gravity inversion of 2d bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods based on the line integral li and maximum difference reduction mdr methods an automated iterative forward modelling scheme li mdr algorithm is developed for the inversion of 2d bedrock topography from a gravity anomaly profile for heterogeneous sedimentary basins the unknown basin topography can be smooth as for intracratonic basins or discontinuous as for rift and strike slip basins in case studies using synthetic data the new algorithm can invert the sedimentary basins bedrock depth within a mean accuracy better than 5 when the gravity anomaly data have an accuracy of better than 0 5 mgal the main characteristics of the inversion algorithm include 1 the density contrast of sedimentary basins can be constant or vary horizontally and or vertically in a very broad but ap rioriknown manner 2 three inputs are required the measured gravity anomaly accuracy level and the density contrast function 3 the simplification that each gravity station has only one bedrock depth leads to an approach to perform rapid inversions using the forward modelling calculated by li the inversion process stops when the residual anomalies the observed minus the calculated falls within an error envelope whose amplitude is the input accuracy level the inversion algorithm offers in many cases the possibility of performing an agile 2d gravity inversion on basins with heterogeneous sediments both smooth and discontinuous bedrock topography with steep spatial gradients can be well recovered limitations include 1 for each station position there is only one corresponding point vertically down at the basement and 2 the largest error in inverting bedrock topography occurs at the deepest points

modeling the tectonic development of the tucano and sergipe alagoas rift basins brazil abstract the tucano and sergipe alagoas basins of northeast brazil form part of a regional extensional basin system that was operative during the mesozoic breakup of south america and africa with both basins developing on precambrian crust the synchronous development of the rift basins suggest that they are genetically linked in space and time whereas the offshore sergipe alagoas basin is characterized by a substantial thickness of post rift sediment the tucano basin either failed to develop or at least preserve a significant thickness of post rift sediment observed primary porosities within both pre and syn rift tucano basin sediment imply that significant post rift sedimentation never occurred failure to develop significant post rift subsidence has important thermal and mechanical implications for the reaction of the lithosphere to rifting and can be explained in terms of 1 depth dependent lithospheric extension in which intracrustal detachments allow the extension of the crust to be decoupled from the thinning of the lithospheric mantle 2 small rates of extension that allow the lithosphere to cool during rifting and or 3 lithospheric rifting during which the flexural strength of the lithosphere remains high with respect to points 2 and 3 forward modeling demonstrates that finite rifting rates over a 20 25 m y period are insufficient to cool the lithosphere to the point where post rift subsidence fails to develop an interesting complication arises when the flexural strength of the lithosphere remains large during rifting it tends to suppress the vertical motions of the lithosphere such as those engendered by the cooling of the lithosphere following rifting thereby reducing significantly the amplitude of the post rift subsidence thus the lack of post rift sedimentation within a basin does not necessarily imply that extension has been limited to the crust from our kinematic modeling of the tucano basin the observed negative free air and bouguer gravity anomalies 120 mgals suggest that the flexural strength of the lithosphere has remained sufficiently large to maintain the load of the sediment we can model successfully the observed tucano basin architecture and gravity anomaly irrespective of whether we assume depth dependent or depth independent lithospheric extension primarily because the flexural strength of the lithosphere tends to buffer or suppress the amplitude of the post rift subsidence in contrast the adjacent sergipe alagoas basin is associated with low amplitude gravity anomalies which may reflect a resetting of flexural strength during rifting prior to rifting however there was no appreciable elevation difference between the tucano and sergipe alagoas regions as might be induced by a hot spot for example implying that the flexural strength of the lithosphere was similar the total thickness of the syn and post rift sediments within the sergipe alagoas basin is about the same as the thickness of rift phase sediments in the tucano basin thus the amount of crustal extension responsible for each basin was similar however since the sergipe alagoas basin contains 4 5 km of post rift sediments lithospheric mantle thinning in this region must have been significantly greater than the crustal extension to overcome the effects of flexural bufferring the need for lithospheric mantle thinning to be greater that crustal extension in the sergipe alagoas region was also a result obtained by modeling the development of the ocean continent boundary between brazil and africa from our coupled kinematic and rheological model of lithospheric extension we predict that the ocean continent boundary should form preferentially at the location of greatest crustal and lithospheric mantle thinning that is within the region of maximum depth independent lithospheric extension the ocean continent boundary formed east of the sergipe alagoas basin despite the fact that the tucano basin represents the region of greatest crustal thinning if extension had been uniform with depth beneath these basins the ocean continent boundary should have formed in the tucano basin as it did not some form of intracrustal detachment appears to have been operative to reduce lithospheric mantle thinning beneath the tucano basin while enhancing it beneath the offshore regions of the sergipe alagoas basin

inversion of gravity field inclination to map the basement relief of sedimentary basins this paper presents a method to map the basement relief of homogeneous sedimentary basins that does not require the knowledge of the basin density contrast to reach this task the proposed method relies on the invariance of the inclination of the anomalous gravity field with the density contrast caused by models constituted by two homogeneous media this invariance occurs because the density contrast appears as a constant factor in both vertical and horizontal gravity components therefore being canceled out when these components are divided during the evaluation of the field inclination for such media the field inclination is independent of the density contrast thus allowing the source geometry reconstruction even when the density contrast is unknown as the inclination is rarely measured the gravity anomaly i e the field vertical component is initially used to compute the horizontal component of the gravity field by applying a suitable linear transform the field inclination is estimated from both components and then used to invert the source geometry by fitting the inclination values under the geologic constraints attributed to the causative sources in this process the density contrast is not required nor introduced as an unknown parameter in the formulated inverse problem moreover it can be estimated later by solving a new inverse problem where the source geometry determined from the inverted inclination is fixed and the constant density contrast is determined by fitting the gravity anomaly this paper applies such ideas to map the basement relief of a sedimentary basin and to estimate its density contrast the inversion is implemented by a random search procedure that excludes extreme models and imposes constraints that the unknown interface is smooth everywhere and assumes known depth values at isolated points investigated by wells the proposed technique is tested with synthetic noisy data from homogeneous and heterogeneous basin models and is applied to invert a gravity profile from the reconcavo basin brazil the results from the real data application are compared with well data and previously published results

stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations we present a new stable method for interpreting the basement relief of a sedimentary basin which delineates sharp discontinuities in the basement relief and incorporates any law known a priori for the spatial variation of the density contrast the subsurface region containing the basin is discretized into a grid of juxtaposed elementary prisms whose density contrasts are the parameters to be estimated any vertical line must intersect the basement relief only once and the mass deficiency must be concentrated near the earth s surface subject to the observed gravity anomaly being fitted within the experimental errors in addition upper and lower bounds on the density contrast of each prism are introduced a priori one of the bounds being zero and the method assigns to each elementary prism a density contrast which is close to either bound the basement relief is therefore delineated by the contact between the prisms with null and nonnull estimated density contrasts the latter occupying the upper part

comprehensive atlas of stress trajectory patterns and stress magnitudes around cylindrical holes in rock bodies for geoscientific and geotechnical applications abstract this study presents a comprehensive atlas comprising maps and graphs which quantify the wide range of possible stress states around circular cylindrical cavities when subjected to the full range of far field stress conditions and internal net pressures a greater understanding of the principal stress trajectories and related stress magnitudes around stressed cylindrical holes in rock formations significantly aids the design of safer and more stable wellbores advances our capacities in hydraulic fracturing and provides additional insights into the nature and stability of volcanic dikes salt domes and caverns used for hydrocarbon and other fluid storage the algorithms used in our study systematically non dimensionalize the analytical kirsch equations using two critical parameters to scale the variable boundary conditions 1 the bi axial stress scalar describes the far field stresses at all depths and for each of the formations penetrated by a cylindrical borehole or natural liquid filled pipe by describing the anisotropy of the two far field principal stresses and 2 the frac number f specifies the net pressure on the cylindrical hole as it relates to the natural background stress in the host rock and the pressure in the penetrated formation at each depth manipulation of these two governing parameters f enables us to view and monitor the stress trajectories in the host rock around a cylindrical hole at any given depth additionally the neutral point locations and their effects on the principal stress orientations near the cylindrical hole have been more thoroughly investigated than in earlier studies the neutral points form the boundaries for the stress cage in overbalanced cylindrical cavities and for the complimentary fracture cage in underbalanced cavities the understanding of stresses induced around cylindrical holes in a rock formation is paramount in geotechnical analyses and stability appraisals of manmade cylindrical holes as well as for the geoscientific interpretation of piercing by cylindrical fluid filled pipes our stress atlas aims to provide fundamental insight and practical support for such analyses

2d gravity inversion of a complex interface in the presence of interfering sources we present a new semiautomatic gravity interpretation method for estimating a complex interface between two mediacontainingdensityheterogeneitiesreferredtoasinterferingsourcesthatgiverisetoacomplexandinterferinggravity field the method combines a robust fitting procedure and the constraint that the interface is very smooth near the interfering sources whose approximate horizontal coordinates aredefinedbytheuser theproposedmethoddiffersfromthe regional residual separation techniques by using no spectral contentassumptionabouttheanomalyproducedbytheinterface to be estimated i e the interface can produce a gravity response containing both low and high wavenumber features asaresult itmaybeappliedtomapthereliefofacomplex interface in a geologic setting containing either shallow ordeep seatedinterferingsources testsconductedwithsyntheticdatashowthatthemethodcanbeofutilityinestimating the basement relief of a sedimentary basin in the presence of saltlayersanddomesorinthepresenceofmaficintrusionsin the basement or in both basement and the sedimentary section the method was applied to real gravity data from two geologic settings having different kinds of interfering sources and interfaces to be interpreted 1 the interface between the upper and lower crusts over the bavali shear zone of southern india and 2 the anorthosite tonalite interface over the east bull lake gabbro anorthosite complex outcrop in ontario canada

reconstruction of geologic bodies in depth associated with a sedimentary basin using gravity and magnetic data summary we present a comprehensive review of the most comm on gravity and magnetic interpretation methods to in depth retrieval of the geometry of two types of geologic bodies associated with a sedimentary basin 1 sedimentary basement relief and 2 salt bodies in reconstructing a basement topography we identify three groups of methods the automatic the spectral and the nonspectral methods the reconstruction of salt bodies geometries from gravity data usually uses the interactive forward modeling but recently gravity inversion methods have been developed to interpret this kind of geological environment

simultaneous 3d depth to basement and density contrast estimates using gravity data and depth control at few points we have developed a gravity inversion method for simultaneouslyestimatingthe3dbasementreliefofasedimentary basin and the parameters defining a presumed parabolic decay of the density contrast with depth in a sedimentary pack assumingpriorknowledgeaboutthebasementdepthatafew points thesedimentarypackisapproximatedbyagridof3d vertical prisms juxtaposed in both horizontal directions of a right handed coordinate system the prisms thicknesses representthedepthstothebasementandaretheparametersto be estimated from the gravity data to estimate the parameters defining the parabolic decay of the density contrast with depthandtoproducestabledepth to basementestimates we imposed smoothness on the basement depths and proximity between estimated and known depths at boreholes we applied our method to synthetic data from a simulated complex 3d basement relief with two sedimentary sections having distinct parabolic laws describing the density contrast variationwithdepth theresultsprovidegoodestimatesofthetrue parameters of the parabolic law of density contrast decay with depth and of the basement relief inverting the gravity data from the onshore and part of the shallow offshore almadabasinonbrazil snortheasterncoastshowsgoodcorrelationwithknownstructuralfeatures

deep pass an aeromagnetic data filter to enhance deep features in marginal basins abstractan aeromagnetic data filter was tested as a tool in enhancing the magnetic responses of deep sources associated with marginal basins our approach consists in amplifying the responses of magnetic sources which extend through the continental slope and continental rise this amplification compensates for the magnetic response attenuation over the continental slope as a result of 1 the seaward increase of the distance between the source and the magnetometer and 2 the seaward decrease in the volume of sources within the continental crust to amplify the source response we multiply the total field anomaly at a given location by the exponential of the bathymetric depth at the same point tests on synthetic and real data showed that the filter was able to recover the locations of linear magnetic responses not clearly seen in the total field anomaly map when compared with the analytic signal amplitude and the total horizontal derivative filters the proposed filter proved to be complementary in enha

high resolution multi proxy evidence for millennial and centennial scale climate oscillations during the last deglaciation in jeju island south korea abstract millennial and centennial scale climate and vegetation changes during the last deglaciation from hanon maar paleolake on jeju island south korea were reconstructed by high resolution multi proxy data pollen anhysteretic remanent magnetization arm total organic carbon toc total nitrogen tn carbon nitrogen c n ratio carbon and nitrogen isotope compositions 15 n and 13 c major element geochemistry and sediment grain size the resolution of our multi proxy data was sufficiently high to enable the detection of millennial and even centennial scale climate change in the study area during the last deglacial transition we found centennial scale cold reversals between 14 650 and 12 900 cal yr bp possibly corresponding to the bolling allerod ba oscillations hanon pollen data implied that climate amelioration around 11 900 cal yr bp terminated the younger dryas yd in the study area and that a cold event around 11 300 cal yr bp probably correlated with the pre boreal oscillation pbo cooling event our results indicate that rising summer insolation and northward expanding low latitudinal warm currents exerted a strong influence on climatological teleconnection via westerlies between the north atlantic and the east asian region during the last deglaciation presumably causing a decoupling between temperature and east asian summer monsoon easm precipitation during the last deglaciation

gravity inversion of 2d basement relief using entropic regularization we have developed a gravity interpretation method for estimating the discontinuous basement relief of a sedimentary basin the density contrast between the basement and the sediments is assumed to be known and it could be either constant or vary monotonically with depth the interpretation model consists of a set of vertical juxtaposed prisms whose thicknesses are the parameters to be estimated we used the entropic regularization that combines the minimization of the first order entropy measure with the maximization of the zeroth order entropy measure of the solution vector we validated the method by applying it to synthetic data produced by a simulated basin bordered by high angle step faults we obtained a good definition of the relief particularly of the discontinuities we also applied the method to a profile across the buyuk menderes valley in west turkey and obtained a solution exhibiting a gravity fault with large slip on the northern border of the valley when applied to the interpretation of a discontinuous basement relief the method has a better performance than the global smoothness method it is comparable to the weighted smoothness method but it does not require the a priori knowledge about the maximum basin depth

gravity inversion of basement relief and estimation of density contrast variation with depth we present a method to estimate the basement relief as well as the density contrast at the surface and the hyperbolic decaying factor of the density contrast with depth assuming that the gravity anomaly and the depth to the basement at a few points are known in both cases the interpretation model is a set of vertical rectangular 2d prisms whose thicknesses are parameters to be estimated and that represent the depth to the interface separating sediments and basement the solutions to both problems are stable because of the incorporation of additional prior information about the smoothness of the estimated relief and the depth to the basement at a few locations presumably provided by boreholes the method was tested with synthetic gravity anomalies produced by simulated sedimentary basins with smooth relief providing not only well resolved estimated relief but also good estimates for the density contrasts at the surface and for the decaying factors of the density contrast with depth the method was ap

determination of crustal interface topography from potential fields we present a method for determination of the topography of an interface separating two uniformly but differently magnetized media the technique is developed within the framework of discrete linear inverse theory and exploits the quasi linearity of the problem to derive a simple efficient algorithm suitable for use on large gridded data sets variation of auxiliary parameters allows a suite of acceptable models to be produced rapidly these parameters can be appraised in light of available geologic and geophysical evidence because very large matrices are involved when large amounts of data are interpreted approximate resolution measures requiring no matrix inversion provide useful information concerning averages of the constructed topography

determination of the crustal and thermal structure of the erzurum horasan pasinler basins eastern turkiye using gravity and magnetic data the erzurum horasan pasinler basin which surrounds miocene rocks is oriented approximately e w and is located in eastern anatolia turkiye east anatolia where ophiolitic and young volcanic rocks are widespread is situated in the alpine himalayan fold thrust fault belt the nw se trending north anatolian transform fault zone and the ne sw trending east anatolian transform fault zone formed by the compressional regime of east anatolia control the main tectonics of the study region while the moho and conrad depths of the study region are 43 0 and 20 9 km respectively the average sedimentary thickness has been determined to be 5 2 km by using the power spectrum method on the other hand it is found that the depth of the moho in the region varies from 41 0 to 44 5 km and the depth of the conrad discontinuity varies between 22 and 26 km as computed using empirical equations the basement of the sedimentary layer is calculated to be 6 km by using inversion results applied to the residual gravity data the curie point depth and average heat flow value in this region are calculated as 18 0 km and 89 1 m wm 2 respectively geotherm calculations reveal that the moho temperature is 1 028 0 c based on the crustal model the high heat flow values obtained are attributed to tectonic activities and melting of the lithospheric mantle caused by upwelling of the asthenosphere

concept of effective density key to gravity depth determinations for sedimentary basins the gravity anomaly observed over a layered sedimentary basin is close to that calculated over a basin with the same configuration and depth but filled by homogeneous sediments with density equal to the effective weighted average density of the real layered basin therefore it is possible to calculate the effective density contrast of a basin from the residual gravity anomaly over it if the depth of the basin is known at least at one point assuming a mathematical function for density depth dependence an expression for the gravity depth dependence using the infinite slab bouguer formula can be developed this expression makes it possible to calculate the depth of a basin or an isopach map from gravity data an exponential function and a new hyperbolic density depth function and their gravity depth functions are analyzed and implemented for determining the depths of basins from gravity data for the san jacinto graben california and the tucson basin southern arizona the hyperbolic functions are m

total variation regularization for depth to basement estimate part 1 mathematical details and applications we have developed an inversion approach that estimates the basement relief of a fault bounded sedimentary basin the sedimentary pack is approximated by a grid of 3d or 2d vertical prisms juxtaposed in the horizontal directions of a right handed coordinate system the prisms thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data to obtain depth to basement estimates we introduce the total variation tv regularization as a stabilizing function this approach lets us estimate a nonsmooth basement relief because it does not penalize sharp features of the solution we have deduced a compact matrix form of the gradient vector and the hessian matrix of the approximation to the tv function that allows a regularized gauss newton minimization approach because the hessian matrix of the approximation to the tv function is ill conditioned we have modified this hessian matrix to improve its condition and to accelerate the convergence of the gauss newton algorithm tests conducted with synthetic data show that the inversion method can delineate discontinuous basements presenting large slips or sequences of small slip step faults tests on field data from the almada basin brazil and from the san jacinto graben california u s a confirm the potential of the method in detecting and locating in depth normal faults in the basement relief of a sedimentary basin

three dimensional gravity or magnetic constrained depth inversion with lateral and vertical variation of contrast depth mapping inversion of gravity or magnetic fields generally assumes that anomalies originate from a main density or magnetization contrast interface this particular inversion takes into account inhomogeneous density or magnetization distributions reflecting sediment compaction and basement heterogeneities above the interface the density can be approximated by an exponential function and below it an intrabasement contrast map can be used the inversion also integrates local depth constraints from wells or seismic data as well as general constraints set on the geometry and the contrast of the interface after field transformations spectral analysis and con straints help to define a starting model characterized mainly by the interface mean depth and the mean parameter contrast between the two media the depth adjustment is completed iteratively under constraints using a space domain formulation derived from the bouguer slab approximation the interface model effect is computed in the wavenumber domain a model data example shows the accuracy of the inversion and illustrates the role of the constraints in a field example of a basin area where constraints can be derived from numerous well data successive inversions of gravity data result in an isodepth map of the basement the compatibility of the map with local depth constraints from wells is obtained by taking into account density heterogeneities related to known lithologic variations in the basement

a new gravity inversion method for multiple subhorizontal discontinuity interfaces and shallow basins 1 we present a method for 3 d gravity inversion designed to obtain density contrast models described by subhorizontal layers limited by irregular discontinuity interfaces and models constituted by shallow basins with light infill it is based on a previously published inversion method that provides in a nearly automatic approach the 3 d geometry of isolated anomalous bodies the basic adjustment constraints are model fitness fitting the anomaly data and model smoothness minimizing the total anomalous mass for models corresponding to subhorizontal layers we consider an additional minimization condition the proximity to prescribed horizontal interfaces this condition is arranged by including an additional weighting inverse proportional to the distance to the interface in the covariance matrix for model parameters the approach works according a growth process that increases step by step the volume of the adjusted anomalous bodies some advantages of the method are simultaneous adjustment of a linear regional gravity trend possibility of including simultaneously positive and negative anomalous structures in the model and unified inversion approach for isolated bodies basins and subhorizontal interface structures we include several simulation examples and an application case layered model for the volcanic island of tenerife

gravity data as a tool for detecting faults in depth enhancement of subtle almada s basement faults brazil we demonstrate the potential of gravity data to detect and to locate in depth subtle normal faults in the basement relief of a sedimentary basin this demonstration is accomplished by inverting the gravity data with the constraint that the estimated basement relief presents local abrupt faults and is smooth elsewhere we inverted the gravity data from the onshore almada basin in northeastern brazil and we mapped several normal faults whose locations and plane geometries were already known from seismic imaging the inversion methoddelineatedwellboththediscontinuitieswithsmallor largeslipsandasequenceofstepfaults usingsyntheticdata weperformedasystematicsearchofnormalfaultslipsversus fault displacement depths to map the fault detectable region inthisspace thismappinghelpstoassesstheabilityofgravityinversiontodetectnormalfaults mappingshowsthatnormalfaultswithsmall0 5 km mediumabout1 km and large about 2 km vertical slips can be detected if the maximummidpointdepthsofthefaultplanesaresmallerthan1 8 3 8 and6 8 km respectively

fast nonlinear gravity inversion in spherical coordinates with application to the south american moho estimating the relief of the moho from gravity data is a computationally intensive non linear inverse problem what is more the modeling must take the earths curvature into account when the study area is of regional scale or greater we present a regularized non linear gravity inversion method that has a low computational footprint and employs a spherical earth approximation to achieve this we combine the highly efficient botts method with smoothness regularization and a discretization of the anomalous moho into tesseroids spherical prisms the computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse the inversion results are controlled by three hyper parameters the regularization parameter the anomalous moho density contrast and the reference moho depth we estimate the regularization parameter using the method of hold out cross validation additionally we estimate the density contrast and the reference depth using knowledge of the moho depth at certain points we apply the proposed method to estimate the moho depth for the south american continent using satellite gravity data and seismological data the final moho model is in accordance with previous gravity derived models and seismological data the misfit to the gravity and seismological data is worse in the andes and best in oceanic areas central brazil and patagonia and along the atlantic coast similarly to previous results the model suggests a thinner crust of 30 35 km under the andean foreland basins discrepancies with the seismological data are greatest in the guyana shield the central solimoes and amazonas basins the parana basin and the borborema province these differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing

gravity inversion of basement relief constrained by the knowledge of depth at isolated points we present an interpretation method for the gravity anomaly of an arbitrary interface separating two homogeneous media it consists essentially of a downward continuation of the observed anomaly and the division of the continued anomaly by a scale factor involving the density contrast between the media the knowledge of the interface depth at isolated points is used to estimate the depth d1 of the shallowest point of the interface the density contrast between the two media and the coefficients c1 and c2 of a first order polynomial representing a linear trend to be removed from data the solutions are stabilized by introducing a damping parameter in the computation of the downward continued anomaly by the equivalent layer method different from other interface mapping methods using gravity data the proposed method 1 takes into account the presence of an undesirable linear trend in data 2 requires just intervals for both rather than the knowledge of its true value and coefficients c1 and c2