A Folding Calculation Method Based on the Preconditioned Conjugate Gradient Inversion Algorithm of Gravity Gradient Tensor

Tian, Yu; Ke, Xiaoping; Wang, Yong

doi:10.1007/s00024-018-1965-z

Cited by 7 publications

(9 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…xz , T yy , T zz , 0 T . The contribution of each component and its differences from the joint inversion can be found in our previous studies (Tian et al, 2019b). Additionally,…”

Section: Inversion Methodsmentioning

confidence: 69%

Sequential inversion of GOCE satellite gravity gradient data and terrestrial gravity data for the lithospheric density structure in the North China Craton

Tian

Wang

2020

Solid Earth

Self Cite

View full text Add to dashboard Cite

Abstract. The North China Craton (NCC) is one of the oldest cratons in the world. Currently, the destruction mechanism and geodynamics of the NCC remain controversial. All of the proposed views regarding the issues involve studying the internal density structure of the NCC lithosphere. Gravity field data are among the most important data in regard to investigating the lithospheric density structure, and gravity gradient data and gravity data each possess their own advantages. Given the different observational plane heights between the on-orbit GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) satellite gravity gradient and terrestrial gravity and the effects of the initial density model on the inversion results, sequential inversion of the gravity gradient and gravity are divided into two integrated processes. By using the preconditioned conjugate gradient (PCG) inversion algorithm, the density data are calculated using the preprocessed corrected gravity anomaly data. Then, the newly obtained high-resolution density data are used as the initial density model, which can serve as constraints for the subsequent gravity gradient inversion. Several essential corrections are applied to the four gravity gradient tensors (Txx, Txz, Tyy, Tzz) of the GOCE satellite, after which the corrected gravity gradient anomalies (T′xx, T′xz, T′yy, T′zz) are used as observations. The lithospheric density distribution result within the depth range of 0–180 km in the NCC is obtained. This study clearly illustrates that GOCE data are helpful in understanding the geological settings and tectonic structures in the NCC with regional scale. The inversion results show that in the crust the eastern NCC is affected by lithospheric thinning with obvious local features. In the mantle, the presented obvious negative-density areas are mainly affected by the high-heat-flux environment. In the eastern NCC, the density anomaly in the Bohai Bay area is mostly attributed to the extension of the Tancheng–Lujiang major fault at the eastern boundary. In the western NCC, the crustal density anomaly distribution of the Qilian block is consistent with the northwest–southeast strike of the surface fault belt, whereas such an anomaly distribution experiences a clockwise rotation to a nearly north–south direction upon entering the mantle.

show abstract

“…xz , T yy , T zz , 0 T . The contribution of each component and its differences from the joint inversion can be found in our previous studies (Tian et al, 2019b). Additionally,…”

Section: Inversion Methodsmentioning

confidence: 69%

Sequential inversion of GOCE satellite gravity gradient data and terrestrial gravity data for the lithospheric density structure in the North China Craton

Tian

Wang

2020

Solid Earth

Self Cite

View full text Add to dashboard Cite

show abstract

“…The L curve is a criterion that is based on a comparison between the actual data fitting function and the model objective function, which is applicable to solving problems with large scales. The effectiveness of this method has been validated in previous studies 2019).…”

Section: mentioning

confidence: 86%

Joint inversion of the lithospheric density struture in the North China Craton based on GOCE satellite gravity gradient data and surface gravity data

Tian¹,

Wang²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Abstract. The North China Craton (NCC) is one of the oldest cratons in the world. Currently, the destruction mechanism and geodynamics of the NCC still remain controversial. All of the proposed views regarding the issues involve studying the internal density structure of the NCC lithosphere. Gravity field data are one of the most important data in regard to investigating the lithospheric density structure, the gravity gradient data and the gravity data possess their own advantages. Given the inconsistency of the on orbit GOCE satellite gravity gradient and surface gravity observation plane height, also effects of the initial density model upon of the inversion results, the joint inversion of gravity gradient and gravity are divided into two integrated processes. By using the preconditioned conjugate gradient (PCG) inversion algorithm, the density data are calculated using the preprocessed remaining gravity anomaly data. The newly obtained high resolution density data are then used as the initial density model, which can be served as the constraints for the subsequent gravity gradient inversion. Several essential corrections are performed for the four gravity gradient tensor (Txx，Txz，Tyy，Tzz) of the GOCE satellite, after which the remaining gravity gradient anomaly (T'xx，

show abstract

“…For a body of a certain volume V within the Earth, the formula for the gravitational potential at any point

P_{1} (x_{0}, y_{0}, z_{0})

in space can be expressed as follows (Pilkington, 2014; Tian et al., 2019):

U (P_{1}) = G ∭_{V} \frac{boldρ}{r} d V,

where G is the gravitational constant,

ρ

is the density of the body, and

r (x_{0}, y_{0}, z_{0}, x, y, z)

is the distance between the calculation point

P_{1} (x_{0}, y_{0}, z_{0})

and the volume V ( x , y , z ). Based on the expressions of the gravitational potential (Equation 1) and its second‐order partial derivatives, the following expressions of the gravity gradient components (

{bold-italicT}_{x x}

{bold-italicT}_{x z}

{bold-italicT}_{y y}

{bold-italicT}_{z z}

) can be obtained (Pilkington, 2014; Tian et al., 2019):

\begin{array}{l} {bold-italicT}_{x x} (P_{1}) = G ρ ∭ \frac{2 {(x - x_{0})}^{2} - {(y - y_{0})}^{2} - {(z - z_{0})}^{2}}{[{(x - x_{0})}^{2} + (y - y_{0})} \end{array}

…”

Section: Methodsmentioning

confidence: 99%

“…For a body of a certain volume V within the Earth, the formula for the gravitational potential at any point   1 0 0 0 , , P x y z in space can be expressed as follows (Pilkington, 2014;Tian et al, 2019):…”

Section: Kernel Function Calculationmentioning

confidence: 99%

Gravity Gradient Inversion of Gravity Field and Steady‐State Ocean Circulation Explorer Satellite Data for the Lithospheric Density Structure in the Qinghai‐Tibet Plateau Region and the Surrounding Regions

Tian

Wang

et al. 2021

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

The Qinghai-Tibet Plateau is the highest, largest, and youngest plateau on Earth (Molnar & Tapponnier, 1975). The Qinghai-Tibet Plateau is known as the roof of the world, averaging over 4,000 m of altitude and covering an area of 2.5 million square kilometers. In the Cenozoic, the continual northward subduction of the Indian Plate toward the Eurasian Plate have vertically thickened the crust, which has caused lithospheric deformation and the flow of deep materials in the Qinghai-Tibet Plateau region (TPR). The TPR is formed under the complex stress actions of Indian Plate subduction effects and blocking effects (Teng et al., 2008) of the surrounding northern regions (Tarim Basin, Turpan Basin, and Junggar Basin), northeastern regions (Ordos Block), and southern regions (South China). After the long period of tectonic deformation in the TPR, the TPR is consist of several major arc-arc collision and arc-continent collision junction zones with different scales. The TPR is generally divided into five blocks, the Himalaya Block, the Lhasa Block, the Qiangtang Block, the Songpan Ganzi Block, and Qaidam Basin from south to north (Pan et al., 2012). In addition, stress has not only concentrated within the TPR but has also been transferred to the surrounding regions (SRs), forming a series of large boundary fault zones, such as Altyn Tagh fault, Karakorum fault, Kunlun fault system, Longmen Shan thrust belt, and Qinling fault. The geographic area within E75°-E114° and N22°-N47° is defined as the study area, which covers the TP-SRs. The topography and main geological structures of the Qinghai-Tibet Plateau and surrounding regions (TP-SRs) are shown in Figure 1.

show abstract

A Folding Calculation Method Based on the Preconditioned Conjugate Gradient Inversion Algorithm of Gravity Gradient Tensor

Cited by 7 publications

References 32 publications

Sequential inversion of GOCE satellite gravity gradient data and terrestrial gravity data for the lithospheric density structure in the North China Craton

Sequential inversion of GOCE satellite gravity gradient data and terrestrial gravity data for the lithospheric density structure in the North China Craton

Joint inversion of the lithospheric density struture in the North China Craton based on GOCE satellite gravity gradient data and surface gravity data

Gravity Gradient Inversion of Gravity Field and Steady‐State Ocean Circulation Explorer Satellite Data for the Lithospheric Density Structure in the Qinghai‐Tibet Plateau Region and the Surrounding Regions

Contact Info

Product

Resources

About