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 anomalie...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.展开更多
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 Grav...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.展开更多
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 ...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.展开更多
In this paper we use gravity data to study fine crustal structure and seismogenic environment beneath Beijing and its surrounding regions.Multi-scale wavelet analysis method is applied to separating gravity fields.Log...In this paper we use gravity data to study fine crustal structure and seismogenic environment beneath Beijing and its surrounding regions.Multi-scale wavelet analysis method is applied to separating gravity fields.Logarithmic power spectrum method is also used to calculate depth of gravity field source.The results show that the crustal structure is very complicated beneath Beijing and its surrounding areas.The crustal density exhibits laterally inhomogeneous.There are three large scale tectonic zones in North China,i.e.,WNW-striking Zhangjiakou-Bohai tectonic zone(ZBTZ),NE-striking Taihang piedmont tectonic zone(TPTZ)and Cangxian tectonic zone(CTZ).ZBTZ and TPTZ intersect with each other beneath Beijing area and both of them cut through the lithosphere.The upper and middle crusts consist of many small-scale faults,uplifts and depressions. In the lower crust,these small-scale tectonic units disappear gradually,and they are replaced by large-scale tectonic units.In surrounding regions of Beijing,ZBTZ intersects with several other NE-striking tectonic units, such as Cangxian uplift,Jizhong depression and Shanxi Graben System(SGS).In west of Taihangshan uplift, gravity anomalies in upper and middle crusts are correlated with geological and topographic features on the surface.Compared with the crust,the structure is comparatively simple in uppermost mantle.Earthquakes mainly occurred in upper and middle crusts,especially in transitional regions between high gravity anomaly and low gravity anomaly.Occurrence of large earthquakes may be related to the upwelling of upper mantle and asthenosphere heat flow materials,such as Sanhe earthquake(M_S8.0)and Tangshan earthquake(M_S7.8).展开更多
South China is characterized by large-area multistage magmatism.It boasts a huge number of polymetallic deposits such as W-Sn,Cu-Au,rare earth deposits,thus serving as a"giant granary"of metal mineral resour...South China is characterized by large-area multistage magmatism.It boasts a huge number of polymetallic deposits such as W-Sn,Cu-Au,rare earth deposits,thus serving as a"giant granary"of metal mineral resources in China(Lüet al.,2021).展开更多
Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study are...Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study area, which is located in the southwestern corner of the Arabian Peninsula bounded by the Red Sea and the Gulf of Aden. In this work, a 3D Moho depth model of the study area is constructed for the first time by inverting gravity data from the Earth Gravitational Model(EGM2008) using the ParkerOldenburg algorithm. This model indicates the shallow zone is situated at depths of 20 km to 24 km beneath coastal plains, whereas the deep zone is located below the plateau at depths of 30 km to 35 km and its deepest part coincides mainly with the Dhamar-Rada ’a Quaternary volcanic field. The results also indicate two channels of hot magmatic materials joining both the Sana’a-Amran Quaternary volcanic field and the Late Miocene Jabal An Nar volcanic area with the Dhamar-Rada’a volcanic field. This conclusion is supported by the widespread geothermal activity(of mantle origin) distributed along these channels,isotopic data, and the upper mantle low velocity zones indicated by earlier studies.展开更多
Fault geometry, kinematics, geophysics, the tectonic stress field and tectonic evolution of the Zhouwang fault in the southern Jiangnan tectonic transition zone of the Lower Yangtze region, eastern China are examined....Fault geometry, kinematics, geophysics, the tectonic stress field and tectonic evolution of the Zhouwang fault in the southern Jiangnan tectonic transition zone of the Lower Yangtze region, eastern China are examined. Field observations show the fault is composed of a series of nearly E–W trending, N–S dipping faults, and four stages of tectonism(sinistral strike-slip, thrust nappe, normal fault, and dextral strike-slip) developed in turn. Geophysical data show that the fault trends almost linearly E–W along a flat, steep gravity gradient at shallow depth, with distinct gravity anomalies to the north and south and different in the north and south. Also, the deep part is characterized by northward dip and a gradual slowing down. Tectonic stress field analysis indicates that the fault experienced four tectonic movements: NNE–SSW compression, NNW–SSE compression, NEE–SWW extension, and E–W compression. Combined with regional tectonic background and previous research results, this indicates that:(1) the Zhouwang fault experienced sinistral strike-slip movement during the Indosinian Period(260–200 Ma);(2) thrust nappes developed during the early Yanshanian Period(163–145 Ma);(3) a normal fault occurred in the late Yanshanian Period(125–65 Ma);and(4) dextral strike-slip movement occurred in the Himalayan Period(ca. 50–37 Ma). The results reveal the tectonic evolution of the fault during Mesozoic deformation in the area, and also reveal the geological evolution and tectonic transformation of the Lower Yangtze region, which is key to our understanding of intracontinental deformation in eastern China.展开更多
To determine the lateral and vertical variations in crustal structure and their influence on the seismicity of the Western North China Craton,the Trans-North China Orogen,and the surrounding regions,the wavelet multi-...To determine the lateral and vertical variations in crustal structure and their influence on the seismicity of the Western North China Craton,the Trans-North China Orogen,and the surrounding regions,the wavelet multi-scale structures,Moho depth,crustal density structures,and isostatic state are modelled using Bouguer gravity anomaly data,topography,and earthquake focal mechanisms.We obtained homogeneous crustal densities and deviations of<1 km between the crustal thicknesses estimated from the isostatic model and those inverted from the Bouguer gravity anomalies in the Ordos Block,the Inner Mongolia Suture Zone,the Sichuan Basin,and the Jizhong Depression.These results provide new evidence for relatively simple and stable continental crustal structures,and indicate that these regions will remain stable in both the vertical and lateral directions.The Hetao Graben,Yinchuan Graben,Weihe Basin,and Shanxi graben system have heterogeneous crustal densities and are isostatically over-compensated.In contrast,the crust beneath the Yinshan Uplift,Lvliang Uplift,and northern and central Taihang Uplift is thin and under-compensated.The heterogeneous crustal densities and non-isostatic state beneath the Tibetan Plateau and Qinling Central China Orogen indicate that these two blocks are unstable in the vertical and lateral directions.Although Cenozoic deformation of the North China Craton is thought to be driven by lithospheric stresses related to the India-Eurasia collision and Pacific slab retreat in South East Asia,we suggest that gravitational potential energy created by the heterogeneous crustal structure modulates these first-order forces.The results of this study could constrain the causes of seismicity in systems surrounding the Ordos Block.展开更多
Using the gravity/GNSS data of 318 stations observed in 2020,this paper optimizes the Bouguer and free-air gravity anomalies around the 2021 Yangbi Ms 6.4 Earthquake,inverses the lithospheric density structure of the ...Using the gravity/GNSS data of 318 stations observed in 2020,this paper optimizes the Bouguer and free-air gravity anomalies around the 2021 Yangbi Ms 6.4 Earthquake,inverses the lithospheric density structure of the focal area,and obtains the distribution of isostatic additional force borne by the lithosphere.The results show that the Bouguer gravity anomaly in western Yunnan varies from-120 to-360 m Gal.As a whole the anomalies are large in the north and small in the south,and the value in the source area of the 2021 Yangbi Ms 6.4 Earthquake is about-260 m Gal.Significant lateral differences indicates that the crust around the great earthquake does not belong to a solid and stable tectonic unit.The lithosphere in the source area is basically in equilibrium,indicating that the occurrence of the great event is not relative to the lithospheric equilibrium,but to the differential movement of the crust in the horizontal direction.In addition,we obtain the teleseismic SKS phases of 51 stations.As a whole,the polarization direction of fast wave in western Yunnan is approximately vertical to the maximum gradient change direction of regional Bouguer gravity anomaly that reflects the change of Moho.展开更多
Integral and differentiation are two mathematical operations in modern calculus and analysis which have been commonly applied in many fields of science.Integration and differentiation are associated and linked as inve...Integral and differentiation are two mathematical operations in modern calculus and analysis which have been commonly applied in many fields of science.Integration and differentiation are associated and linked as inverse operation by the fundamental theorem of calculus.Both integral and differentiation are defined based on the concept of additive Lebesgue measure although various generations have been developed with different forms and notations.Fractals can be considered as geometry with fractal dimension(e.g.,non-integer)which no longer possesses Lebesgue additive property.Accordingly,the ordinary integral and differentiation operations are no longer applicable to the fractal geometry with singularity.This paper introduces a recently developed concept of fractal differentiation and integral operations.These operations are expressed using the similar notations of the ordinary operations except the measures are defined in fractal space or measures with fractal dimension.The calculus operations can be used to describe the new concept of fractal density,the density with fractal dimension or density of matter with fractal dimension.The concept and methods are also applied to interpret the Bouguer anomaly over the mid-ocean ridges.The results show that the Bouguer gravity anomaly depicts singularity over the mid-ocean ridges.The development of new calculus operations can significantly improve the accuracy of geodynamic models.展开更多
基金jointly funded by the Ministry of Science and Technology of the People’s Republic of China (Grant No. 2019YFA0708601-02)the National Natural Science Foundation of China (Grant Nos. 41404070 and 41374101)the China Geological Survey (Grant Nos. DD20201116, DD20190448, DD20221647, DD20221649 and DD201609-05)
文摘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.
基金“Wings of Quality”Program of QICS(No.2020-zlzy-015)。
文摘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.
基金sup-ported by the National Natural Science Foundation of China(Nos.41530963,91858215 and 41906048)the Fundamental Research Funds for the Central Universities(No.201964015)the Laboratory for Marine Mineral Resources,Qingdao National Laboratory for Marine Science and Technology(No.MMRZZ201801).
文摘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.
基金supported by professional fund for basic scientific research of Chinese Central-level Public-welfare College/ Institute from Chinese Finance Ministry,and Institute of Crustal Dynamics,China Earthquake Administration (ZDJ2007-1)
文摘In this paper we use gravity data to study fine crustal structure and seismogenic environment beneath Beijing and its surrounding regions.Multi-scale wavelet analysis method is applied to separating gravity fields.Logarithmic power spectrum method is also used to calculate depth of gravity field source.The results show that the crustal structure is very complicated beneath Beijing and its surrounding areas.The crustal density exhibits laterally inhomogeneous.There are three large scale tectonic zones in North China,i.e.,WNW-striking Zhangjiakou-Bohai tectonic zone(ZBTZ),NE-striking Taihang piedmont tectonic zone(TPTZ)and Cangxian tectonic zone(CTZ).ZBTZ and TPTZ intersect with each other beneath Beijing area and both of them cut through the lithosphere.The upper and middle crusts consist of many small-scale faults,uplifts and depressions. In the lower crust,these small-scale tectonic units disappear gradually,and they are replaced by large-scale tectonic units.In surrounding regions of Beijing,ZBTZ intersects with several other NE-striking tectonic units, such as Cangxian uplift,Jizhong depression and Shanxi Graben System(SGS).In west of Taihangshan uplift, gravity anomalies in upper and middle crusts are correlated with geological and topographic features on the surface.Compared with the crust,the structure is comparatively simple in uppermost mantle.Earthquakes mainly occurred in upper and middle crusts,especially in transitional regions between high gravity anomaly and low gravity anomaly.Occurrence of large earthquakes may be related to the upwelling of upper mantle and asthenosphere heat flow materials,such as Sanhe earthquake(M_S8.0)and Tangshan earthquake(M_S7.8).
基金jointly supported by the National Natural Science Foundation of China(Grant Nos.92062108,41630320 and 41574133)the China Geological Survey project(Grant Nos.DD20190012 and DD20160082)the National Key R&D Program of China(Grant No.2016YFC0600201)
文摘South China is characterized by large-area multistage magmatism.It boasts a huge number of polymetallic deposits such as W-Sn,Cu-Au,rare earth deposits,thus serving as a"giant granary"of metal mineral resources in China(Lüet al.,2021).
文摘Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study area, which is located in the southwestern corner of the Arabian Peninsula bounded by the Red Sea and the Gulf of Aden. In this work, a 3D Moho depth model of the study area is constructed for the first time by inverting gravity data from the Earth Gravitational Model(EGM2008) using the ParkerOldenburg algorithm. This model indicates the shallow zone is situated at depths of 20 km to 24 km beneath coastal plains, whereas the deep zone is located below the plateau at depths of 30 km to 35 km and its deepest part coincides mainly with the Dhamar-Rada ’a Quaternary volcanic field. The results also indicate two channels of hot magmatic materials joining both the Sana’a-Amran Quaternary volcanic field and the Late Miocene Jabal An Nar volcanic area with the Dhamar-Rada’a volcanic field. This conclusion is supported by the widespread geothermal activity(of mantle origin) distributed along these channels,isotopic data, and the upper mantle low velocity zones indicated by earlier studies.
基金supported by the Second-level Project of Nanjing Geological Survey Center of the China Geological Survey(Grant No.DD20190043)the National Natural Science Foundation of China(Grant Nos.41572177,41272213,41573023,41072161,41502193,41272222)。
文摘Fault geometry, kinematics, geophysics, the tectonic stress field and tectonic evolution of the Zhouwang fault in the southern Jiangnan tectonic transition zone of the Lower Yangtze region, eastern China are examined. Field observations show the fault is composed of a series of nearly E–W trending, N–S dipping faults, and four stages of tectonism(sinistral strike-slip, thrust nappe, normal fault, and dextral strike-slip) developed in turn. Geophysical data show that the fault trends almost linearly E–W along a flat, steep gravity gradient at shallow depth, with distinct gravity anomalies to the north and south and different in the north and south. Also, the deep part is characterized by northward dip and a gradual slowing down. Tectonic stress field analysis indicates that the fault experienced four tectonic movements: NNE–SSW compression, NNW–SSE compression, NEE–SWW extension, and E–W compression. Combined with regional tectonic background and previous research results, this indicates that:(1) the Zhouwang fault experienced sinistral strike-slip movement during the Indosinian Period(260–200 Ma);(2) thrust nappes developed during the early Yanshanian Period(163–145 Ma);(3) a normal fault occurred in the late Yanshanian Period(125–65 Ma);and(4) dextral strike-slip movement occurred in the Himalayan Period(ca. 50–37 Ma). The results reveal the tectonic evolution of the fault during Mesozoic deformation in the area, and also reveal the geological evolution and tectonic transformation of the Lower Yangtze region, which is key to our understanding of intracontinental deformation in eastern China.
基金supported by National Key Research and Development Program of China (Grant No. 2016YFC0600501)National Basic Research Program of China (Grant No. 2015CB452605)+2 种基金National Natural Science Foundation of China (Grant Nos. 41702075 and 41572315)Geological Survey Project of China (Grant No. DD20160045)the State Key Program of National Natural Science of China (Grant No. 41430320)
文摘To determine the lateral and vertical variations in crustal structure and their influence on the seismicity of the Western North China Craton,the Trans-North China Orogen,and the surrounding regions,the wavelet multi-scale structures,Moho depth,crustal density structures,and isostatic state are modelled using Bouguer gravity anomaly data,topography,and earthquake focal mechanisms.We obtained homogeneous crustal densities and deviations of<1 km between the crustal thicknesses estimated from the isostatic model and those inverted from the Bouguer gravity anomalies in the Ordos Block,the Inner Mongolia Suture Zone,the Sichuan Basin,and the Jizhong Depression.These results provide new evidence for relatively simple and stable continental crustal structures,and indicate that these regions will remain stable in both the vertical and lateral directions.The Hetao Graben,Yinchuan Graben,Weihe Basin,and Shanxi graben system have heterogeneous crustal densities and are isostatically over-compensated.In contrast,the crust beneath the Yinshan Uplift,Lvliang Uplift,and northern and central Taihang Uplift is thin and under-compensated.The heterogeneous crustal densities and non-isostatic state beneath the Tibetan Plateau and Qinling Central China Orogen indicate that these two blocks are unstable in the vertical and lateral directions.Although Cenozoic deformation of the North China Craton is thought to be driven by lithospheric stresses related to the India-Eurasia collision and Pacific slab retreat in South East Asia,we suggest that gravitational potential energy created by the heterogeneous crustal structure modulates these first-order forces.The results of this study could constrain the causes of seismicity in systems surrounding the Ordos Block.
基金financially supported by the National Natural Science Foundation of China (Nos.42274008,U1839208)the National Key R&D Program of China (No.2018YFC1503704)。
文摘Using the gravity/GNSS data of 318 stations observed in 2020,this paper optimizes the Bouguer and free-air gravity anomalies around the 2021 Yangbi Ms 6.4 Earthquake,inverses the lithospheric density structure of the focal area,and obtains the distribution of isostatic additional force borne by the lithosphere.The results show that the Bouguer gravity anomaly in western Yunnan varies from-120 to-360 m Gal.As a whole the anomalies are large in the north and small in the south,and the value in the source area of the 2021 Yangbi Ms 6.4 Earthquake is about-260 m Gal.Significant lateral differences indicates that the crust around the great earthquake does not belong to a solid and stable tectonic unit.The lithosphere in the source area is basically in equilibrium,indicating that the occurrence of the great event is not relative to the lithospheric equilibrium,but to the differential movement of the crust in the horizontal direction.In addition,we obtain the teleseismic SKS phases of 51 stations.As a whole,the polarization direction of fast wave in western Yunnan is approximately vertical to the maximum gradient change direction of regional Bouguer gravity anomaly that reflects the change of Moho.
基金supported by the National Key Technology R&D Program of China(No.2016YFC0600501)the State Key Program of the National Natural Science of China(No.41430320)。
文摘Integral and differentiation are two mathematical operations in modern calculus and analysis which have been commonly applied in many fields of science.Integration and differentiation are associated and linked as inverse operation by the fundamental theorem of calculus.Both integral and differentiation are defined based on the concept of additive Lebesgue measure although various generations have been developed with different forms and notations.Fractals can be considered as geometry with fractal dimension(e.g.,non-integer)which no longer possesses Lebesgue additive property.Accordingly,the ordinary integral and differentiation operations are no longer applicable to the fractal geometry with singularity.This paper introduces a recently developed concept of fractal differentiation and integral operations.These operations are expressed using the similar notations of the ordinary operations except the measures are defined in fractal space or measures with fractal dimension.The calculus operations can be used to describe the new concept of fractal density,the density with fractal dimension or density of matter with fractal dimension.The concept and methods are also applied to interpret the Bouguer anomaly over the mid-ocean ridges.The results show that the Bouguer gravity anomaly depicts singularity over the mid-ocean ridges.The development of new calculus operations can significantly improve the accuracy of geodynamic models.
