the result of absorption and dispersion, besides spherical divergence. High frequency components of the pulse suffer more pronounced effects of attenuation than low frequency components resulting in resolution loss in radargrams. The quality of the GPR images is then strongly dependent on an adequate correction of the attenuation effects. We present a practical approach to approximately correct the attenuation effects based on their influence on the amplitude and phase spectra of GPR signals. The key point of this approach is the fact that in low and moderate losses dielectric media the propagated signal suffers significant changes only in its amplitude spectrum; that is, the phase spectrum of the propagated signal remains practically unaltered for the usual travel time ranges. Based on this fact, we show using real data (both CMP and radargram) that the judicious application of the well known tools of time gain and spectral balancing can efficiently correct the attenuation effects, from the practical point of view. The proposed approach can be applied in heterogeneous media and it does not demand the precise knowledge of the attenuation parameters of the media. This approach should be understood as part of an interpretative data processing, which can be done by using the interpreter's knowledge on the studied area and even during the fieldwork. As an additional benefit, the judicious application of spectral balancing promotes a partial deconvolution of the data without changing its phase. In this way, the spectral balancing acts in a similar way to a zero phase deconvolution. Usually, in GPR data, the resolution increase obtained with spectral balancing is greater than those obtained with spike and predictive deconvolutions.

Current hydrogeological research in NE Brazil aims to better understand factors controlling storage and percolation of ground water in crystalline terrains, due to the fact that a large proportion (about 60%) of this region is formed by igneous and metamorphic rocks. As part of this effort, we present an integrated geophysical–geological study of a fractured bedrock aquifer located in the Caicara farm, near Equador city, Rio Grande do Norte State, NE Brazil. Pumped wells in this site present very different yields, in spite of short distance of only 20 m. The main lithologies of the site are quartzite and micaschist. Combined interpretation of geophysical images (Resistivity and Ground Penetrating Radar—GPR) and field structural geologic data revealed that the fractured bedrock aquifer is composed of three sets of discontinuities: SW-dipping subhorizontal joints, parallel to the ductile fabric of the country rocks which are probably release joints; NE-dipping subhorizontal fractures, oblique to ductile trend; and subvertical fractures which are orthogonally distributed along N–S and E–W directions. Important subvertical fracture zones occur at a regular spacing of about tens of meters. Fractures in the E–W direction are relatively open, as compared to fractures in the N–S direction. Probably, E–W fractures were opened by the current neotectonic stress regime in NE Brazil, which is controlled by E–W compression and N–S extension. It was possible to rank the hydrogeologic potentiality of water well siting as a function of fracture density and proximity to recharge zones, in this way explaining why wells could present very different yield results on the site. The most favorable places for well siting are intersections of subvertical fracture zones located near drainage because highly fractured zones could be, in this way, connected with recharge zones mainly in alluvial deposits. On the other hand, the least favorable places for well siting lie outside subvertical fractures and far from recharge zones. Intermediate hydrogeological potentialities occur in two cases: at a point near the recharge zone but where there is a low density of fractures, or at point far from the recharge zone but where there is a high density of fractures.

We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

To obtain a unique and stable solution to the gravity inverse problem, a priori information reflecting geological attributes of the gravity source must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov's regularization method, where the a priori information is introduced via a stabilizing functional, which may be suitably designed to incorporate some relevant geological information. However, there is no unifying approach establishing general uniqueness conditions for a gravity inverse problem. Rather, there are many theorems, usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution. In Part I of these companion papers, we show that translating the mathematical uniqueness conditions into geological constraints is an important step not only in establishing the type of geological setting where a particular method may be applied but also in designing new gravity inversion methods. As an example, we analyze three uniqueness theorems in gravimetry restricted to the class of homogeneous bodies with known density and show that the uniqueness conditions established by them are more probably met if the solution is constrained to be a compact body without curled protrusions at their borders. These conditions, together with stabilizing conditions (assuming a simple shape for the source), form a guideline to construct sound gravity inversion methods. A historical review of the gravity interpretation methods shows that several methods implicitly follow this guideline. In Part II we use synthetic examples to illustrate the theoretical results derived in Part I. We also illustrate that the presented guideline is not the only way to design sound inversion methods for the class of homogeneous bodies. We present an alternative approach which produces good results but whose design requires a good dose of the interpreter's art.

The eastern continental margin of South America comprises a series of rift basins developed during the breakup of Pangea in the Jurassic–Cretaceous. We integrated high resolution aeromagnetic, structural and stratigraphic data in order to evaluate the role of reactivation of ductile, Neoproterozoic shear zones in the deposition and deformation of post-rift sedimentary deposits in one of these basins, the Paraiba Basin in northeastern Brazil. This basin corresponds to the last part of the South American continent to be separated from Africa during the Pangea breakup. Sediment deposition in this basin occurred in the Albian–Maastrichtian, Eocene–Miocene, and in the late Quaternary. However, our investigation concentrates on the Miocene–Quaternary, which we consider the neotectonic period because it encompasses the last stress field. This consisted of an E–W-oriented compression and a N–S-oriented extension. The basement of the basin forms a slightly seaward-tilted ramp capped by a late Cretaceous to Quaternary sedimentary cover ~ 100–400 m thick. Aeromagnetic lineaments mark the major steeply-dipping, ductile E–W- to NE-striking shear zones in this basement. The ductile shear zones mainly reactivated as strike-slip, normal and oblique-slip faults, resulting in a series of Miocene–Quaternary depocenters controlled by NE-, E–W-, and a few NW-striking faults. Faulting produced subsidence and uplift that are largely responsible for the present-day morphology of the valleys and tablelands in this margin. We conclude that Precambrian shear zone reactivation controlled geometry and orientation, as well as deformation of sedimentary deposits, until the Neogene–Quaternary.

Despite being widely used, Euler deconvolution has received little attention in its theoretical aspects. We obtain analytical estimators [Formula: see text] and [Formula: see text] for the horizontal [Formula: see text] and the vertical [Formula: see text] source positions, which are the parameters to be estimated when the structural index is assigned a tentative value. By analyzing the estimators’ properties, we show two things. (1) Scattering of the alternative solutions associated with different data window positions has two components: data noise and the use of a wrong tentative value for the structural index, (2) The differences [Formula: see text] and [Formula: see text], as a function of the data window position, exhibit antisymmetric and symmetric behaviors, respectively, about [Formula: see text] when the magnetization and the geomagnetic field inclinations are 90°, 0°, or 45°. For intermediate inclinations there is a moderate departure from the symmetry properties. This analysis shows that the criterion for determining the structural index as the tentative value producing the smallest solution scattering is theoretically sound but occasionally fails in practice because data noise also contributes to solution scattering. In addition, the lower sensitivity of the averages of estimates of the horizontal position (as compared with the vertical position) occurs because [Formula: see text] displays an antisymmetric behavior with respect to the true horizontal position while the estimates of the vertical position display a symmetric behavior with respect to the same point.

— We discuss and illustrate graphically with simple 2-D problems, four common pitfalls in geophysical nonlinear inversion. The first one establishes that the Lagrange multiplier, used to incorporate a priori information in the geophysical inverse problem, should be the largest value still compatible with a reasonable data fitting. This procedure should be used only when the interpreter is sure about the importance of the a priori information used to stabilize the inverse problem relative to the geophysical observations. Because this is rarely the case, the user should use the smallest Lagrange multiplier still producing stable solutions. The second pitfall is an attempt to automatically estimate the Lagrange multiplier by decreasing it along the iterative process used to solve the nonlinear optimization problem. Consequently, at the last iteration, the Lagrange multiplier may be so small that the problem may become ill-posed and any computed solution in this case is meaningless. The third pitfall is related to the incorporation of a priori information by a technique known as “Jumping.” This formulation, from the viewpoint of the class of Acceptable Gradient Methods, is incomplete and may lead to a premature halt in the iteration, and, consequently, to solutions far from the true one. Finally, the fourth pitfall is an inadequate convergence criterion which stops the iteration when the data misfit drops just below the noise level, irrespective of the fact that the functional to be minimized may not have attained its minimum. This means that the a priori information has not been completely incorporated, so that this stopping criterion partially neutralizes the effect of the stabilizing functional, and opens the possibility of obtaining unstable, meaningless estimates.

To produce a unique and stable solution in potential‐field interpretation, an inversion method must introduce particular constraints. These constraints will inevitably restrict the type of geological setting where the method may be applied. We present a nonmathematical overview of most stabilizing constraints used in inversion methods. Our purpose is to demonstrate that the inversion results are valuable only if the mathematical stabilizing constraints are translated from the geological setting. We identify five basic types of constraints: (1) lower and upper bounds of parameter estimates; (2) proximity of a parameter estimate to a specified value; (3) proximity between pairs of parameter estimates; (4) concentration of the anomalous source about a geometrical element such as an axis; and (5) source compactness. In practice, if used in isolation, constraints (1), (2), (4), and (5) will not produce geologically meaningful results, regardless of the geological setting of the interpretation area. Constraint (3) may produce geologically meaningful results if the anomalous source has a spatially smooth attribute such as the physical property. We illustrate that constraints 1–4, if used in isolation, cannot delineate the geometry of a simulated sill intruded into a sedimentary basin. The basic constraints may (and should) be combined in inversion to produce geologically meaningful results. We present two examples of effective constraint combination: (1) proximity to a specific value and mass concentration about an axis (used to delineate the thickness variation of a sill intruded in a sedimentary basin) and (2) inequality, proximity of a parameter estimate to a specified value, and proximity between pairs of parameter estimates (used to map a discontinuous basement relief). Usually, the stabilizing constraints are too restrictive to hold at all points of a given geological environment. In this case, we use different constraints in different sub‐areas. Each constraint is based on its compatibility with the actual geology of the subarea.

We present a constraint which incorporates in the geophysical inverse problem a priori information about the source convexity. Two kinds of convexity are considered: directional convexity, defined as the attribute of a body being intersected at most at two points by a straight line with a fixed spatial orientation, and global convexity, defined as the attribute of a body being intersected at most at two points by any arbitrarily oriented straight line. The interpretation model consists of several juxtaposed 2-D prisms whose positions, widths, and physical property are established by the interpreter. The depth to the top and the thickness of each prism are the parameters to be determined. The directional convexity is incorporated by minimizing a functional which expresses the number of times that several lines, parallel to a given direction and spaced at regular intervals, intersect the interpretation model. On the other hand, the global convexity is introduced in an algorithmic way by constraining the depths to the top and to the bottom of each prism to be, respectively, smaller or greater than the average of the depths to the top or to the bottom of the adjacent prisms. The use of the presented convexity contraint is demonstrated using synthetic gravity data produced by an isolated source. We found that convexity constraints (either directional along the horizontal axis or global) alone are insufficient to produce strongly stable solutions, although they reduce substantially the solution instability. Despite the “slight” instability, the directional convexity constraint leads to a reasonable delineation of the source shape and produces a better resolution of its base as compared with the inverse method imposing smoothness constraints on the top and bottom surfaces of the anomalous source. The potential use of the convexity constraint is the possibility of combining it with other constraints to produce geologically meaningful solutions. As an example, the global convexity was combined with the minimum moment of inertia of the anomalous masses about a vertical axis passing through its center of mass. This combination allowed introducing a priori information about a diapir shape. This is important because a maximum spread at the diapir middle portion indicates that it ascended like a viscous bubble in an isotropic medium. On the other hand, a spread located at its top indicates that the host medium is mechanically anisotropic, exhibiting horizontal planes of weakness where the mobile material was forced into. So, this combination of constraints alows introducing a priori information about the diapir emplacement. The combination of global convexity and minimum moment of inertia may also be applied to isolated intrusions, as illustrated with the real gravity anomaly produced by the granitic body of Castelsarrasin, in the Aquitaine Basin, France. The estimated source has its top located between 0.45 and 0.57 km from the surface, a base 6.4 km deep, and center of mass at a depth of 3.5 km, which agree reasonably with a priori geological and geophysical information about the body.

Euler deconvolution is a commonly employed magnetic interpretation method because it requires only a little a priori knowledge about the magnetic source geometry, and, more importantly, because it requires no information about the magnetization vector. As a result, it may be successfully applied in areas where the geology is poorly known. However, it requires a priori knowledge about the nature of an equivalent source producing a magnetic anomaly with the same falloff rate of the observed anomaly. This is a crucial limitation of the method, requiring that a parameter known as structural index ( η ) be determined. The customary application of the Euler method and the process of estimating η are benefited by having a large number of data and solutions preventing its application to ground magnetic surveys which may consist of a limited number of observations. We show that if the structural index is estimated by a new criterion, Euler deconvolution becomes a feasible technique to interpret anomalies defined by just a few observations. This new criterion is based on the correlation between the total-field anomaly h o and the estimates of the base level b . These estimates are obtained for each position of the moving data window along the observed profile and for several tentative values for the structural index. However, differently from the customary method, instead of estimating the structural index as the tentative value producing the smallest solution dispersion, the best estimate of η is taken as the tentative value leading to the smallest correlation between h o and the estimates of b . This criterion is deduced from the Euler's equation, so it does not depend on the inclination and declination of the geomagnetic field. The good results obtained with this new criterion in determining the correct structural index is illustrated in tests using synthetic data from different latitudes and the feasibility in using this criterion in applying Euler deconvolution to ground surveys is illustrated with a real magnetic anomaly defined by just 12 observations and produced by a basic/ultrabasic body at the emerald deposit of Socoto, Bahia, Brazil. The results of Euler deconvolution, combined with the geological information that the basic/ultrabasic body outcrops, show that the intrusive body may be approximated by an outcropping horizontal cylinder with a diameter of 68 m and center at a depth of 34 m, which is consistent with the geologic knowledge of the deposit.

We present a new stable gravity inversion method applied to the mapping of an interface separating two homogeneous media. In contrast with previous similar methods, it does not impose an overall smoothness on the estimated interface to stabilize the solution. The density contrast between the media is assumed to be known. The interpretation model for the upper medium consists of rectangular juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated. The true interface is assumed to be flat everywhere except at faults. To incorporate this attribute into the estimated relief, we developed an iterative process in which three kinds of constraints are imposed on parameters: (1) proximity between values of adjacent parameters, (2) lower and upper bounds to parameters, and (3) proximity between the values of parameters and fixed numerical values. Starting with an initial solution which presents an overall smooth relief, the method enhances initially estimated geometric features of the interface; that is, flat areas will tend to become flatter and steep areas will tend to become steeper. This is accomplished by weighting the constraints, which requires proximity between adjacent parameters. The weights are initialized with values equal to unity and are updated automatically to enhance any discrepancy between adjacent depths that have been detected at the initial solution. Constraints 2 and 3 are used both to compensate for the decrease in solution stability caused by the introduction of small weights and to reinforce flatness at the basin bottom. Constraint 2 imposes that any depth be nonnegative and smaller than an a priori known maximum depth value, whereas constraint 3 imposes that all depths be closest to a value greater than the maximum depth. The trade‐off between these conflicting constraints is attained with a final relief presenting flat bottom and steep borders. The method was tested with a synthetic gravity anomaly produced by a simulated sedimentary cratonic extensional basin whose basement consists of steep edges and a flat bottom. The results showed an improvement in the resolution of the relief, leading to a reliable mapping both of the sharp discontinuities at the borders and of the lateral extent of the base of the basin. Additionally, the method produced excellent estimates for the average dip angles of the basin edges (presumably controlled by normal faults), indicating, in this way, its potential in interpreting data produced by this kind of basin. The method was applied to the Bouguer anomaly from the northern portion of Steptoe Valley, Nevada, delineating an isolated basin with a wider, flat base and relatively straight borders as compared with the estimate imposing overall smoothness on the relief.