Gravity Anomalies Research Articles

A stable downward continuation method for processing gravity data using the equivalent sources with compactness and smoothing constraints

The downward continuation of the potential field is often a necessary step in data processing and interpretation, in which equivalent source is an available method. Unfortunately, due to the physical property distribution of the equivalent source obtained from the observed data inversion, this is an unstable operation. Particularly in the case of noisy data, the generation of false signals can severely obscure the useful information in the original data. To deal with the instability fundamentally, we have developed a constrained equivalent-source method to improve the physical property distribution in the equivalent layer for stable downward continuation of the gravity anomaly. In this method, the compactness constraint is applied to reduce divergent signals, and multiple smoothing is used to further eliminate the signals causing instability. Experiments on synthetic gravity anomalies show that the proposed method yields cleaner images of the physical properties and more accurate amplitudes of the downward-continuing gravity field. Application to measured data also shows that the proposed method can significantly attenuate the divergent signals and enhance the amplitude of the effective signals.

Mineral prospectivity mapping based on Support vector machine and Random Forest algorithm – A case study from Ashele copper–zinc deposit, Xinjiang, NW China

The utilization of machine learning (ML) techniques in conjunction with multi-source geoscience datasets for comprehensive metallogenic prognosis (MP) has emerged as a novel means of geological prospecting. Nevertheless, the representativeness of features and composition of datasets employed in constructing the ML model for MP may substantially impact the prediction model's overall performance and augment the metallogenic prediction's uncertainty. In this study, the Ashele copper-zinc deposit was chosen to conduct the case study to resolve these challenges. In order to improve the representativeness of features employed in ML modeling, the ore-controlling geological and rock geochemical exploration criteria were digitized and subjected to spatial analysis to extract information closely linked to mineralization. To investigate the impact of differences in dataset composition on the performance of predictive models, multiple labeled datasets were generated by randomly sampling from known boreholes. The predictive SVM and RF models were trained using the labeled datasets, validated using 10-fold cross-validation, and assessed using multiple metrics. The evaluation findings indicate that all ML models, subsequent to the enhancement of feature representativeness, exhibited satisfactory performance, as evidenced by a consistent predictive accuracy of approximately 0.88. Additionally, the study revealed that variations in the labeled datasets could adversely affect the predictive models' performance. However, this effect could be alleviated by selecting merit-based predictive models constructed from diverse dataset compositions. A comparative analysis of the ML predictive models revealed that the RBF kernel SVM and RF models demonstrated exceptional performance, with an AUC of 0.972 and 0.968, respectively. As a result, an integrated prediction model was developed by overlaying the RBF kernel SVM and RF models, successfully identifying 98% of the mineralized boreholes in the top 15% of the study area. The spatial distribution of gravity and magnetic anomalies in the study area corresponded well with the prospecting areas identified by the machine learning predictive model, further validating the efficacy of ML methods in MP.

New insights from an emplacement model for the Santa Eulália Plutonic Complex (SW Iberian Peninsula)

The Santa Eulália Plutonic Complex is formed by two main granites: G0 and G1. The G0 granite hosts metasedimentary carbonate and pelitic rocks (roof pendants) and elongated masses of mafic–intermediate rocks (the M-group). The host rocks form a diverse sequence of igneous, metasedimentary and metamorphic rocks. The study area is constrained by Variscan structures formed in a transpressional/transtensional sinistral tectonic regime (the Tomar–Badajoz–Córdoba sinistral shear zone) and is cut by the Alter do Chão and Assumar faults. The geological complexity of the area makes it difficult to determine the emplacement mechanism of the pluton. We propose a model for the ascent and emplacement of the pluton that can also be applied to similar post-collision Variscan granites. The gravity anomalies suggest that the pluton is slightly asymmetrical and extends to the SSE beneath the host rocks; its main root is >8 km thick in its deepest areas. The available radiometric data for an extended area embracing several regional plutons suggest a west–east magmatic alignment. The Variscan structures probably formed efficient crustal discontinuities enabling the generation and ascent of magma. Our model involves a west–east magmatic axis for magma spreading along extensional fractures (T-fractures) related to the Tomar–Badajoz–Córdoba shear zone. The opening movement along these fractures created divergent forces that allowed the ascent and emplacement of the plutonic rocks. The importance of these fractures is represented well by outcrops of porphyritic biotite granites (the Ervedal, Fronteira and G1 granites).

Augmented Gravity Field Modelling by Combining EIGEN_6C4 and Topographic Potential Models

One of the key goals of geodesy is to study the fine structure of the Earth’s gravity field and construct a high-resolution gravity field model (GFM). Aiming at the current insufficient resolution problem of the EIGEN_6C4 model, the refined ultra-high degree models EIGEN_3660 and EIGEN_5480 are determined with a spectral expansion approach in this study, which is to augment EIGEN_6C4 model using topographic potential models (TPMs). A comparative spectral evaluation for EIGEN_6C4, EIGEN_3660, and EIGEN_5480 models indicates that the gravity field spectral powers of EIGEN_3660 and EIGEN_5480 models outperform the EIGEN_6C4 model after degree 2000. The augmented models EIGEN_3660 and EIGEN_5480 are verified using the deflection of the vertical (DOV) of China and Colorado, gravity data from Australia and mainland America, and GNSS/leveling in China. The validation results indicate that the accuracy of EIGEN_3660 and EIGEN_5480 models in determining height anomaly, DOV, and gravity anomaly outperform the EIGEN_6C4 model, and the EIGEN_5480 model has optimal accuracy. The accuracy of EIGEN_5480 model in determining south–north component and east–west component of the DOV in China has been improved by about 21.1% and 23.1% compared to the EIGEN_6C4 model, respectively. In the mountainous Colorado, the accuracy of EIGEN_5480 model in determining south–north component and east–west component of the DOV has been improved by about 28.2% and 35.2% compared to EIGEN_6C4 model, respectively. In addition, gravity value comparison results in Australia and mainland America indicate that the accuracy of the EIGEN_5480 model for deriving gravity anomalies is improved by 16.5% and 11.3% compared to the EIGEN_6C4 model, respectively.

Iapetus Ocean serpentinites and Mesozoic intra-platform basins revealed by gravity and magnetic modelling across the Greater East Shetland Platform (Northern North Sea, UK)

The Greater East Shetland Platform and its intra-platform basins (i.e. the Dutch Bank Basin and East Orkney Basin) are examples of poorly explored areas in the UK Continental Shelf (Northern North Sea), hosting a locally thick (1–8 km) Devonian-to-Tertiary sedimentary succession that unconformably overlies the Caledonian crystalline basement.Starting from a grid of seismic reflection lines, six recently acquired profiles were selected, interpreted and depth-converted. The resulting geological cross sections were integrated with forward modelling of the observed Bouguer gravity and magnetic anomalies, and constrained by the available wellbore-derived petrophysical parameters.Our seismic interpretation and modelling suggest that the first-order contributors to the observed Bouguer gravity anomalies are related to the scattered distribution of the Mesozoic sedimentary sequences in the intra-platform basins. Furthermore, the main sources of the modelled magnetic anomalies are related to high-susceptibility (≤0.05 SI units) bodies in the crustal basement that locally correspond to zones of high reflectivity imaged in the seismic profiles. Such deep sources are interpreted as paleo-domains inherited from the pre-Devonian tectonic evolution of the study area and assembled during the Caledonian Orogeny. This may be relatable to the offshore extension of first-order pre-Devonian tectonic lineaments exposed in the Scottish Highlands and Orkney-Shetland islands.

Identifikasi Sesar dengan Menggunakan Metode Gaya Berat (Studi Kasus: Sulawesi Tengah)

The study of the geological structure of Sulawesi Island, especially the Central Sulawesi region, is very interesting because it has high complexity as a result of the dynamic interactions of the world's three main plates. Indications of high seismic activity and deformation processes in the Central Sulawesi region can be found from the morphological appearance and activity of several existing faults such as the Palu-Koro fault, the Lawanopo fault, and the Matano fault. The data used in this study are secondary data measuring the distribution of gravitational field anomalies (FAA) and topographical data using the Topex application. At CBA values ranging from 31 mGal to 56 mGal. The height anomaly on the CBA contour map is shown in red to light purple which has a value range of 40.7 mGal to 62.7mGal. Low anomaly is shown in light green to blue which has a value range of 27.3 mGal to 3.2 mGal. The regional gravity anomaly values range from 5.1 mGal to 62.8 mGal with a distribution of gravity anomalies from south to north. While in this study it can only be explained that the residual anomaly value is influenced by rock type and density. The high anomaly found in the southern part is thought to be caused by rocks having high density and being in a sedimentary rock environment which has low density.

Research on the Tectonic Characteristics and Hydrocarbon Prospects in the Northern Area of the South Yellow Sea Based on Gravity and Magnetic Data

To further explore the geological structure and the Mesozoic–Paleozoic hydrocarbon prospects in the northern area of the South Yellow Sea (SYS), multiple geological and geophysical data were systematically gathered and compiled, including gravity and magnetic data, seismic surveys, drilling data, and previous research results. The characteristics and genesis of the gravity and magnetic anomalies are examined. This study employs residual gravity anomalies and multiple edge detection methods to identify fault lineament structures and assess the tectonic framework. Moreover, the study utilizes 2.5D gravity-seismic joint modellings and regression analysis to estimate the basement depth. Additionally, the study examines the basement characteristics and discusses the thickness of the Mesozoic–Paleozoic strata. Finally, the study further identifies prospects for hydrocarbons in the Mesozoic–Paleozoic. Our findings show that the faults are incredibly abundant and that the intensity of fault activity weakens gradually from NW to SE. Specifically, NE (NEE) trending faults are interlaced and cut off by NW (NWW), near-EW, and near-SN trending secondary faults, which form an en-echelon composite faults system with a dominant NE (NEE) orientation. Thick Mesozoic–Paleozoic strata are preserved, but we observe distinct variations in basement characteristics and the pre-Cenozoic structural deformation along the N-S direction. Therefore, the Northern Basin of SYS (NBSYS) and the Middle Uplift of SYS (MUSYS) are characterized by alternating sags and bulges in the S-N direction and in the E-W direction, respectively, forming a chessboard tectonic framework. Considering the oil and gas accumulation model, we identify three target hydrocarbon prospects in the NBSYS and two favorable hydrocarbon prospects in the MUSYS.

Improved Bathymetry in the South China Sea from Multisource Gravity Field Elements Using Fully Connected Neural Network

Traditional bathymetry inversion methods that rely on an altimetry-derived gravity anomaly (GA) and/or a vertical gravity gradient anomaly (VGG) have been widely used for bathymetry prediction in the South China Sea. However, few studies attempt new methods to combine multisource gravity data to improve the accuracy of the bathymetry. In this study, we introduce a fully connected deep neural network (FC-DNN) to merge GA, VGG, and the deflection of vertical (DOV) to predict the bathymetry in the South China Sea. Single beam sounding depths were used as sample data for neural network training. Independent shipboard depths and GEBCO2023, topo_25.1, and ETOPO2022 models were applied as validation data. The assessment results showed that the FC-DNN model reached a high precision level with an STD of 49.20 m. More than 70% of the differences between the FC-DNN bathymetric model and other depth models were less than 100 m. Furthermore, the spectral analysis results showed that the FC-DNN bathymetry model has stronger energy in medium and short wavelengths than other models, which indicates that additional gravity field element DOVs can recover richer topographic signals in those particular bands.

A Novel 2.5D Deep Network Inversion of Gravity Anomalies to Estimate Basement Topography

Summary A novel 2.5D intelligent gravity inversion technique has been developed to estimate basement topography. A deep neural network (DNN) is used to address the fundamental nonuniqueness and nonlinearity flaws of geophysical inversions. The training data set is simulated by adopting a new technique. Using parallel computing algorithms, thousands of forward models of the subsurface with their corresponding gravity anomalies are simulated in a few minutes. Each forward model randomly selects the values of its parameter from a set of predefined ranges based on the geological and structural characteristics of the target area. A DNN model is trained based on the simulated data set to conduct the nonlinear inverse mapping of gravity anomalies to basement topography in offshore Abu Dhabi, United Arab Emirates. The performance of the trained model is assessed by making predictions on noise-free and noise-contaminated gravity data. Eventually, the DNN inversion model is used to estimate the basement topography using pseudogravity anomalies. The results show the depth of the basement is between 7.4 km and 9.3 km over the Ghasha hydrocarbon reservoir. This paper is the 2.5D and improved version of the research (SPE-211800-MS) recently presented and published in the Abu Dhabi International Petroleum Exhibition & Conference (31 October–3 November 2022) proceedings.

Multilayer Densities of the Crust and Upper Mantle in the South China Sea Using Gravity Multiscale Analysis

The South China Sea (SCS) is the result of several major tectonic plates’ interaction, and a more detailed density structure is essential to study the tectonic evolution of the marginal seas. In the past decades, density studies in the SCS have focused more on profiles, and the lateral density structure has been less mentioned by scholars. Previously, gravity data have been used many times to study the SCS; this can satisfy the demands of large-scale lateral studies, but a point that cannot be ignored is that the gravity method has certain deficiencies in vertical resolution. Therefore, this paper applies a gravity multiscale analysis method to isolate the Bouguer gravity anomaly signal in the SCS, and then uses the power spectrum method to estimate the mean field source depth, which corresponds to the decomposed gravity anomaly signal. On this basis, we modeled stratified crustal and upper mantle structures in the SCS to determine the lateral density distribution at different depths. The results show the following: (1) There are two large high-density materials in the SCS. The first one is located near the Yinggehai Basin, where the depth ranges from 42.4 km to 71.2 km, with a diameter of nearly 220 km; the second one is located near the northwest sub-basin, where the depth ranges from 106.8 km to 128.8 km, which is probably part of the Paleo-Pacific remnant in the SCS. (2) The proto South China Sea subduction zone is located in the northwestern part of the Sulu Sea and has a northeast–southwest trend.

Gold deposits in the central part of the Aldan-Stanovoy shield in anomalies of geopotential filds

The analysis of potential geophysical filds of the central part of the Aldan-Stanovoy shield was carried out. Based on the modern automated program KOSCAD 3D, the following transformations of gravity and magnetic anomalies were carried out: a calculation of statistical and gradient characteristics, two-dimensional energy adaptive fitering, and a calculation of the data correlation coeffient. Based on the results of processing and interpretation of geological and geophysical materials, the block structure of the study area was clarifid and geophysical criteria for the localization of gold mineralization in the central part of the Aldan-Stanovoy shield were identifid.

Tectonic division of the pre-cenozoic basement of the South China Sea in earth monitoring

The past five decades have witnessed satellite remote sensing become one of most efficient tools for surveying the Earth at local, regional, and global spatial scales. The nature of the basement tectonic unit is closely related to the origin and evolution of the basin. However, such research carried out in the South China Sea (SCS) is relatively limited. In this research, by analyzing the fault structure, gravity and magnetic anomaly characteristics of the SCS, the ophiolite belts, spreading edge zones and the regional deep faults are considered as the boundaries of the tectonic units, and the SCS area can be divided into seven basement tectonic units: Cathaysia massif, Indochina massif, the SCS basin, Philippine island arc belt, Nansha massif, Sunda massif and Sibu accretionary prism. These tectonic units have different tectonic sequences, sedimentary formations and metamorphic types, in addition, they affect the Cenozoic basins overlying them to form different structural types. The research results will help to further understand the pre-Cenozoic basement structure and the tectonic evolution history of the SCS.

Integrated application of gravity, aeromagnetic, and electromagnetic methods in exploring the Ganzi geothermal field, Sichuan Province, China

The Ganzi geothermal field is located in the Songpan-Ganzi orogenic belt in Sichuan Province. Many hot springs are exposed along the Yalahe valley in Ganzi geothermal field, which is a favorable area for high-temperature geothermal resource exploration. However, the geological model of heat exchange, the regional structure controlling hydrothermal convection and the development model of geothermal reservoirs are still unclear. Therefore, further studies are necessary to meet the geothermal exploration requirements in the middle and deep strata of this geothermal field. In this study, a geological model of the geothermal system of Ganzi geothermal field is proposed. We are convinced that there exists a hydrothermal convection system in the Ganzi geothermal field, the heat transfer of which is accomplished through deep-rooted major faults. Therefore, the identification of deep-rooted major faults and the description of geothermal reservoirs are the research objects of the integrated geophysical methods. The main factors controlling the geothermal reservoirs in the deep-rooted Xianshuihe major fault and Yalahe fault zones are analyzed by using gravity, aeromagnetic, and electromagnetic methods and techniques. The analysis results of regional gravity and aeromagnetic anomalies show that the Xianshuihe major fault has produced obvious gravity and aeromagnetic anomalies on the surface, and thus the position and strike of this fault can be accurately predicted by inversion of the aeromagnetic anomalies. Geothermal reservoirs show low-resistivity anomalies in the electromagnetic profile. The inversion results of the controlled source audio-frequency magnetotelluric (CSAMT) data show that geothermal reservoirs are mainly developed along the Yalahe valley, and the west side of the valley is more favorable for geothermal exploration. This study is of guiding significance to the efficient exploitation and utilization of the Ganzi geothermal field.

Fast 3D gravity and magnetic modelling using midpoint quadrature and 2D FFT

To avoid the problem of the traditional methods consuming large computational resources to calculate the kernel matrix and 2D discrete convolution, we present a novel approach for 3D gravity and magnetic modelling. This method combines the midpoint quadrature method with a 2D fast Fourier transform (FFT) to calculate the gravity and magnetic anomalies with arbitrary density or magnetic susceptibility distribution. In this scheme, we apply the midpoint quadrature method to calculate the volume element of the integral. Then, the convolution of the weight coefficient matrix with density or magnetization is efficiently computed via the 2D FFT. Finally, the accuracy and efficiency of the proposed algorithm are validated by using an artificial model and a real topography model. The numerical results demonstrate that the proposed algorithm’s computation time and the memory requirement are decreased by approximately two orders of magnitude compared with the space-wavenumber domain method.

Cook Ice Shelf and Ninnis Glacier Tongue Bathymetry From Inversion of Operation Ice Bridge Airborne Gravity Data

AbstractThe seafloor depths under the Cook Ice Shelf and Ninnis Glacier Tongue have not been directly measured, despite their importance for understanding ocean circulation and ice shelf change. We model the bathymetry underneath the floating ice and surrounding ocean using airborne gravity data. Our model is constrained by few ship‐based seafloor measurements near the ice front and by ice‐base measurements over areas of grounded ice from radar data. Localized basins (∼1,400 m deep) are found beneath both ice shelves. The shallowest modeled bathymetry (∼200 m) represents the offshore extension of Cape Freshfield. Near the grounding line, seafloor depths are found to be deeper than the observed depth of the modified Circumpolar Deep water in the region (<350 m), key factor for basal melt analyses. From transit flight gravity anomalies, we suggest the relocation of the mapped edge of the continental shelf and a narrowing of the Cook Shelf Depression.

Utilization and modeling of satellite gravity data for geohazard assessment in the Yogyakarta area of Java Island, Indonesia

A geohazard assessment was conducted in the Aerotropolis area of the new Yogyakarta international airport, located in the Yogyakarta special region province, Indonesia. The study involved the analysis and modeling of 3-D inversions of earth gravity anomaly data obtained from the high-resolution of Global Gravity Model (GGM). The main objective of the study was to identify subsurface geological structures such as faults, active volcanoes, and sedimentary layers that may pose potential hazards to the Yogyakarta aerotropolis area. The complete Bouguer anomaly in the study region was calculated using modern terrain correction methods that relied on full-scale topography gravity data from the SRTM2gravity model. A 2-D radial spectrum analysis was then performed on this anomaly data, which revealed that the average thickness of sedimentary layers was estimated to be more than 100 ​m. The rock density contrast was determined using the residual gravity anomaly inversion, which showed a range of −0.086 ​g/cm3 to 0.043 ​g/cm3. The analysis of gravity anomalies and rock density contrast provided results that aligned with the regional geological conditions of the Yogyakarta region, including the pattern of igneous rock intrusion with high density contrast, the presence of the Merapi magma chambers associated with low negative density contrast, and the Opak normal fault path at low and high contrast boundaries, which could lead to natural hazards in the region.

Identification of the Manna Segment Sumatran Fault Using GGMplus Gravity Anomaly Data with the Second Vertical Derivative (SVD) Method

This study uses the gravity method to assess the characteristics of the Manna segment fault, a part of the Sumatran fault. This research aims to contribute to the existing knowledge by providing additional insights into the fault's characteristics, which is essential for future disaster mitigation efforts. The Manna segment fault is geographically situated between coordinates 4.4⁰S - 3.9⁰ S and 102.7⁰ E – 103.2⁰ E, making this area prone to earthquake hazards. The gravity anomaly data, including free air and topography, were collected from 62,501 data points. The Simple Bouguer Anomaly (SBA) values obtained ranged from 25 mGal to 95 mGal. By utilizing the Second Vertical Derivative (SVD) method and dividing the study area into three regions with multiple sections, the analysis revealed that the minimum and maximum SVD values were relatively similar. This suggests that the Manna fault can be classified as a strike-slip fault, with SVD values ranging from Elkins-20 mGal to 6 mGal. The study identified branches of the main fault in regions 2 and 3 based on the SVD map. Overall, this study enhances our understanding of the Manna segment fault, providing valuable insights into its characteristics and contributing to future disaster mitigation efforts.

3-D gravity inversion for the basement relief reconstruction through modified success-history-based adaptive differential evolution

SUMMARY A gravity inversion procedure using the success-history-based adaptive differential evolution (SHADE) algorithm is presented to reconstruct the 3-D basement relief geometry in sedimentary basins. We introduced exponential population size (number) reduction (EPSR) to reduce the computational cost and used self-adaptive control parameters to solve this highly nonlinear inverse problem. Model parametrization was carried out by discretizing the sedimentary cover via juxtaposed right prisms, each placed below each observation point. Resolvability characteristics of the 3-D inverse problem were revealed through some cost function topography landscapes. The fine-tuned control parameter namely, population number allowed us to get best benefit from the algorithm. Additionally, a stabilizing function as a relative constraint was used to avoid undesired effects originated from the ill-posedness of the problem. In the synthetic data cases, the strategy we propose outperformed the linear population number reduction strategy which has won various IEEE–CEC competitions so far. Thorough uncertainty assessments via probability density function and principal component analysis demonstrated the solidity of the obtained inverse models. In the real data case, residual gravity anomalies of two well-known major grabens of Aegean Graben System (Türkiye), calculated thanks to the finite element method, were inverted. It was determined that the inverse solutions obtained for these basement reliefs, whose depths are still controversial, are statistically reliable. Moreover, these depths were found to be less than the depths reported in most previous studies. We conclude that the SHADE using EPSR strategy that we propose is a powerful alternative inversion tool for highly nonlinear geophysical problems.

An enhanced view on the Mediterranean Sea crust from potential fields data

The Earth’s crust is exceptionally important to understand the geological evolution of our planet and to access natural resources as minerals, critical raw materials, geothermal energy, water, hydrocarbons, etc.. However, in many regions of the world it is still poorly modelled and understood. Here we present the latest advance on three-dimensional modelling of the Mediterranean Sea crust based on freely available global gravity and magnetic field models. The proposed model, based on the inversion of gravity and magnetic field anomalies constrained by available a-priori information (such as interpreted seismic profiles, previous studies, etc.), provides, with an unprecedented spatial resolution of 15 km, the depths of the main modelled geological horizons (Plio-Quaternary, Messinian and Pre-Messinian sediments, crystalline crust and upper mantle), coherent with the known available constraints, together with the three-dimensional distribution of density and magnetic susceptibility. The inversion is carried out by means of a Bayesian algorithm, which allows to modify at the same time the geometries and the three dimensional distributions of density and magnetic susceptibility, always respecting the constraints introduced by the initial information. In addition to unveil the structure of the crust beneath the Mediterranean Sea, the present study also shows the informative content of freely available global gravity and magnetic models, thus putting the base for the development of future high resolution models of the Earth crust at global level.

Two New Methods Based on Implicit Expressions and Corresponding Predictor-Correctors for Gravity Anomaly Downward Continuation and Their Comparison

Downward continuation is a key technique for processing and interpreting gravity anomalies, as it has a major role in reducing values to horizontal planes and identifying small and shallow sources. However, it can be unstable and inaccurate, particularly when continuation depth increases. While the Milne and Adams–Bashforth methods based on numerical solutions of the mean-value theorem have partly addressed these problems, more accurate and realistic methods need to be presented to enhance results. To address these challenges, we present two new methods, Milne–Simpson and Adams–Bashforth–Moulton, based on implicit expressions and their predictor-correctors. We test the validity of the presented methods by applying them to synthetic models and real data, and we obtain stability, accuracy, and large depth (eight times depth intervals) downward continuation. To facilitate wider applications, we use calculated vertical derivatives (of the first order) by the integrated second vertical derivatives (ISVD) method to replace theoretical ones from forward calculations and real ones from observations, obtaining reasonable downward continuations. To further understand the effect of introduced calculation factors, we also compare previous and presented methods under different conditions, such as with purely theoretical gravity anomalies and their vertical derivatives at different heights from forward calculations, calculated gravity anomalies and their vertical derivatives at non-measurement heights above the observation by upward continuation, calculated vertical derivatives of gravity anomalies by the ISVD method at the measurement height, and noise. While the previous Adams–Bashforth method sometimes outperforms the newly presented methods, new methods of the Milne–Simpson predictor-corrector and Adams–Bashforth–Moulton predictor-corrector generally present better downward continuation results compared to previous methods.