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.

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.

Evaluation and extraction of weak gravity and magnetic anomalies

In this paper, I introduce what are called weak gravity and magnetic anomalies and propose standards for estimating their reliability. I also introduce new techniques for processing this kind of weak anomaly. These techniques consist of interference elimination and weak signal extraction. Practical applications have proved their effectiveness, Weak gravity and magnetic anomalies will get more attention with the development of targeted exploration.

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.

Hawking radiation from gravity’s rainbow via gravitational anomaly

Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigates Hawking radiation from the modified Schwarzschild black hole from gravity＇s rainbow from the anomaly point of view. Unlike the general Schwarzschild space-time, the metric of this black hole depends on the energies of probes. The obtained result shows to restore the underlying general covariance at the quantum level in the effective field, the covariant compensating flux of energy-momentum tensor, which is related to the energies of the probes, should precisely equal to that of a （1 ＋ 1）-dimensional blackbody at the Hawking temperature.

Relationship between the regional tectonic activity and crustal structure in the eastern Tibetan plateau discovered by gravity anomaly

The eastern Tibetan plateau has been getting more and more attention because it combines active faults,uplifting, and large earthquakes together in a high-population region. Based on the previous researches, the most of Cenozoic tectonic activities were related to the regional structure of the local blocks within the crustal scale. Thus,a better understanding of the crustal structure of the regional tectonic blocks is an important topic for further study. In this paper, we combined the simple Bouguer gravity anomaly with the Moho depths from previous studies to investigate the crustal structure in this area. To highlight the crustal structures, the gravity anomaly caused by the Moho relief has been reduced by forward modeling calculations. A total horizontal derivative（THD） had been applied on the gravity residuals. The results indicated that the crustal gravity residual is compatible with the topography and the geological settings of the regional blocks,including the Sichuan basin, the Chuxiong basin, the Xiaojiang fault, and the Jinhe fault, as well as the Longmenshan fault zone. The THD emphasized the west margin of Yangtze block, i.e., the Longriba fault zone and the Xiaojiang fault cut through the Yangtze block. The checkboard pattern of the gravity residual in the SongpanGarze fold belt and Chuandian fragment shows that the crust is undergoing a southward and SE-directed extrusion,which is coincident with the flowing direction indicatedfrom the GPS measurements. By integrating the interpretations, the stepwise extensional mechanism of the eastern Tibetan plateau is supported by the southeastward crustal deformation, and the extrusion of Chuandian fragment is achieved by Xianshuihe fault.

Refining geoid and vertical gradient of gravity anomaly

We have derived and tested several relations between geoid （N） and quasi-geoid （~） with model validation. The elevation correction consists of the first-term （Bouguer anomaly） and second-term （vertical gradient of gravity anomaly）. The vertical gradient was obtained from direct measurement and terrain calcula- tion. The test results demonstrated that the precision of geoid can reach centimeter-level in mountains less than 5000 meters high.

Bouguer Gravity Anomaly in the Andean Orogenic Belt and its Dynamic Implications for Regional Tectonic Evolution

Calculated Bouguer gravity anomalies from the Andean orogenic belt interpreted as derived from regional gravity data to aid understanding of the lithospheric structure and tectonic evolution of the belt.These anomalies reveal lithospheric structures distributed throughout the belt,including linear and circular structures.NE-trending structures reflect sinistral transpression across the northern part of the belt,and NW-trending structures represent dextral transtension in the southern part.These results are supported by gravity-anomaly patterns that demonstrate mantle flow in a trench-parallel direction both northward and southward away from the stagnation band that is beneath the subducting Nazca slab.This mantle flow has served as an important driving force in the evolution of the Andean orogenic belt.Features of the modified tectonic model of the Andean orogenic belt are consistent with the spatial variation in and interpretation of Bouguer gravity anomalies.

Interpretation of residual gravity anomaly caused by simple shaped bodies using very fast simulated annealing global optimization

A very fast simulated annealing（VFSA） global optimization is used to interpret residual gravity anomaly.Since,VFSA optimization yields a large number of best-fitted models in a vast model space;the nature of uncertainty in the interpretation is also examined simultaneously in the present study.The results of VFSA optimization reveal that various parameters show a number of equivalent solutions when shape of the target body is not known and shape factor ＇q＇ is also optimized together with other model parameters.The study reveals that amplitude coefficient k is strongly dependent on shape factor.This shows that there is a multi-model type uncertainty between these two model parameters derived from the analysis of cross-plots.However,the appraised values of shape factor from various VFSA runs clearly indicate whether the subsurface structure is sphere,horizontal or vertical cylinder type structure.Accordingly,the exact shape factor（1.5 for sphere,1.0 for horizontal cylinder and 0.5 for vertical cylinder）is fixed and optimization process is repeated.After fixing the shape factor,analysis of uncertainty and cross-plots shows a well-defined uni-model characteristic.The mean model computed after fixing the shape factor gives the utmost consistent results.Inversion of noise-free and noisy synthetic data as well as field data demonstrates the efficacy of the approach.

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

The Ying-Qiong Basin is located on the northwestern margin of the South China Sea and at the junction of the South China Block and the Indochina Block.It is characterized by complex geological structures.The existing seismic data in the study area is sparse due to the lack of earthquake activities.Because of the limited source energy and poor coverage of seismic data,the knowledge of deep structures in the area,including the spatial distribution of deep faults,is incomplete.Contrarily,satellite gravity data cover the entire study area and can reveal the spatial distribution of faults.Based on the wavelet multi-scale decomposition method,the Bouguer gravity field in the Ying-Qiong Basin was decomposed and reconstructed to obtain the detailed images of the first-to sixth-order gravitational fields.By incorporating the known geological features,the gravitational field responses of the main faults in the Ying-Qiong Basin were identified in the detailed fields,and the power spectrum analysis yielded the depths of 1.4,8,15,26.5,and 39 km for the average burial depths of the bottom surfaces from the first-to fifth-order detailed fields,respectively.The four main faults in the Yinggehai Basin all have a large active depth range:fault A(No.1)is between 5 and 39 km,fault B is between 26.5 and 39 km,and faults C and D are between 15 and 39 km.However,the depth of active faults in the Qiongdongnan Basin is relatively shallow,mainly between 8 and 26.5 km.