Joint inversion of gravity and vertical gradient data based on modified structural similarity index for the structural and petrophysical consistency constraint

Joint inversion is one of the most effective methods for reducing non-uniqueness for geophysical inversion.The current joint inversion methods can be divided into the structural consistency constraint and petrophysical consistency constraint methods,which are mutually independent.Currently,there is a need for joint inversion methods that can comprehensively consider the structural consistency constraints and petrophysical consistency constraints.This paper develops the structural similarity index(SSIM)as a new structural and petrophysical consistency constraint for the joint inversion of gravity and vertical gradient data.The SSIM constraint is in the form of a fraction,which may have analytical singularities.Therefore,converting the fractional form to the subtractive form can solve the problem of analytic singularity and finally form a modified structural consistency index of the joint inversion,which enhances the stability of the SSIM constraint applied to the joint inversion.Compared to the reconstructed results from the cross-gradient inversion,the proposed method presents good performance and stability.The SSIM algorithm is a new joint inversion method for petrophysical and structural constraints.It can promote the consistency of the recovered models from the distribution and the structure of the physical property values.Then,applications to synthetic data illustrate that the algorithm proposed in this paper can well process the synthetic data and acquire good reconstructed results.

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.

Predicting bathymetry based on vertical gravity gradient anomaly and analyses for various influential factors

The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of vertical gravity gradient(VGG)of a rectangular prism,the governing equations for determining sea depths to invert bathymetry.The governing equation is solved by linearization through an iterative process,and numerical simulations verify its algorithm and its stability.We also study the processing methods of different interference errors.The regularization method improves the stability of the inversion process for errors.A piecewise bilinear interpolation function roughly replaces the low-frequency error,and numerical simulations show that the accuracy can be improved by 41.2%after this treatment.For variable ocean crust density,simulation simulations verify that the root-mean-square(RMS)error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one.Finally,two test regions in the South China Sea are predicted and compared with ship soundings data,RMS errors of predictions are 71.1 m and 91.4 m,respectively.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

Tectonics of the Solomon Sea Basin from Vertical Gravity Gradient and Seismic Data

The Solomon Sea Basin is a Cenozoic back-arc spreading basin within the convergence system of the Pacific and Indo-Australian plates.Against the background of subduction polarity reversal,the current Solomon Sea Basin gradually formed a rhombic morphology with the subduction of the basin along the New Britain Trench and the Trobriand Trough.By analyzing the vertical gravity gradient,natural earthquake and seismic reflection data,this study determines the structural characteristics of the Solomon Sea Basin.It was found that the tectonics of the basin are characterized by the original expansion structure within the central part in addition to the structure induced by the latest subduction along the basin margin.The original spreading structure of the basin presented an east–west linear graben and horst controlled by normal faults during the basin expansion period.As a result of the subduction and slab-pull of the Solomon Sea Basin,extensional structure belts parallel to the New Britain Trench formed along the basin margin.

Distribution law and susceptibility of geohazards across a gradient belt of the Western Sichuan Plateau

Across a gradient belt of the Western Sichuan Plateau,geohazards have seriously limited economic and social development.According to incomplete statistics,15,673 geohazards have been recorded in the study area.In order to mitigate the threat of geohazards to human engineering activities in the region,an overall understanding of the distribution pattern of geohazards and susceptibility assessment are necessary.In this paper,a gradient belt of the Western Sichuan Plateau and its zoning criteria were defined.Subsequently,on the basis of relief amplitude,distance to faults,rainfall,and human activities,three indicators of endogenic process were introduced:Bouguer gravity anomaly gradient,vertical deformation gradient,and horizontal deformation gradient.Thereafter,the distribution patterns of geohazards were investigated through mathematical statistics and ArcGIS software.By randomly selecting 10,449 hazards,a geohazard susceptibility map was generated using the Information Value(IV)model.Finally,the IV model was validated against 5224 hazards using the Area Under Curve(AUC)method.The results show that 47.6%of the geohazards were distributed in the zone of steep slope.Geohazards showed strong responses to distance to faults,human activities,and annual rainfall.The distribution of geohazards in the gradient belt of the Western Sichuan Plateau is more sensitive to vertical internal dynamics factors(such as vertical deformation gradient and Bouguer gravity anomaly gradient)without any apparent sensitivity to horizontal internal dynamics factors.The areas of high and very-high risk account for up to 32.22%,mainly distributed in the Longmenshan and Anning River faults.According to the AUC plot,the success rate of the IV model for generating the susceptibility map is 76%.This susceptibility map and geohazard distribution pattern can provide a reference for geological disaster monitoring,preparation of post-disaster emergency measures,and town planning.

Bathymetry predicted from vertical gravity gradient anomalies and ship soundings

In this paper, the admittance function between seafloor undulations and vertical gravity gradient anomalies was derived. Based on this admittance function, the bathymetry model of 1 minute resolution was predicted from vertical gravity gradient anomalies and ship soundings in the experimental area from the northwest Pacific. The accuracy of the model is evaluated using ship soundings and existing models, including ETOPO1, GEBCO, DTU10 and V15.1 from SIO. The model＇s STD is 69. 481m, comparable with V15.1 which is generally believed to have the highest accuracy.

The North-South Seismic Belt： Vertical Deformation Velocity Gradient Research

The vertical deformation gradient can reflect the rate of vertical change in unit distance,and the vertical deformation velocity gradient can reflect the strength of the earth's crust tectonic activities. In this paper,using long period leveling data combined with GPS data,the vertical deformation gradient values are calculated. Leveling data and GPS data are two different means of monitoring deformation,but the result is approximately the same vertical deformation gradient. The results show that the spatial distribution of the vertical deformation velocity gradient and tectonic distribution has an obvious correlation. The most significant gradient anomalies along the North-South Seismic Belt are Xianshuihe fault, Longmenshan fault and Xiaojiang-Zemuhe fault, while the second gradient anomalies in the northeastern Qinghai-Tibetan plateau are Zhuanglanghe fault and Lenglongling fault. The Menyuan M_S6. 4 earthquake in 2016 occurred in this abnormal area. However,according to the vertical deformation high gradient area distribution,there is also the possibility of an earthquake occurrence in the Tianzhu and Jingtai area.The area of convergence of three major fault zones is the strongest tectonically active region of the North-South Seismic Belt.

Vertical patterns of the flora of seed plants in Dawei Mountain in Yunnan Province, Southwest China

Abstract Vertical gradients incorporate multiple resources gradients which vary continuously. Therefore, research on mountain floristic patterns along vertical gradients is important to reveal regular patterns of the flora along environmental gradients and to under- stand the changes in biodiversity along these gradients and their biological fitness. This study was designed to explore the character- istics of the floral compositions and ecological significance of floristic patterns along the vertical gradients of the National Nature Reserve of Dawei Mountain, located in the southeast of Yunnan Province. We analyzed the structural characteristics of the flora and the distribution patterns of its floristic components as a function of elevation on the basis of our field investigations along vertical vegetation transects. We carried out a systematic cluster analysis in order to determine the dividing line of floristic changes by eleva- tion along gradients and studied the effects of mountain climate on the vertical variation of floristic composition. The study shows： 1） that the obvious boundary, which differentiates tropical distribution, is located at an elevation of approximately 1,500 m, which separates the tropical rain forests from the evergreen broad-leaved forests; 2） that humid rain forests are found below 700 m elevation, mountain rain forests between 700 and 1,500 m, monsoon evergreen broad-leaved forests between 1,300 and 1,800 m and mountain mossy evergreen broad-leaved forests above 1,800 m. Non-representative mountain mossy dwarf forests （above 2,100 m） in the area are found on the windward sides and barren lands on mountain slopes; 3） that Hopea mollissima is one of the major component species of mountain rain forests, but it should not be considered as the major indicator species in humid rain forests as is generally accepted.

Numerical investigation of temperature gradient-induced thermal stress for steel–concrete composite bridge deck in suspension bridges

A3D finite element model(FEM)with realistic field measurements of temperature distributions is proposed to investigate the thermal stress variation in the steel–concrete composite bridge deck system.First,a brief literaturereview indicates that traditional thermal stress calculation in suspension bridges is based on the2D plane structure with simplified temperature profiles on bridges.Thus,a3D FEM is proposed for accurate stress analysis.The focus is on the incorporation of full field arbitrary temperature profile for the stress analysis.Following this,the effect of realistic temperature distribution on the structure is investigated in detail and an example using field measurements of Aizhai Bridge is integrated with the proposed3D FEM model.Parametric studies are used to illustrate the effect of different parameters on the thermal stress distribution in the bridge structure.Next,the discussion and comparison of the proposed methodology and simplified calculation method in the standard is given.The calculation difference and their potential impact on the structure are shown in detail.Finally,some conclusions and recommendations for future bridge analysis and design are given based on the proposed study.

Distribution characteristics of SOM and nitrogen on the eastern slope of Gongga Mountain

The distribution of soil organic matter (SOM) and nitrogen on Gongga Mountain was studied in this paper. The results showed that the content of SOM and nitrogen (N) of A horizon had an ascending trend with the increase of the elevation. The vegetation types distributed higher than the mixed broad-leaved and coniferous forest have the irregular trends. In the transitional zone vegetation such as mixed trees and treeline, the content of SOM and N is higher than other vegetation types. The distribution of SOM and N of A horizon is dependent on the synthetic effect of climate and vegetation types. The vertical distribution of SOM and N in soil profiles has the similar trends for all kinds of vegetation types, i.e., the content of A horizon is higher than that of the B and C horizons, which is the same to the distribution of dead animal and plant in soil. The soil C:N is between 7 and 25, which is relatively low comparing to the appropriate C:N of 25-30. The ratio of soil carbon to nitrogen (C:N)increases with the increase of the elevation, but its vertical distribution in soil horizons varies with different vegetation types. The N exists in SOM mainly in the form of organic nitrogen, and the soil C:N correlates significantly with SOM.

Study on Nitrogen Distribution in Leaf, Stem and Sheathat Different Layers in Winter Wheat Canopyand Their Influence on Grain Quality

Vertical distribution of nitrogen in wheat canopy, nitrogen remobilization and their influence on grain quality of winter wheat were studied. Two winter wheat cultivars, Jingdong8, a common cultivar, and Zhongyou9507, a high quality cultivar, were selected. Leaf nitrogen showed an obvious decreasing trend from the canopy top to the ground surface for all treatments in growth duration. There was no apparent vertical nitrogen gradient in stem and sheath of Zhongyou9507 compared with Jingdong8. Zhongyou9507 had more nitrogen remobilization from leaf, stem and sheath than Jingdong8 from middle grain filling to waxening, especially the nitrogen remobilization amount in stem and sheath, which was higher than that in Jingdong8 during growth duration. Higher vertical nitrogen gradients in Jingdong8 at anthesis had disadvantages on its grain quality. But higher vertical nitrogen gradients between middle and lower layers of Jingdong8 at grain filling stage enhanced its grain quality. Higher vertical nitrogen gradients in upper layer at anthesis and upper layer leaf and middle layer stem and sheath at grain filling stage had advantages on protein accumulation in grain of Zhongyou9507. There were positive correlations between foliar nitrogen remobilization amount and grain quality at later growth stage for the two cultivars. There was a positive correlation between quality of Jingdong8 and stem and sheath nitrogen remobilization amount from anthesis to early grain filling, and that of Zhongyou9507 emerged from anthesis to early grain filling and from middle grain filling to waxening. Contribution of leaf nitrogen to the quality of Jingdong8 was larger than nitrogen from stem and sheath. High protein content of Zhongyou9507 was attributed to the nitrogen condition in its leaf, stem and sheath. Nitrogen in stem and sheath played a more important role on the grain quality of Zhongyou9507 than on that of Jingdong8.

Experimental study on thermal environment in large-space building with low sidewall air supply

The thermal environmental characteristics are experim-entally studied in terms of different air supply volumes and outdoor meteorological parameters in a large-space building which is air conditioned with a low sidewall air supply.The experimental results show that the indoor vertical temperature distributions under different condition are similar.The maximum vertical temperature difference（MVTD）is up to about 20 ℃,and it linearly changes with the sol-air temperature.The indoor vertical temperature gradients（VTGs）in the upper,central and lower zones are different.The influence of the sol-air temperature on the VTGs in the upper and the lower zones is greater than that in the central zone.The characteristics of the VTGs in the three zones affected by the air supply volume are the same as those affected by the sol-air temperature.Besides,because of the small air velocity,the predicted mean vote（PMV）on comfort in the occupied zone is slightly high and the air temperature difference between the head and the ankle is usually more than 3 ℃.

On-road vehicle verification based on VS-HOG and ELM

A solution is proposed for the real-time vehicle verification which is an important problem for numerous on- road vehicle applications. First, based on the vertical symmetry characteristics of vehicle images, a vertical symmetrical histograms of oriented gradients （VS-HOG） descriptor is proposed for extracting the image features. In the classification stage, an extreme learning machine （ELM） is used to improve the real-time performance. Experimental data demonstrate that, compared with other classical methods, the vehicle verification algorithm based on VS-HOG and ELM achieves a better trade-off between cost and performance. The computational cost is reduced by using the algorithm, while keeping the performance loss as low as possible. Furthermore, experimental results further show that the proposed vehicle verification method is suitable for on-road vehicle applications due to its better performance both in efficiency and accuracy.

An Expression for Gravity Generated by an Anomalous Geological Body and Its Application in Bathymetry Inversion

The gravity anomaly and vertical gravity gradient due to anomalous geological bodies are mainly computed by numerical methods,so it is difficult and time-consuming to use the gravity-geological method to invert seafloor topography.This paper addresses this issue by deriving an expression for gravity generated by a cylinder based on a series expansion.The choice of number for terms in the series is estimated by comparing with the numerical method,especially when the depth H=4000m,the accuracy of 1 mGal(1 Gal=10^(-2)m/s^(2))can be achieved when the series are 9.The expressions can be used to establish the relationships between the shape of an anomalous body and the generated vertical gravity and vertical gravity gradient,respectively.Finally,the potential applications of the expressions in inverting seafloor topography are illustrated by synthetic examples.

Paleotectonic residual strain energy in Southwest China

Based on the orthotropic elastic theory of rock masses, the X-ray method was used to measure the distribution of macro-residual strain energy density along a depth profile,using core samples taken from 47 large-aperture deep boreholes in four regions of Southwest China： the Longmenshan, Anninghe, Honghe, and Xianshuihe fault zones.Then, the vertical gradients of the macro-residual strain energy density and the macroresidual strain energy contained in high-energy cuboid block segments along each fault zone were determined. The results demonstrate that the macro-residual strain energy stored at shallow levels in the rock mass in these fault zones may be partly responsible for generating many large earthquakes and may explain why the large earthquakes in this region are typically shallow.

Transformations between Aeromagnetic Gradients in Frequency Domain

Aeromagnetic gradients are often used to enhance details or add new insights for interpretation. The gradients may be measured or derived from the total field or from transformation between horizontal and vertical gradients. At present, vertical, horizontal, and triaxial aeromagnetic gradiometers are in operation throughout the world, while the first two are used more widely. Transformations between horizontal and vertical gradients are needed for acquiring three gradient components or for checking the validity of measured gradients. Transformation of potential field by fast Fourier transform technique in frequency domain is popularly used; however, when applied to transforming between gradients, there is a problem that needs resolving. Because those expressions of transform operators are undefined when u or v is equal to zero or u and v are simultaneously equal to zero （u is the frequency in x-direction, and v is the frequency in y-direction）, the operators cannot be sampled at these frequencies. Consequently, the transformation cannot be implemented by fast Fourier transform technique directly. In this article, shift sampling theory is employed for resolving this problem. Model test results show that the technique has good accuracy, and the real case of transformation indicates that the computed results agree better with the measured gradients; it demonstrates not only the effective- ness of method but also the reliability of the measured gradients.

Characteristics of the crustal magnetic anomaly and regional tectonics in the Qinghai-Tibet Plateau and the adjacent areas

Study of the characteristics of the crustal magnetic anomaly in the Qinghai-Tibet Plateau and the adjacent areas helps better understand the lithospheric structure and evolution, as well as the regional geodynamic processes. Here we analyze the distri- bution laws of the crustal magnetic anomaly and its vertical gradient, the decay characteristics of the anomaly, the contribu- tions from different wavelength bands to the anomaly, and the relationship between the anomaly and the crustal regional tec- tonics in the plateau and nearby, based on a new and higher degree geomagnetic model NGDC-EMM-720-V3 constructed from the surface, aeromagnetic, marine and satellite survey data. The results reveal that the positive and negative anomalies in the Qinghai-Tibet Plateau are weak, while those of the surrounding areas are strong. The boundary agrees well with the border of the plateau regional tectonics. The anomaly is nearly east-west in the central and western plateau, arc-shaped in the south- western and eastern, and nearly north-south in the southeastern, consistent with the tectonic trends. There are strong negative anomaly loci in the east and west syntaxis, whereas no significant differences exist among the Cenozoic blocks in the plateau interior. No direct correspondence exists between the anomaly and the crustal depth. On the background of a weak magnetic anomaly in the plateau, relatively stronger short wavelength fields from the shallower crust are overlapped in the Lhasa, Qilian, Qaidam, and Sichuan-Yunnan rhombic blocks. A strong negative anomaly in the east-west direction is distributed along the Himalayas, mainly caused by the middle and long wavelength bands in the deep and central crust. The magnetic structural lay- ers are stable in the Sichuan and Tarim basins. The anomalies at different altitudes over the southern plateau vary strongly, showing a drastic variation in the magnetic structure from the deep crust to the shallow crust.