Pre-seismic gravity anomalies before Linkou Ms6.4 earthquake by continuous gravity observation of Crustal Movement Observation Network of China

A Ms6.4 earthquake occurred at Linkou country, Heilongjiang Province （44.8°N, 129.9°E） on January 2, 2016 at a depth of 580 km. Pre-seismic graviW anomalies obtained at a 1 Hz sampling rate from Crustal Movement Observation Network of China （CMONOC） are analyzed after the earthquake. The results show that： （1） different from previous studies, both pre-seismic amplitude perturbation and co-seismic amplitude perturbation are not critical inversely proportional to epicentral distance; （2） unlike shallow earthquake, the pre-seismic and co-seismic amplitude perturbation of gravity illustrate syn- chronous spatial variation characters with decrease of epicentral distance for Linkou earthquake. This may because Linkou earthquake is a deep earthquake and occurred in Pacific Plate subduction zone; （3） compared to basement and semi-basement, cave can provide a better observation environment for gPhone gravimeter to detect pre-seismic gravity anomalies.

A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6500 m

Understanding the topographic patterns of the seafloor is a very important part of understanding our planet.Although the science involved in bathymetric surveying has advanced much over the decades,less than 20%of the seafloor has been precisely modeled to date,and there is an urgent need to improve the accuracy and reduce the uncertainty of underwater survey data.In this study,we introduce a pretrained visual geometry group network(VGGNet)method based on deep learning.To apply this method,we input gravity anomaly data derived from ship measurements and satellite altimetry into the model and correct the latter,which has a larger spatial coverage,based on the former,which is considered the true value and is more accurate.After obtaining the corrected high-precision gravity model,it is inverted to the corresponding bathymetric model by applying the gravity-depth correlation.We choose four data pairs collected from different environments,i.e.,the Southern Ocean,Pacific Ocean,Atlantic Ocean and Caribbean Sea,to evaluate the topographic correction results of the model.The experiments show that the coefficient of determination(R~2)reaches 0.834 among the results of the four experimental groups,signifying a high correlation.The standard deviation and normalized root mean square error are also evaluated,and the accuracy of their performance improved by up to 24.2%compared with similar research done in recent years.The evaluation of the R^(2) values at different water depths shows that our model can achieve performance results above 0.90 at certain water depths and can also significantly improve results from mid-water depths when compared to previous research.Finally,the bathymetry corrected by our model is able to show an accuracy improvement level of more than 21%within 1%of the total water depths,which is sufficient to prove that the VGGNet-based method has the ability to perform a gravity-bathymetry correction and achieve outstanding results.

A method for extracting the preseismic gravity anomalies over the Tibetan Plateau based on the maximum shear strain using GRACE data

The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite data can be used to detect gravity changes associated with large earthquakes.However,previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes.Moreover,the noise of the north–south stripe in GRACE data is difficult to eliminate,thereby resulting in the loss of some gravity information related to tectonic activities.To explore the preseismic gravity anomalies in a more refined way,we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity,inspired by the concept of crustal strain.The offset index method is then adopted to describe the gravity anomalies,and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate,respectively.In this work,experiments are carried out on the Tibetan Plateau and its surrounding areas,and the following findings are obtained:First,from the observation scale of the fault zone,we detect the occurrence of large-area gravity anomalies near the epicenter,oftentimes about half a year before an earthquake,and these anomalies were distributed along the fault zone.Second,from the observation scale of the plate,we find that when an earthquake occurred on the Tibetan Plateau,a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate.Moreover,the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8,which suggests a new idea for the application of gravity satellite data to earthquake research.

Constraining the crustal structure under the central and western Tian Shan based on teleseismic receiver functions and gravity anomalies

The Tian Shan is a vast range that spans several countries in Asia.Understanding its evolutionary history may provide valuable insights into intracontinental orogenic dynamics.In this study,we explored the crustal characteristics of the Tian Shan and their relationships to the tectonic evolution of the region.A new H-stacking method that combines the P receiver function and gravity anomalies was used to estimate the thickness and ratio of P-to S-wave velocities(Vp/Vs)for 91 broadband seismic stations in the central and western Tian Shan.Our results revealed significant lateral variations in crustal thickness and Vp/Vs.A—45-km-thick crust and an intermediate-high Vp/Vs(-1.74-1.84)were found in the Kazakh Shield and Tarim Basin,which we interpreted to indicate a mafic crystalline basement and lower crust.The central Tian Shan varied greatly in crustal thickness(40-64 km)and Vp/Vs ratio(1.65-2.00).which may be due to crustal shortening,mafic underplating,and crustal melting.In contrast,we observed a relatively thin crust(42-50 km)with an intermediate Vp/Vs ratio(-1.78)in the western Tian Shan.The differences in the crustal structures between the western and central Tian Shan imply that the Talas-Fergana Fault may be trans-lithospheric.

Using WGM2012 to Compute Gravity Anomaly Corrections of Leveling Observations in China

Gravity Anomaly Correction(GAC)is a very important term in leveling data processing.In most cases,it is troublesome for field surveyors to measure gravity when leveling.In this paper,based on the complete Bouguer Gravity Anomaly(BGA)map of WGM2012,the feasibility of replacing in-situ gravity surveying in China is investigated.For leveling application,that is to evaluate the accuracy of WGM2012 in China.Because WGM2012 is organized with a standard rectangle grid,two interpolation methods,bilinear interpolating and Inverse Distance Weighted(IDW)interpolating,are proposed.Four sample areas in China,i.e.,Hanzhong,Chengdu,Linzhi and Shantou,are selected to evaluate the systems bias and precision of WGM2012.Numerical results show the average system bias of WGM2012 BGA in west China is about-100.1 mGal(1 mGal=10^(-5) m/s^(2))and the standard deviation is about 30.7 mGal.Tests in Shantou indicate the system bias in plain areas is about-130.4 mGal and standard deviation is about 6.8 mGal.All these experiments means the accuracy of WGM2012 is limited in high mountain areas of western China,but in plain areas,such as Shantou,WGM2012 BGA map is quite good for most leveling applications after calibrating the system bias.

Gravity anomalies determined from mean sea surface model data over the Gulf of Mexico

With the improvements in the density and quality of satellite altimetry data,a high-precision and high-resolution mean sea surface model containing abundant information regarding a marine gravity field can be calculated from long-time series multi-satellite altimeter data.Therefore,in this study,a method was proposed for determining marine gravity anomalies from a mean sea surface model.Taking the Gulf of Mexico(15°–32°N,80°–100°W)as the study area and using a removal-recovery method,the residual gridded deflections of the vertical(DOVs)are calculated by combining the mean sea surface,mean dynamic topography,and XGM2019e_2159 geoid,and then using the inverse Vening-Meinesz method to determine the residual marine gravity anomalies from the residual gridded DOVs.Finally,residual gravity anomalies are added to the XGM2019e_2159 gravity anomalies to derive marine gravity anomaly models.In this study,the marine gravity anomalies were estimated with mean sea surface models CNES_CLS15MSS,DTU21MSS,and SDUST2020MSS and the mean dynamic topography models CNES_CLS18MDT and DTU22MDT.The accuracy of the marine gravity anomalies derived by the mean sea surface model was assessed based on ship-borne gravity data.The results show that the difference between the gravity anomalies derived by DTU21MSS and CNES_CLS18MDT and those of the ship-borne gravity data is optimal.With an increase in the distance from the coast,the difference between the gravity anomalies derived by mean sea surface models and ship-borne gravity data gradually decreases.The accuracy of the difference between the gravity anomalies derived by mean sea surface models and those from ship-borne gravity data are optimal at a depth of 3–4 km.The accuracy of the gravity anomalies derived by the mean sea surface model is high.

Characteristics of gravity anomalies and tectonic analysis of Enderby Land in East Antarctica and its adjacent areas

Enderby Land in East Antarctica and its adjacent areas,which are closely related to the Indian Plate in their geological evolution,have become one of the key zones for studies on how the Antarctic continent evolves.Based on the isostasy and flexure theories of the lithosphere and using the CRUST1.0 model as the depth constraint,this paper uses the gravity field model EIGEN-6C4 and topographic data to calculate the isostatic gravity anomalies of Enderby Land and its adjacent areas.Then,the crustal thickness of the study area is calculated,and three comprehensive geophysical interpretation profiles that vertically span the study area are plotted.The results show that the flexural isostatic gravity anomalies in Enderby Land and its adjacent areas are closely related to the regional tectonic setting,and the anomalies in different regions differ substantially,ranging from−50×10^(−5)m/s^(2)to 85×10^(−5)m/s^(2).A zone of high isostatic gravity anomalies(30×10^(−5)−80×10^(−5)m/s^(2))is distributed outside the Cooperation Sea and Queen Maud Land,which may be plate remnants generated by early rifting.Except for the Kerguelen Plateau,which was formed by a hotspot and has a crustal thickness of 15 km,the thickness of the oceanic crust in other parts of the study area changes slightly by approximately 4–9 km,with the thinnest part being in Enderby Basin.The thickness of the inland crust along the coastline increases with the elevation,with the maximum thickness reaching 34 km.The isostatic gravity anomalies corresponding to the zone of high magnetic anomalies along the continental margin of Queen Maud Land are negative and small,with an isostatic adjustment trend indicating Moho surface uplift,and those on the edge of central Enderby Land are near zero,approaching the isostatic state,which may be caused by the magmatism at the early stage of rifting.The continental-oceanic boundary should be close to the contour line of the crustal thickness 10–12 km on the outer edge of the coastline.

Implications on Gravity Anomaly Measurements Associated with Different Lithologies in Turkana South Subcounty

The use of gravity data has demonstrated capability for monitoring lithological changes on a large scale as a consequence of differentiating basement and sedimentary of buried valleys. Gravity anomalies are associated with lateral contrasts in density and therefore deformation by faulting or folding will be manifested if accompanied by lateral density changes, otherwise, the vice versa is true. The study’s objective is to evaluate the effectiveness of gravity method in establishing different lithologies in an area. The study has revealed that regional anomaly gravity map presents high anomalies in the Northern region in the NW-SE trend and low anomalies in the southern trend in NW-SE, while the residual anomaly gravity map shows different trends for the low and high gravity anomalies. The gravity anomalies are well interpreted in line with the lithologies of the study area rather than the deformation of the same lithologies. There are observed high values of gravity anomaly values (ranging from -880.2 to -501.2 g.u.) where there are eolian unconsolidated rocks overlying the basement compared to low gravity anomaly values (ranging from -1338.9 to -1088.7 g.u.) where the andesites, trachytes and phonolites overly the basement. The different regional gravity anomalies relate well with different rock densities in the study area along the line profile for radially averaged power spectrum. The gravity highs are noted in the eastern point and are associated with andesites, trachytes, basalts and igneous rocks, while the gravity lows are associated with sandstone, greywacke, arkose, and eolian unconsolidated rock. The utilization of the information from the Power spectrum analysis demonstrates that the depth to the deepest basement rock is 12.8 km which is in the eastern flank, while the shallowest to the basement of 1.1 km to the western flank.

Structural characteristics and tectonic division of the Zambezi Delta basin in the offshore East Africa:evidences from gravity and seismic data

The Zambezi Delta basin is a passive marginal basin located on the East African coast that has good oil and gas exploration potential.Due to the special geological evolutionary background of the Beira High in the Zambezi Delta basin,it has a low gravity anomaly,and the existing seismic survey lines do not cover the whole basin;therefore,it is difficult to interpret the structural characteristics of the whole basin based solely on gravity or seismic data.Based on satellite altimetry gravity anomaly data,this study infers the distribution characteristics of faults in the Zambezi Delta basin by using the normalized vertical derivative of the total horizontal derivative(NVDR-THDR)technique.Then,constrained by seismic data,the gravity anomaly at the Moho interface is extracted by using the fast forward method of the double-interface model of the gravity anomaly,and this anomaly is then removed from the Bouguer gravity anomaly to obtain the sedimentary layer gravity anomaly.The thickness of the sedimentary strata is obtained by inversing the sedimentary basement depth of the whole basin.Then,uplifts and depressions are divided based on a sedimentary layer thickness of 3 km.This research demonstrates that the Zambezi Delta basin mainly features nearly SN-trending and NE-trending faults and that these faults exhibit east-west partitioning.The nearly SN-trending strike-slip faults controlled the sedimentary development of the basin,and the NE-trending tensile faults may have acted as migration channels for oil,gas and magma.The“overcompensation”effect of the Moho interface gravity anomaly on the gravity anomaly of the sedimentary layer is caused by the depression of the Moho interface beneath the Beira High,which results in a low gravity anomaly value for the Beira High.The pattern of uplifts and depressions trends NE and has the structural characteristics of east-west blocks.

Interpretation of Geological and Gravity Data from the Bamiléké Plateau (West-Cameroon): Implication for the Understanding of Its Underground Lithotectonic Geometry

The Bamiléké Plateau represents a key domain in the understanding of the geodynamics associated with the central Cameroon shear. The study aimed to highlight the subsurface architecture of the plateaus basement setting with focus on high potential areas for hydrogeological and mining development projects. To this end, geological field observations were carried out. Since the structures sought were near-surface, a separation approach based on the upward continuation method was applied to the Bouguer anomaly grid. A set of processing techniques, including vertical derivative or DZ, analytical signal or SA and categorization of gravity signatures, was applied to generate the residual map. The synthesis geological model, obtained from analysis and interpretation of the various transformed maps and 2.5D modeling of two gravity profiles P1 and P2 highlights the following features: 1) intrusions of steep-sided granitic batholiths from Dschang to Bandjoun (profile P1), increasing in width from NW (Dschang) to SE (Bandjoun);2) larger volume batholiths with moderate sides located at Bafang and Bangangté (profile P1). These plutonic massifs were weakened by brittle deformation, which favored the emplacement of phonolite or anorthosite dykes within them. The emplacement of these dykes was accompanied by compressional faults with high dip between Dschang and Bandjoun and extensional faults with medium dip between Bafang and Bangangté. These fault zones (trending N85E to N95E) are ideal for hydrogeological investigations in a basement setting, as well as a series of dyke networks that could potentially be preferred zones for the circulation and accumulation of useful substances. The resulting geological sections P1 and P2 highlight the influence of granitic intrusions in the geological system of the study area, as well as the structural control associated with the various dyke intrusions. All the models obtained can serve as fundamental references for hydrogeological and mining exploration project on the Bamiléké Plateau.

Edge enhancement of gravity anomalies and gravity gradient tensors using an improved small sub-domain filtering method

In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance gravity anomalies and gravity gradient tensors. We discuss the effect of Gaussian white noise on the improved small sub-domain filtering method, as well as analyze the effect of window size on geological body edge recognition at different extension directions. Model experiments show that the improved small sub-domain filtering method is less affected by noise, filter window size, and geological body edge direction so it can more accurately depict geological body edges than the conventional small sub-domain filtering method. It also shows that deeply buried body edges can be well delineated through increasing the filter window size. In application, the enhanced gravity anomalies and calculated gravity gradient tensors of the Hulin basin show that the improved small sub-domain filtering can recognize more horizontal fault locations than the conventional method.

Cascade Kalman filter for gravity anomaly distortion correction based on second order potential model

Using a gravity anomaly covariance function based on the second-order Ganssian Markov gravity anomaly potential model, the state equation of a gravity anomaly signal is obtained in marine gravimetry. Combined with the system state equation and the measurement equation, a new method of the cascade Kalman filter is proposed and applied to the correction of gravity anomaly distortion. In the signal processing procedure, an inverse Kalman filter is used to restore the gravity anomaly signal and high frequency noises first. Then an adaptive Kalman filter, which uses the gravity anomaly state equation as the system equation, is set to estimate the actual gravity anomaly data. Emulations and experiments indicate that both the cascade Kalman filter method and the single inverse Kalman filter method are effective in alleviating the distortion of the gravity anomaly signal, but the performance of the cascade Kalman filter method is better than that of the single inverse Kalman filter method.

A method for gravity anomaly separation based on preferential continuation and its application

Based on the preferential continuation method proposed by Pawlowski （1995）, we propose a method and procedure for gravity anomaly separation with the preferential upward continuation operator in the case that the various sources are uncorrelated with one another and the continuation height is enough large. We also present a method for estimating optimum upward-continuation height, based on analyzing the characteristics of the preferential upward continuation operators of a synthesized gravity anomaly varying with different continuation heights. The method is tested on the raw Bouguer gravity data over an iron deposit. The result shows that the method separates the data into regional anomaly and residual anomaly efficiently and clearly.

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

Characteristic of Gravity and Magnetic Anomalies in the Daba Shan and the Sichuan basin, China: Implication for Architecture of the Daba Shan

The Dabashan nappe structural belt links the Hannan block to the west with the Huangling block to the east between Yangxian and Xiangfan. The Dabashan arc-shaped fold belt formed during late Jurassic and was superposed on earlier Triassic folds. To achieve an improved understanding of the deep tectonics of the Dabashan nappe structural belt, we processed and interpreted the gravity and magnetic data for this area using new deep reflection seismic and other geophysical data as constraints. The results show that the Sichuan basin and Daba Mountains lie between the Longmenshan and Wulingshan gravity gradient belts. The positive magnetic anomalies around Nanchong-Tongjiang-Wanyuan-Langao and around Shizhu result from the crystalline basement. Modeling of the gravity and magnetic anomalies in the Daba Mountains and the Sichuan basin shows that the crystalline basement around Nanchong-Tongjiang-Wanyuan-Langao extends to the northeast underneath the Wafangdian fault near Ziyang. The magnetic field boundary in the Zhenba-Wanyuan-Chengkou-Zhenping area is the major boundary of the Dabashan nappe thrusting above the Sichuan Basin. This boundary might be the demarcation between the south Dabashan and the north Dabashan structural elements. The low gravity anomaly between Tongjiang and Chengkou might be partly caused by thickened lower crust. The local low gravity anomaly to the south of Chengkou-Wanyuan might result from Mesozoic strata of low density in the Dabashan foreland depression area.

Frozen subduction in the Yangtze block:insights from the deep seismic profiling and gravity anomaly in east Sichuan fold belt

The Sichuan basin is the main part of the middle-upper Yangtze block, which has been experienced a long-term tectonic evolution since Archean. The Yangtze block was regarded as a stable block until the collision with the Cathaysia block in late Neoproterozoic. A new deep seismic reflection profile conducted in the eastern Sichuan fold belt（ESFB） discovered a serials of south-dipping reflectors shown from lower crust to the mantle imply a frozen subduction zone within the Yangtze block. In order to prove the speculation, we also obtain the middle-lower crustal gravity anomalies by removing the gravity anomalies induced by the sedimentary rocks and the mantle beneath the Moho, which shows the mid-lower crustal structure of the Sichuan basin can be divided into eastern and western parts. Combined with the geochronology and Aeromagnetic anomalies, we speculated the Yangtze block was amalgamated by the West Sichuan and East Sichuan blocks separated by the Huayin-Chongqing line. The frozen subduction zone subsequently shifted to a shear zone accommodated the lower crustal shortening when the decollement at the base of the Nanhua system functioned in the upper plate.

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

Theoretical analysis and practical observations show that fault dislocations can change the gravity field around the fault. Gravity changes which were caused by the repeated dislocations over a long period of time were superimposed on the Bougeur gravity anomalies. These anomalies became the evidence of historical movement of fault as well as provide a way for the study of paleo earthquakes. This paper investigates inversion methods for the geological dislocation modeling of faults using the local Bouguer's gravity anomalies. To remove the effects of the irrelevant part of gravity anomalies to fault movements, we propose the robust nonlinear inversion method and set up the corresponding algorithm. Modeling examples indicate that the Marquardt's and Baye's least squares solutions depart from the true solution due to the attraction of gross errors in the data. The more seriously the data is contaminated, the more seriously the solutions are biased. In contrast, the proposed robust Marquardt's and Baye's inversion solutions can still maintain consistency with the solution without gross errors, even though 50 percent of the data is contaminated. This indicates that the proposed robust methods are effective. Using the proposed methods, we invert the geological dislocation models of the faults around the Erhai Lake in West Yunnan. The results show that the Northern Cangdong fault and the Erhai fault are normal dip slip faults with about 4 to 5 km dislocations; and that the Southern Cangdong fault has a less dip slip compared with the former two. A satisfactory fitting between the theoretical values of the inversion solution and the actual local gravity field is achievable.

Bathymetry predicting using the altimetry gravity anomalies in South China Sea

In South China Sea(112°E-119°E, 12°N-20°N), 81159 ship soundings published by NGDC(National Geophysics Data Center) and the altimetry gravity anomalies published by SIO(Scripps Institute of Oceanography) were used to predict bathymetry by GGM(gravity-geologic method) and SAS(Smith and Sandwell) method respectively. The residual 40576 ship soundings were used to estimate precisions of the predicted bathymetry models. Results showed that: the standard deviation of difference between the GGM model and ship soundings was 59.75 m and the relative accuracy was 1.86%. The SAS model is60.07 m and 1.87%. The power spectral densities of the ETOPO1, SIO, GGM and SAS models were also compared and analyzed. At last, we presented an integrated bathymetry model by weighted averaging method, the weighted factors were determined by precisions of the ETOPO1, SIO, GGM, and SAS model respectively.

Crustal Uplift in the Longmen Shan Mountains Revealed by Isostatic Gravity Anomalies along the Eastern Margin of the Tibetan Plateau

This study examines the relationship between high positive isostatic gravity anomalies （IGA）, steep topography and lower crustal extrusion at the eastern margin of the Tibetan Plateau. IGA data has revealed uplift and extrusion of lower crustal flow in the Longmen Shan Mountains （the LMS）. Firstly, The high positive IGA zone corresponds to the LMS orogenic belt. It is shown that abrupt changes in IGA correspond to zones of abrupt change of topography, crustal thickness and rock density along the LMS. Secondly, on the basis of the Airy isostasy theory, simulations and inversions of the positive IGA were conducted using three-dimensional bodies. The results indicated that the LMS lacks a mountain root, and that the top surface of the lower crust has been elevated by 11 km, leading to positive IGA, tectonic load and density load. Thirdly, according to Watts＇s flexural isostasy model, elastic deflection occurs, suggesting that the limited （i.e. narrow） tectonic and density load driven by lower crustal flow in the LMS have led to asymmetric flexural subsidence in the foreland basin and lifting of the forebulge. Finally, based on the correspondence between zones of extremely high positive IGA and the presence of the Precambrian Pengguan-Baoxing complexes in the LMS, the first appearance of erosion gravels from the complexes in the Dayi Conglomerate layer of the Chengdu Basin suggest that positive IGA and lower crustal flow in the LMS took place at 3.6 Ma or slightly earlier.

High-Order Radial Derivatives of Harmonic Function and Gravity Anomaly

The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.