Inversion Of Anomalies Research Articles

Non‐linear stochastic inversion of gravity data via quantum‐behaved particle swarm optimisation: application to Eurasia–Arabia collision zone (Zagros, Iran)

ABSTRACTPotential field data such as geoid and gravity anomalies are globally available and offer valuable information about the Earth's lithosphere especially in areas where seismic data coverage is sparse. For instance, non‐linear inversion of Bouguer anomalies could be used to estimate the crustal structures including variations of the crustal density and of the depth of the crust–mantle boundary, that is, Moho. However, due to non‐linearity of this inverse problem, classical inversion methods would fail whenever there is no reliable initial model. Swarm intelligence algorithms, such as particle swarm optimisation, are a promising alternative to classical inversion methods because the quality of their solutions does not depend on the initial model; they do not use the derivatives of the objective function, hence allowing the use of L1 norm; and finally, they are global search methods, meaning, the problem could be non‐convex. In this paper, quantum‐behaved particle swarm, a probabilistic swarm intelligence‐like algorithm, is used to solve the non‐linear gravity inverse problem. The method is first successfully tested on a realistic synthetic crustal model with a linear vertical density gradient and lateral density and depth variations at the base of crust in the presence of white Gaussian noise. Then, it is applied to the EIGEN 6c4, a combined global gravity model, to estimate the depth to the base of the crust and the mean density contrast between the crust and the upper‐mantle lithosphere in the Eurasia–Arabia continental collision zone along a 400 km profile crossing the Zagros Mountains (Iran). The results agree well with previously published works including both seismic and potential field studies.

Analysis of self-potential anomalies due to 2D horizontal cylindrical structures—an artificial neural network approach

The application of artificial neural network committee machine (ANNCM) for the inversion of self-potential anomalies caused by a long 2D horizontal circular cylinder is presented. ANNCM inversion extracts the parameters of the source including depth to the center of the cylinder(z), the angle between the horizontal axis and the axis of polarization(α), and the constant term(A) involving the current polarization (I) and resistivity of the earth(ρ). The inversion is demonstrated on theoretical models with and without random noise in order to study the effect of noise on the method and then extended to real field data. The ANNCM analysis of self-potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey, has shown satisfactory results in comparison with other inversion techniques that are in vogue.

Fourier forward modeling of vector and tensor gravity fields due to prismatic bodies with variable density contrast

Prismatic bodies with variable density contrasts are very useful in modeling and inversion of gravity anomalies for sedimentary basins, in which some simple mathematical functions offer better approximations for the density-depth relationship of the basin fill than a constant density model. We have explored Fourier-domain modeling of vector and tensor gravity anomalies due to 2D and 3D prismatic bodies following a wide class of variable density functions. We placed the emphasis on general polynomial models because they provided a flexible way to approximate arbitrary density functions. The recently proposed Gauss-fast Fourier transform method was applied to improve the accuracy of inverse Fourier transform. The numerical performance of the presented method was examined by comparing with space-domain analytical, seminumerical, or completely numerical solutions. Singularity and numerical stability of the algorithm were also analyzed with ranges of numerical stability for polynomial density models of different orders specified. Truncation errors of Fourier forward methods were estimated quantitatively using relevant model parameters, and the behavior was observed through theoretical analysis and model tests. Synthetic models, of 2D and 3D prisms with variable density contrasts, found the accuracy, efficiency, and flexibility of the method. We also interpreted a real data example of the gravity profile across the San Jacinto graben.

Crust and mantle lithospheric structure of the Iberian Peninsula deduced from potential field modeling and thermal analysis

We investigate the lithospheric structure of the Iberian Peninsula and lateral crustal density variations using a three-step approach. First the crustal and mantle lithosphere thicknesses are calculated from joint geoid and elevation modeling combined with thermal analysis further constrained by seismic data. We then compute the 3D gravity effect of the resulting lithospheric structure to separate the measured Bouguer anomaly into its regional and local components. Finally we invert the residual gravity anomalies to highlight lateral average crustal density variations and discuss them in terms of crustal structures. Our results show that for the majority of the study area the crustal thickness does correlate with the regional topography pattern. The highest topography – above 1500m – shows thicknesses above 44km with local values up to 48km. Crustal thicknesses in the range of 36–40km are obtained in the uplifted Alpine areas while a thinner crust is observed in sedimentary basins and in the Iberian Massif (30 to 35km) with the exception of SW Iberia region where the crust thins from 30 to 28km. Thick lithosphere – above 140km – is found along the Pyrenees, the Cantabrian Mountains, the Iberian Chain and in the Betics while the thinnest lithosphere is found in SW Iberia (90km). 3D inversion of residual anomalies show that for the majority of the area the average density of the crust is in the range of 2810±10kgm−3. The denser crust is found in the NW and SW regions of the Iberian Massif (+30kgm−3 on average) and locally in the Pyrenees (above +70kgm−3), NW of the Iberian Chain (+15kgm−3 on average) and in the southern Internal Betics (+70kgm–3). The least dense crust is found in the central and western Betic Chain (−30kgm−3 on average) and in sedimentary basin depocenters.

A new approach for density contrast interface inversion based on the parabolic density function in the frequency domain

Density contrast interface inversion is one of the primary subjects in gravity fields for understanding the Earth's interior structure. In this paper, we presented a new 3D approach for density contrast interface inversion based on the parabolic density function in the frequency domain. The Parabolic density function is adopted to better reflect the real density structure in the subsurface. And the frequency-domain algorithm is utilized to enhance computational efficiency of the forward modeling and inversion. We first derived formula of the frequency-domain parabolic density function, and then presented its procedure for forward modeling and inversion of gravity anomalies to determine density interfaces underground. We also proposed the related techniques for determining the model density parameters and the referencing datum depth, as well as for accelerating convergence. The synthetic data test demonstrated that the new approach and its related techniques are effective and reliable. Finally, we utilized the new approach to obtain the Moho depth distribution in the Sichuan–Yunnan region, China. The result of our approach is consistent well with that from the receiver function, and is better than that from the conventional constant density function approach.

Estimation of multiple density-depth parameters from gravity inversion: Application to detached hanging wall systems of strike limited listric fault morphologies

An inversion algorithm is developed to simultaneously estimate the fault plane geometry and the parameters pertaining to either densities or depths of multiple geologic formations within the hanging wall system of a strike-limited listric fault from the observed gravity anomalies. Fault planes of the structures are described by polynomial functions of arbitrary but specific degree. The applicability of the algorithm is demonstrated on both synthetic and real field gravity anomalies. In the synthetic example, pseudorandom noise is added to the gravity anomalies of the structure prior to inversion. From the inversion of gravity anomalies produced by a synthetic structure it was found that the estimated parameters more or less mimic the true parameters even in the presence of random noise. The estimated densities and depths of the formations from independent inversion of real-world gravity anomalies from the margin of the Chintalpudi sub-basin in India correlate well with the available drilling information.

Three‐Dimensional Density Structure of North China's Craton Crust and Its Geological Implications

AbstractOne of the goals of geological interpretation on gravity anomalies is to reveal three‐dimensional density structure of the earth's crust, for which density inversion is crucial. This paper presents multiple‐scale density inversion of gravity anomalies. Firstly wavelet transform is employed to decompose gravity anomalies. Secondly, power spectrum analysis is performed to estimate the average depth of the field source for each layer, and then the generalized density inversion method is used to calculate the depth of each layer. Finally, such multi‐scale density inversion is conducted for the North China region, resulting in the density structure of its crust. The results demonstrate that this approach is effective. The followed analysis indicates that low density anomalies in orogenic belts mainly reflect the granite bodies distributed there. In comparison with shallow density disturbance in eastern North China, depressions bearing oil and gas seem to have low‐density anomalies of small amplitude. It implies that the density information extracted by wavelet multi‐scale inversion has some guiding significance for deployment of oil and gas exploration.

Three-dimensional density interface inversion of gravity anomalies in the spectral domain

Based on the Fourier transform, the Parker–Oldenburg algorithm in the frequency domain was extended for the three-dimensional case where the density changes with depth. From this, a gravity interface inversion formula was derived in which the assumed density can be varied laterally and vertically. Iterative convergence is assured by fixing a particular depth as the datum plane below the surface to reduce the interface fluctuation. The results of an example set of synthetic gravity data indicate that the proposed method gives high precision and rapid convergence, with high practical value for the inversion of density interfaces. This method was also used to determine the Moho depth beneath northern China. The results were confirmed by seismic sounding data. Differences between seismic sounding data and inverted depth were insignificant and were in the range of −0.92–1.67 km.

Modeling 3‐D density distribution in the mantle from inversion of geoid anomalies: Application to the Yellowstone Province

AbstractWe developed a three‐dimensional scheme to invert geoid anomalies aiming to map density variations in the mantle. Using an ellipsoidal‐Earth approximation, the model space is represented by tesseroids. To assess the quality of the density models, the resolution and covariance matrices were computed. From a synthetic geoid anomaly caused by a plume tail with Gaussian noise added, the inversion code was able to recover a plausible solution about the density contrast and geometry when it is compared to the synthetic model. To test the inversion algorithm in a natural case study, geoid anomalies from the Yellowstone Province (YP) were inverted. From the Earth Gravitational Model 2008 expanded up to degree 2160, lower crust‐ and mantle‐related negative geoid anomalies with amplitude of approximately 70 m were obtained after removing long‐wavelength components (>5400 km) and crustal effects. We estimated three density models for the YP. The first model, the EDM‐1 (estimated density model), uses a starting model with density contrast equal to 0. The other two models, the EDM‐2 and EDM‐3, use an initial density derived from two S‐velocity models for the western United States, the Dynamic North America Models of S Waves by Obrebsky et al. (2011) and the Northwestern United States Teleseismic Tomography of S Waves (NWUS11‐S) by James et al. (2011). In these three models, a lower and an upper bound for the density solution was also imposed as a priori information. Regardless of the initial constraints, the inversion of the residual geoid indicates that the lower crust and the upper mantle of the YP have a predominantly negative density contrast (~ −50 kg/m3) relative to the surrounding mantle. This solution reveals that the density contrast extends at least to 660 km depth. Regional correlation analysis between the EDM‐1 and NWUS11‐S indicates an anticorrelation (coefficient of ~ −0.7) at 400 km depth. Our study suggests that the mantle density derived from the inversion of geoid could be integrated with seismic velocity models to image mantle anomalous features beyond the depth limit of investigation achieved combining gravity and seismic tomography. ©2013. American Geophysical Union. All Rights Reserved.

Forward modelling and inversion of self-potential anomalies caused by 2D inclined sheets

Self-potential anomalies observed over sulfide ore bodies can be closely associated with electrochemical reactions and the ohmic potential drop within the rocks. Self-potential surveys based on laboratory measurements of electrochemical potentials allow us either to measure the amplitude of the anomalies generated by this mechanism or to determine the model parameters. In order to achieve these goals, two sheets of zinc and copper were joined together to simulate sheet-like ore bodies. Self-potential surveys were conducted over 684 electrodes with the purpose of revealing the influence of various angles of the sheet. In a laboratory experiment, four different inclinations were chosen to perform the forward modelling. The last part of this paper involves the inversion of measured data to recover the distribution of generated self-potential signals. The inversion results show a satisfactory agreement with the laboratory measured data. Finding the geometry of the buried source from the shape of the SP response is not intended as it is fixed in advance. The first aim of this paper is to show how the SP response is affected under the presence of a 2D conductive structure (sheet-like) in tank experiments. The second aim is to obtain one of the model parameters (coefficient M) using data regression.

Structural interpretation of the Erzurum Basin, eastern Turkey, using curvature gravity gradient tensor and gravity inversion of basement relief

article i nfo The Erzurum Basin has received more attention in petroleum potential research because of its particularity in geographic and tectonic position. There remains debate on the basement structure of the basin since igneous rocks and faults make the structure and stratigraphy more complicated. We utilize gravity data to understand the structure of the Erzurum Basin. This study describes an edge enhancement technique based on the eigen- values and determinant obtained from the curvature gravity gradient tensor (CGGT). The main goal of this technique is to delineate structural boundaries in complex geology and tectonic environment using CGGT. The results obtained from theoretical data, with and without Gaussian random noise, have been analyzed in determining the locations of the edges of the vertical-sided prism models. The zero contours of the smallest eigenvalue delineate the spatial location of the edges of the anomalous sources. In addition, 3-D gravity inversion of Bouguer anomalies has been used with purpose to estimate the structure of the substrata to allow modeling of the basement undulation in the Erzurum basin. For this reason, the Parker-Oldenburg algorithm helped to investigate this undulation and to evidence the main linear features. This algorithm re- veals presence of basement depths between 3.45 and 9.06 km in the region bounded by NE-SW and E-W trending lineaments. We have also compared the smallest eigenvalue zero contours with the HGM images and Tilt derivative (TDR) of Bouguer anomaly map of the study area. All techniques have agreed closely in detecting the horizontal locations of geological features in the subsurface with good precision.

Inversion of self-potential anomalies caused by simple-geometry bodies using global optimization algorithms

Three naturally inspired meta-heuristic algorithms—the genetic algorithm (GA), simulated annealing (SA) and particle swarm optimization (PSO)—were used to invert some of the self-potential (SP) anomalies originated by some polarized bodies with simple geometries. Both synthetic and field data sets were considered. The tests with the synthetic data comprised of the solutions with both noise-free and noisy data; in the tests with the field data some SP anomalies observed over a copper belt (India), graphite deposits (Germany) and metallic sulfide (Turkey) were inverted. The model parameters included the electric dipole moment, polarization angle, depth, shape factor and origin of the anomaly. The estimated parameters were compared with those from previous studies using various optimization algorithms, mainly least-squares approaches, on the same data sets. During the test studies the solutions by GA, PSO and SA were characterized as being consistent with each other; a good starting model was not a requirement to reach the global minimum. It can be concluded that the global optimization algorithms considered in this study were able to yield compatible solutions with those from widely used local optimization algorithms.

An Algorithm for Gravity Anomaly Inversion in HPC

In the paper we analyse results from the inversion of geophysical anomalies in high performance computing platforms. We experiment the solution of this ill-posed problem, trying to bypass the complexity of the calculations using simple algorithms that require huge calculation capacities offered by parallel systems. The gravity anomalies are considered because of the simplicity of the gravity modeling in geophysics.

Inversion of anomalies due to remanent magnetisation: an example from the Black Hill Norite of South Australia

There has been a recent renewal of interest in estimation of magnetisation direction for improved magnetic field interpretation. In this study we review practical issues of recovering magnetisation direction using magnetic moments of the causative body. We also investigate the recovery of magnetisation directly from multi-stage inversion of magnetic field data. We apply these methods to the well-studied magnetic anomalies over the Black Hill Norite of South Australia. Both magnetic moment analysis and inversion recover consistent magnetisation directions, and these can be used in further studies to estimate geological structure. The magnetisation directions agree closely with measured remanent magnetisation directions. This implies that the anomalies are principally due to the remanence of a high Koenigsberger ratio (Q).

Euler deconvolution of gravity anomalies from thick contact/fault structures with extended negative structural index

The concept of extended Euler homogeneity of potential fields is examined with respect to all variables of length dimension in their analytical expressions. This reveals the possible existence of positive degrees of homogeneity or corresponding negative structural indices considered as extensions of the Thompson’s structural indices in Euler deconvolution. This approach is implemented for a contact gravity model, represented by a 2D semi-infinite slab with large thickness relative to its depth. Applying Euler deconvolution on synthetic and field data indicates that the positive degree of homogeneity, i.e., the extended negative structural index, is the appropriate one for the inversion of gravity anomalies from contact structures.

Interpretation of spontaneous potential anomalies from some simple geometrically shaped bodies using neural network inversion

A new approach is proposed in order to interpret spontaneous potential (self-potential) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on using neural network inversion of SP anomalies, particularly modular algorithm, for estimating the parameters of different simple geometrical bodies. However, Hilbert transforms are involved to determine the origin location in order to reduce the parameters which minimize the ambiguity in the inverted models. The inversion has been tested first on synthetic data from different models, using only one well-trained network. The results of inversion show that the parameter values derived by the inversion are identical to the true values of parameters. Noise analysis has been also examined, where the results of the inversion produce acceptable results up to 10% of white Gaussian noise. The validity of the neural network inversion is demonstrated through published real field SP taken from southern Bavarian Woods, Germany. A comparable and acceptable agreement is shown between the results of inversion derived by the neural network and those from the real field data.

Inversion of self-potential anomalies caused by 2D inclined sheets using neural networks

The modular neural network (MNN) inversion method has been used for inversion of self-potential (SP) data anomalies caused by 2D inclined sheets of infinite horizontal extent. The analysed parameters are the depth (h), the half-width (a), the inclination (α), the zero distance from the origin (xo) and the polarization amplitude (k). The MNN inversion has been first tested on a synthetic example and then applied to two field examples from the Surda area of Rakha mines, India, and Kalava fault zone, India. The effect of random noise has been studied, and the technique showed satisfactory results. The inversion results show good agreement with the measured field data compared with other inversion techniques in use.

The three-dimensional lithospheric structure of the Falkland Plateau region based on gravity modelling

The lithospheric structure of the Falkland Plateau region has been modelled by making an initial estimate on the basis of local isostasy and then refining the geometries by inversion of gravity anomalies. The model predicts a crustal thickness beneath the Falkland Plateau Basin that is more than twice that previously inferred from seismic evidence. The preferred explanation is that the seismic survey detected high-velocity (?underplated) lower crust rather than upper mantle. This is compatible with the results of deep seismic experiments over the conjugate Filchner Block of Antarctica and also appears likely on the basis of the position of the Falkland Plateau Basin in relation to the Karoo–Ferrar magmatic province at the time of extension. Continental crust is inferred to be continuous beneath the northern part of the Falkland Plateau, as there are consistent magnetic and flexural anomalies associated with the continent–ocean boundary. Flexural modelling of the southern margin of the plateau indicates lateral variations in strength, with the strongest lithosphere beneath the Falkland Plateau Basin. This may indicate thick oceanic crust beneath the southern part of the basin or the effect of thinning relatively weak continental crust and replacing it with relatively strong underplating.

An Inversion of Gravity Anomalies by Using a 2.5 Dimensional Rectangle Gridded Model and the Simulated Annealing Algorithm

AbstractIn accordance with the present state of gravity anomaly inversion, we use the 2.5 dimensional model construction method to divide the underground density structure into rectangle gridded units to simulate density models with arbitrary interfaces or bodies, then perform gravity forward modeling. This model construction is flexible and adaptable especially for the complicated geological models with horizontal varying densities usually appearing in practical situations. We employ the improved very fast simulated annealing algorithm (VFSA), which has obvious advantage of finding the global optimal solution in inverse problems to perform gravity anomaly inversion. Only the value of each rectangle unit needs to be inversed, the interfaces or shapes and the density distributions can be simultaneously determined during gravity anomaly inversion. Through the complicated model test, this approach is proved effective and practicable. The application in the lower Yangtze area of Jiangsu shows that this inversion approach could increase the accuracy of inversion under the constrained conditions of prior seismic data, the objective strata of Devonian‐Silurian and related geological problems could also be solved efficiently.

Self-Potential Inversion Using Genetic Algorithm

A new technique is presented for automatic inversion of SP anomalies due to a polarized infinitely conductive simple geometrical source model structures, based on an artificial intelligence search strategy entitled genetic algorithm (GA) and the evolution theory. The genetic algorithm is used to find the minimum of fitness or cost func- tion of the unknown depth, polarization angle, and shape factor. The study of synthetic examples shows fast and stable recovery of the true parameters even if the input data contain different percentages of noise. The GA leads to very realistic values for the inverted parameters in all tested examples and the root-mean squared error (rms) between the true and inverted field is accepted. The technique is further applied to real examples from Germany and Turkey.