On the calculation of vertical derivatives of potential fields for downward continuation and related filters

A three-dimensional inversion technique is developed to investigate the structure of the oceanic crust, using high quality offshore bathymetry, gravity and seismic data. The gravity signatures associated with variations in the thickness of the oceanic crust are isolated from the observed free-air anomaly by subtracting the gravitational effects of seafloor topography and the upper mantle thermal structure, downward continued to the mean depth of the crust/mantle interface and converted onto the relief on that surface. The thickness of the oceanic crust is then calculated by subtracting sea water depth from the depth of the gravity-inferred crust/mantle interface. Seismic refraction data was introduced directly as a constraint in the construction of the initial model for the configuration of the crust/mantle interface and the iterative process of the 3- D joint inversion to reduce the ambiguity in gravityinterpretation. This technique can be easily applied to the off-shore areas to interpret bathymetry, gravity and seismic data that have been routinely collected for the purpose of geophysical exploration. Compared to the unconstrained gravity inversion, this technique can predict a 3-D crustal model that fits better both gravity and seismic observation data of the study area. Introduction The non-uniqueness is an inherent problem in gravity inversion: the observed gravity field cannot be inverted to obtain a unique subsurface structure, unless some additional restrictions are imposed'. The ambiguity in gravity interpretation may he reduced by placing bounds on the density contrast and depth of the subsurface structure, which can be determined by applying certain physical principles. In the present study we propose a method to use seismic data to constrain the depth and configuration of a subsurface density discontinuity in a 3-D gravity modeling. The results of the seismically constrained gravity interpretation are in good agreement with seismic results, and the misfit of the predicted gravity field to the observed does not increase. Methodology The method is simple in principle: in a study area where both seismic and gravity data are available, we use seismic data to construct a framework for gravity modeling, and use gravity inversion technique to resolve the details of the configuration and depth of the subsurface density discontinuity. The implementation of the method may include the following steps. In the initial model for a subsurface interface, those points (nodes) that follow the projections of the seismic profiles are given the depths determined in seismic refraction (or reflection) surveys. Other points on the interface may be chosen at a constant depth (e.g., the average depth of the interface in the area, or the mean value of !he seismic depths). Doing so may introduce discontinuity, or the artificial impulse-shaped variations, to the configuration of the interface. To solve this problem we further CU1several narrow bands on that interface, These narrow hands are centered by the projections of the seismic profiles.

In some oilfields with 3D seismic data, the deeper structure cannot be observed due to poor quality deep seismic data. Layer stripping using both seismic and gravity data is a solution for this problem but it cannot get satisfactory results because the horizontal variations in formation density are ignored. We present a variable-density formation separation technique to address this problem. Based on 3D seismic depth data and laterally-variable density derived from 3D seismic velocity data, the upper formation gravity effect is calculated by forward modeling and removed from the Bouguer gravity. The formation-separated gravity anomaly with variable density is obtained, which mainly reflects the deeper geological structure. In block XX of North Africa, the shallow formations seismic data is excellent but the data at the top of basement is poor. The formation-separated gravity anomaly processed under the control of 3D seismic data fits well with the known seismic interpretation and wells. It makes the geological interpretation more reliable.

Imaging Pleistocene volcanic edifices along the Egyptian Red Sea margin: Insights from reflection seismics and 3D constrained inversion of gravity and magnetic data

Gravity and magnetic surveys were used to delineate potential gold mineralization zones in the Sefwi belt of Ghana. The study area is an intrusive dominated area that hosts pockets of small scale mining operations locally referred to as Galamsey. These Galamsey operations are not guided by a scientific approach to back the trend of gold mineralization which is conventionally mined. The study aimed at mapping lithological units, structural setting and relating Galamsey sites to delineate potential zones of gold mineralization. A Scintrex CG5 gravimeter and GEM's Overhauser magnetometer were used for gravity and magnetic data acquisition respectively. The magnetic data were corrected and enhancing filters such as reduction to the pole (RTP), analytical signal and first vertical derivative were applied using Oasis montaj 7.1. Gravity data were also reduced to the geoid using the Oasis montaj software to produce a complete Bouguer anomaly map. The regional/residual separation technique produced a residual gravity map. The RTP and analytical signal filters from the magnetic data and residual gravity anomaly map from the gravity data helped in mapping belt type (Dixcove) Birimian granitoids and mafic intrusive unit, interpreted as gabbro. The first vertical derivative filter was useful in mapping NE/SW minor faults and crosscutting dykes largely concentrated in the belt type Birimian granitoids. All the three mapped Galamsey sites fell on a minor fault and are associated with the belt type granitoids which were used in delineating four potential zones of gold mineralization.

High resolution marine gravity data and 3D post-stack seismic data from the central North Sea have been jointly interpreted. The accuracy of the gravity data allowed the detection of density contrasts related to a Quaternary sub-glacial melt-water channel, a shallow gas accumulation and a Tertiary gas chimney. The combination of gravity and seismic data is shown to particularly improve the detection of the shallow gas accumulation. The interpretation included visual correlation of gravity images and seismic data performed in a seismic workstation environment, as well as 2.5D gravity modelling along selected seismic profiles. The successful application of this method on shallow targets requires a limited complexity of the shallow strata as well as targets defined by a distinct density contrast and a reasonable size. Data requirements include high-resolution bathymetric and free air gravity data. Bouguer gravity data, which are commonly used in exploration, cannot be used here as densities may vary within the uppermost layer below the sea bottom.

In this paper an approach aimed at integrating many different geophysical/geological data is discussed. It is based on a recursive process of forward and inverse modelling of seismic and non-seismic data. The experimental data set of the Enhanced Seismic In Thrust belts (ESIT) research project, funded by Eni E&P, Enterprise Oil Italiana and the European Union, was used in order to apply the approach to a real case of complex geological setting. Near-vertical reflection seismic, long-offset seismic, high-resolution magnetotelluric, gravity, borehole and surface geological data were involved in the process. We demonstrate how a ‘self-feeding’ integration loop is an efficient way to produce a unique geophysical model that responds to several basic requirements, such as optimized inversion/modelling in each parameter space, best fit in each geophysical domain, best seismic imaging, reliable geological meaning and cost/benefit ratio optimization. Introduction Integration of multiple data sets in complex geological settings represents one of the most challenging objectives in geophysics. This is true especially in the case of geophysical projects based on the acquisition of highly redundant data sets and characterized by many different sources of information. In fact, particularly in complex areas where the quality of standard seismic is poor, alternative non-seismic approaches are required. An exploration strategy based on many different and complementary methodologies always produces a complex data set, and integrating all the information in consistent and reliable models can fail if an appropriate integration strategy is not applied. In previous work (Dell'Aversana & Morandi 2000, 2002; Dell'Aversana 2001), we introduced an integration approach based on recursive forward and inverse modelling of seismic, magnetotelluric and gravity data. We showed that the so- called ‘global offset’ seismic approach (which also includes high-fold, long-offset data) can improve significantly the process of building reliable models by a quantitative integration with MT and gravity data and with the support of borehole information. In a subsequent paper (Dell'Aversana et al. 2002b), we demonstrated how, by applying prestack depth migration to global offset data, it is possible to improve the depth imaging in difficult geological settings, also when the S/N ratio of the conventional near-vertical reflection data is very low. This result can be obtained especially if non-seismic data are used for defining accurate multi-parametric models. These models can contribute to the definition of an appropriate velocity field for seismic data migration, as will be clarified in this paper. In fact, recent experiments and applications showed how the continuous profiling magnetotelluric method can produce reliable resistivity sections that can support both the velocity field definition and the geological interpretation in case of low-quality seismic sections (Zerilli & Dell'Aversana 2002). Here, we continue the discussion about the integration of many data sets, but also introduce several important additional concepts. We take the opportunity offered by the large multiple data set collected during the ESIT research project (Buia et al. 2002; Dell'Aversana et al. 2002b). We demonstrate that an appropriate quantitative integration of global offset seismic, continuous profiling high-resolution magnetotelluric (HRMT), gravity, borehole and geological data is a reliable and cost-effective process. Each source of information contributes to different aspects of the process, due to the varying benefits and limitations of each of the different methodologies used. Based on many different geophysical parameters, the final result is a well-calibrated model that is consistent with the best seismic imaging. The geological consistency is considered as a fundamental requirement at each step of the process.

Near-surface flood volcanics can create havoc when attempting geophysical imaging and geological understanding of the sub-surface. Abrolhos Bank, offshore Brazil, is one such area, and recent licensing of offshore blocks nearby or on the Banks has increased the economic stake in this problem. Extensive 3 dimensional modeling has been conducted using recently acquired marine seismic, gravity and magnetics data. Integrated geophysical analysis of these complimentary datasets has greatly improved our understanding of the extent of the flood basalts, as well as the thickness of the sub-volcanic sediments and the basement structure. No single one of these geophysical methods would have given us all this information in isolation: only the joint use of all three methods allowed the full range of interpretation. We interpreted the seismic data together with magnetic depth estimation techniques to constrain the depth to basement. We inverted on the gravity data in 3 dimensions to produce an isopach of the basalt, which was in turn constrained with the seismic and magnetic data interpretation. We have considered the important question of the source of the flood basalts: we found no evidence of basaltic feeder dikes in any of the magnetic, gravity or seismic data in the area, so a distal source seems most likely.

<p>Combining two or more geophysical datasets with different resolutions and characteristics is now a common practice to recover one or more physical properties. Building 3D geological models for mineral exploration targeting is often an expensive task even for inversion of a single dataset, because of extremely complicated structures with small scale targets. In this context, seismic methods, among all other traditional techniques in mineral exploration, are receiving increasing attention due to their higher resolution in depth. With more limited spatial coverage and higher resolution, they are usually used to refine the interpretation of potential field data.</p><p>As each seismic survey is designed for a particular intention with specific targets and may not be available in all regions of interests, we develop an iterative cooperative inversion algorithm for inverting gravity and seismic travel-time data. This enables the utilization of localized high-resolution seismic data in a larger full 3D volume which is covered by gravity data. Geological information in the form of probabilistic geological modelling is used to extend information away from the high-resolution data and constrain the inversion result. We use these data as the prior model and to derive constraints incorporated into the objective function of gravity inversion. This allows us to obtain information about the probability of the presence of lithologies associated with the formation of mineral systems. To ensure structural consistency between density and velocity we develop a geologically constrained structure-based coupling technique following the same principle as the cross-gradient technique but with a higher degree of freedom in spatial directions. We apply local structure-based constraints conditioned by a geological probability distribution, which is considering direction and magnitude and provide a higher degree of freedom for model variations. An investigation of the proposed methodology and a proof-of-concept using realistic synthetic data are presented. Our results reveal that the methodology has the potential to constrain the gravity inversion results using the limited seismic data.</p>

The IGRF-corrected 2009 aeromagnetic data over the Lower Benue and Upper Anambra basins Nigeria was subjected to both Vertical and Horizontal Derivatives, Analytical Signal and CET grid analysis, these digital processing tools were achieved both on map and profile analysis. From the analysis of both the Vertical and Horizontal Derivatives the study area could be divided into two regions based on the degree of distortion to the magnetic signatures the Northern and the Western edge of the area is covered by short wavelength magnetic anomalous signatures that are the characteristic of outcrop and shallow intrusive magnetic bodies, while the remaining part of the study area is characterized by medium to long wavelength magnetic signatures that are attributes of deep sited magnetic rocks in areas of medium to thick sedimentations. Result of the Analytical Signal which is in local amplitude reveals regions with outcrop of magnetic rocks having amplitudes ranging from 0.230 to 0.40 (shown as pink color), area with magnetic rock intruding into sedimentary formations at shallow depths, with amplitudes ranging from 0.094 to 0.229 cycles (shown as red color), while regions with magnetic rock intruding into sedimentary formations at greater depths, having very low amplitudes ranging from -0.085 to 0.055 cycles (shown in yellow to green color). Analyses due to CET grid analysis equally reveal the basement rocks to the North and Southern edge of the study area. Intrusions into the sedimentary formation are also revealed. The research discovered that the lower (southern) part of the area (on Angba and Otukpo area) shows structures (Basaltic rocks) that intrude into the basement which could have predate the sedimentation period, several fracture and fault lines are detected on the CET map, most prominent among them is that at the Southeastern corner of the area which trends NE-SW which can be attributed to an onshore extension of Charcots fault zone , and that which trends N-S is a fault line that controls the course of River Niger. These three features are responsible for the depressions where sediments can accumulate.

Applications of Machine Learning to the geosciences are increasing in numbers during the last two decades because of its computation power. In this work we propose a method to estimate the basement depth from gravity data using a supervised machine learning approach. We used the Bishop synthetic model to represent a variety of examples of input – target (i.e., gravity data – depth of the basement) training dataset. We so generated a large set of examples, using an overlapping moving window along the profiles in the N-S and E-W direction, associating the corresponding depth values of the basement to each of the windows. Due to its data-driven nature, the neural networks perform better as the number of examples provided in the training phase increases. However, increasing the number of examples leads to a higher computational cost in terms of speed and hardware needed. In the Big Data era this is not a huge issue, thanks to the increasingly present services of cloud computing. We found a good compromise on an average machine between speed and performance by using about 300k examples. A trial-and-error approach was used to find the hyperparameters that have the best compromise between performance and computation time.We used, as a testing dataset, the gravity data due to a surface modelled from the Himalaya region DEM, with noisy and noise-free data. We found that this avoided overfitting and helped to verify the ability of the trained network to generalize to other cases, even with noisy data. The method was successfully applied also to a real dataset case: the isostatic anomaly of the Yucca Flat sedimentary basin (Nevada, USA) showing good agreement with previous inverse-modelling of the data, even if the author consider a set of layers with increasing density vs. depth, while in our case we used a mean density contrast of -0.7 g/cm3.

Substantial progress has been achieved over the last four decades to better understand a deep structure in the Himalayas and Tibet. Nevertheless, the remoteness of this part of the world still considerably limits the use of seismic data. A possible way to overcome this practical restriction partially is to use products from the Earth’s satellite observation systems. Global topographic data are provided by the Shuttle Radar Topography Mission (SRTM). Global gravitational models have been derived from observables delivered by the gravity-dedicated satellite missions, such as the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE). Optimally, the topographic and gravity data should be combined with available results from tomographic surveys to interpret the lithospheric structure, including also a Moho relief. In this study, we use seismic, gravity, and topographic data to estimate the Moho depth under orogenic structures of the Himalayas and Tibet. The combined Moho model is computed based on solving the Vening Meinesz–Moritz (VMM) inverse problem of isostasy, while incorporating seismic data to constrain the gravimetric solution. The result of the combined gravimetric-seismic data analysis exhibits an anticipated more detailed structure of the Moho geometry when compared to the solution obtained merely from seismic data. This is especially evident over regions with sparse seismic data coverage. The newly-determined combined Moho model of Tibet shows a typical contrast between a thick crustal structure of orogenic formations compared to a thinner crust of continental basins. The Moho depth under most of the Himalayas and the Tibetan Plateau is typically within 60–70 km. The maximum Moho deepening of ~76 km occurs to the south of the Bangong-Nujiang suture under the Lhasa terrane. Local maxima of the Moho depth to ~74 km are also found beneath Taksha at the Karakoram fault. This Moho pattern generally agrees with the findings from existing gravimetric and seismic studies, but some inconsistencies are also identified and discussed in this study.

Near surface conditions in Saudi Arabia represent the major challenge for acquisition of reliable and meaningful land seismic data. In Saudi Aramco, a major effort is underway to investigate the benefits of integrating gravity and electromagnetic data with seismic data to better estimate near surface velocities for processing large 3D seismic volumes. In 2010 a gravity and electromagnetic acquisition program was carried out in three areas characterized by different near surface geologic conditions. The type of methodologies being employed consist of dedicated high-end electromagnetic and gravity acquisition specifications, geophysical data integration via simultaneous joint inversion, and seismic processing with advanced imaging workflows such as pre-stack redatuming (time) and pre-stack depth migration. Well log analysis in shallow boreholes provides the local petrophysical relationships among velocity, resistivity and density to be used in a simultaneous joint inversion scheme. Given the shallow targets, the resolution offered by the electromagnetic and gravity data is typically within the wavelength of the velocity anomalies affecting seismic imaging. Therefore, near surface non-seismic data act as an ideal complementary dataset to seismic. Results obtained to date reveal density and resistivity anomalies correlated with regions of poor seismic data quality. EM and gravity data analysis and inversion are being carried out in a singledomain approach as well as by applying quantitative simultaneous joint inversion schemes with seismic travel-time data. The generated near surface multi-parameter models are used to correct the seismic data with successive reprocessing in time and depth domains. Encouraging results are being observed from the reprocessing indicating that the multi-physics data and the quantitative integration schemes are succeeding in addressing the near surface velocity estimation problem.

The enhancement of potential field data using filters based on horizontal and vertical derivatives is common. As well as the direct use of the gradients themselves they are used in filters such as sunshading, total horizontal derivative, analytic signal, horizontal and vertical tilt angles, the Theta map and other filters. These techniques are high-pass filters of different types and so enhance noise as well as detail in the data. A new derivative operator is introduced in this paper, which generalizes the effects of some of the previously mentioned filters. This filter is a linear combination of the horizontal and vertical field derivatives, normalized by the analytic signal amplitude. The filter is demonstrated on aeromagnetic and gravity data from South Africa.

The Bawean fault is one of the faults that needs to be watched out for because it is located in the north of Madura Island, which has a population of up to millions of people. One of the mitigation measure that can be taken is the mapping of Bawean Fault to determine characteristics of Bawean Fault. In this research, Bawean Fault mapping was conducted using derivative analysis with gravity data from TOPEX website in the form of FAA (Free Air Anomaly) data. That data, then processed to obtain FHD (First Horizontal Derivative) to determine suspected fault line and SVD (Second Vertical Derivative) value to determine fault mechanism. The steps to obtaining the FHD ((First Horizontal Derivative) value and SVD (Second Vertical Derivative) value are determining the average density using Nettleton method separating regional and residual anomalies using the moving average method, processing regional anomalies with derivative analysis until the FHD (First Horizontal Derivative) and SVD (Second Vertical Derivative) maps are obtained. An cross section was then made on the suspected fault line to determine the exact fault line and fault mechanism. The results obtained from the FHD (First Horizontal Derivative) and SVD (Second Vertical Derivative) map incisions show that the Bawean Fault has a mechanism of thrust fault. However, by considering various sources, it can be concluded that the Bawean Fault has an oblique fault mechanism with the influence of a thrust mechanism.

Approximating the locations and lateral boundaries of anomalous bodies (i.e. geological structures or contacts) is an important task in the interpretation of gravity field data. Edge-approximating algorithms based on the computation of directional derivatives are widely used for enhancing the gravity anomalies of the source bodies. These algorithms effectively aid geological mapping and interpretation by locating abrupt lateral changes in density, and may also bring out subtle details in the data without specifying any prior information about the nature and type of the sources. Therefore, some model parameters of source bodies may be estimated in this way, which may guide the inverse modelling procedure. In this paper we aim to review the effectiveness of the commonly used edge-approximating algorithms such as vertical derivative, total horizontal derivative, analytic signal, profile curvature, tilt angle and theta map in terms of their accuracy on the determination of locations and lateral boundaries of source bodies. These detections were performed on both noise-free and noisy synthetic gravity data. Additionally, a real gravity data set from a well-known geological setting, the Aegean graben system (western Turkey), was considered and the derived anomaly maps were compared with known mapped geology.