Comparison of spectral and spatial methods for a Moho recovery from gravity and vertical gravity-gradient data

In global studies investigating the Earth’s lithospheric structure, the spectral expressions for the gravimetric forward and inverse modeling of the global gravitational and crustal structure models are preferably used, because of their numerical efficiency. In regional studies, the applied numerical schemes typically utilize the expressions in spatial form. Since the gravity-gradient observations have a more localized support than the gravity measurements, the gravity-gradient data (such as products from the Gravity field and steady-state Ocean Circulation Explorer - GOCE - gravity-gradiometry satellite mission) could preferably be used in regional studies, because of reducing significantly the spatial data-coverage required for a regional inversion or interpretation. In this study, we investigate this aspect in context of a regional Moho recovery. In particular, we compare the numerical performance of solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy in spectral and spatial domains from the gravity and (vertical) gravity-gradient data. We demonstrate that the VMM spectral solutions from the gravity and gravity-gradient data are (almost) the same, while the VMM spatial solutions differ from the corresponding spectral solutions, especially when using the gravity-gradient data. The validation of the VMM solutions, however, reveals that the VMM spatial solution from the gravity-gradient data has a slightly better agreement with seismic models. A more detailed numerical analysis shows that the VMM spatial solution formulated for the gravity gradient is very sensitive to horizontal spatial variations of the vertical gravity gradient, especially in vicinity of the computation point. Consequently, this solution provides better results in regions with a relatively well-known crustal structure, while suppressing errors caused by crustal model uncertainties from distant zones. Based on these findings we argue that the gravity-gradient data are more suitable than the gravity data for a regional Moho recovery.     

Combined Gravimetric–Seismic Crustal Model for Antarctica

The latest seismic data and improved information about the subglacial bedrock relief are used in this study to estimate the sediment and crustal thickness under the Antarctic continent. Since large parts of Antarctica are not yet covered by seismic surveys, the gravity and crustal structure models are used to interpolate the Moho information where seismic data are missing. The gravity information is also extended offshore to detect the Moho under continental margins and neighboring oceanic crust. The processing strategy involves the solution to the Vening Meinesz-Moritz’s inverse problem of isostasy constrained on seismic data. A comparison of our new results with existing studies indicates a substantial improvement in the sediment and crustal models. The seismic data analysis shows significant sediment accumulations in Antarctica, with broad sedimentary basins. According to our result, the maximum sediment thickness in Antarctica is about 15 km under Filchner-Ronne Ice Shelf. The Moho relief closely resembles major geological and tectonic features. A rather thick continental crust of East Antarctic Craton is separated from a complex geological/tectonic structure of West Antarctica by the Transantarctic Mountains. The average Moho depth of 34.1 km under the Antarctic continent slightly differs from previous estimates. A maximum Moho deepening of 58.2 km under the Gamburtsev Subglacial Mountains in East Antarctica confirmed the presence of deep and compact orogenic roots. Another large Moho depth in East Antarctica is detected under Dronning Maud Land with two orogenic roots under Wohlthat Massif (48–50 km) and the Kottas Mountains (48–50 km) that are separated by a relatively thin crust along Jutulstraumen Rift. The Moho depth under central parts of the Transantarctic Mountains reaches 46 km. The maximum Moho deepening (34–38 km) in West Antarctica is under the Antarctic Peninsula. The Moho depth minima in East Antarctica are found under the Lambert Trench (24–28 km), while in West Antarctica the Moho depth minima are along the West Antarctic Rift System under the Bentley depression (20–22 km) and Ross Sea Ice Shelf (16–24 km). The gravimetric result confirmed a maximum extension of the Antarctic continental margins under the Ross Sea Embayment and the Weddell Sea Embayment with an extremely thin continental crust (10–20 km).     

南海北部地壳密度结构:基于约束三维重力反演

地壳结构的揭示是研究陆缘伸展机制的基础.尽管在南海北部陆缘已开展了大量地壳尺度的二维地震探测,但目前还存在许多覆盖空白的地区,这些调查所得到的结果无法提供地壳结构的区域视图.为了揭示南海北部的地壳结构,本研究将水深和沉积物厚度信息作为约束条件,对空间重力异常进行区域三维反演,并利用地震研究的结果来衡量反演结果的质量.沿地震测线的密度切片显示,重力反演结果与地震研究结果具有良好的一致性.本研究通过选择两个与地震研究结果最匹配的密度异常等值面分别作为康拉德面和莫霍面,获取了莫霍面深度和上、下地壳的厚度.根据假设的相应初始地壳厚度,本研究进一步计算了全地壳、上地壳和下地壳的拉张因子.通过与已发表的居里面深度比较,发现南海北部大部分地区的居里面深度均位于莫霍面之下,其中西沙海槽的拉张因子βw大于3.5并且缺乏岩浆活动,是地幔橄榄岩蛇纹石化的潜在区域.南海北部陆缘的地壳拉张因子显示其经历了伸展方向为128°和160°的两组张裂运动,分别对应于神弧运动和珠琼运动一幕及二幕,在张裂过程中应力场发生了顺时针旋转.此外,上、下地壳的拉张因子表明北部陆缘普遍存在正向和反向差异伸展,陆架区域表现为反向差异伸展,洋陆过渡带为正向差异伸展,推测这种正向和反向差异伸展可能是由下地壳流动导致的,由地壳厚度差异引起的横向梯度力、软流圈浮力和沉积物负载共同驱动.     

基于变密度模型的位场界面反演

在波数域中用重力反演莫霍面深度时通常假定壳幔密度差为一常数,但这只是一种近似的密度模型,本文采用了密度随深度呈指数变化的变密度模型来反演莫霍面深度,给出了利用指数密度模型在波数域中计算重力异常的正演公式及界面深度的反演公式.利用指数密度模型及重力资料反演了青藏高原莫霍面的深度,分析了莫霍面的特征.结果表明,青藏高原莫霍面呈现出边缘浅、中部深的特点,边缘变化快、梯度大,中间变化梯度趋缓.中心地带的羌塘地体莫霍面深度达74 km,向四周慢慢变浅至67 km左右,边缘地区突然变浅至50km左右.通过常密度模型、变密度模型及地震反演得到的莫霍面的比较,证实变密度模型更适合于莫霍面结构的反演.     

A method of estimating the Moho density contrast with a tentative application of EGM08 and CRUST2.0

Based on Vening Meinez-Moritz global inverse isostatic problem, the Moho density contrast is formulated as that of finding a solution of a Fredholm integral equation of the first kind. We present solutions to this equation by combining global models of gravity (EGM08), topography (DTM2006) and seismic crust (CRUST2.0) to a resolution of 2°×2°. The test computations yielded Moho density contrasts ranging from 81.5 kg/m3 (in Pacific) to 988 kg/m³ (Tibet), with averages of 678 ± 78 and 334 ± 108 kg/m³ for continental and oceanic regions, respectively, and a global average of 448 ± 187 kg/m³. Estimated Moho depths range from 8 to 75 km with continental and oceanic averages of 36.6 ± 5.3 km and 12.9 ± 5.8 km, respectively, and a global average of 21 ± 12.5 km.     

基于卫星重磁资料的南海深部构造研究

南海深部构造对研究南海构造演化和油气勘探具有重要意义.本文对南海地区的自由空气重力异常进行布格校正、海水层校正和沉积层校正,得到布格重力异常,再对布格重力异常进行区域异常和局部异常分离,利用位场界面反演方法对区域布格异常进行反演计算得到研究区域的莫霍面深度分布;采用全变倾角化极方法对研究区域的卫星磁异常数据进行化极处理,并进一步对化极磁异常作向上延拓,得到延拓后化极磁异常结果.分析布格重力异常、莫霍面深度及化极磁异常特征,结合天然地震层析成像的证据,得到以下结论：推测南海北部陆缘的古俯冲带位置是从118.5°E,24°N沿北东向延伸至109°E,15°N;红河断裂入海后经过莺歌海盆地在海南岛南部转为南北向与越东断裂相接并延伸至万安盆地;推测中特提斯洋的部分闭合位置是从110°E,2°N到101°E,21°N.     

Expressions for the Global Gravimetric Moho Modeling in Spectral Domain

We apply a newly developed numerical method to improve the Moho geometry by the implementation of gravity data. This method utilizes expressions for the gravimetric forward and inverse modeling derived in a frequency domain. Methods for a spectral analysis and synthesis of the gravity field and crust density structures are applied in the gravimetric forward modeling of the consolidated crust-stripped gravity disturbances, which have a maximum correlation with the (a priori) Moho model. These gravity disturbances are obtained from the Earth’s gravity disturbances after applying the topographic and stripping gravity corrections of major known anomalous crust density structures; in the absence of a global mantle model, mantle density heterogeneities are disregarded. The isostatic scheme applied is based on a complete compensation of the crust relative to the upper mantle density. The functional relation is established between the (unknown) Moho depths and the complete crust-stripped isostatic gravity disturbances, which according to the adopted isostatic scheme have (theoretically) a minimum correlation with the Moho geometry. The system of observation equations, which describes the relation between spherical functions of the isostatic gravity field and the Moho geometry, is defined by means of a linearized Fredholm integral equation of the first kind. The Moho depths are determined based on solving the gravimetric inverse problem. The regularization is applied to stabilize the ill-posed solution. This numerical procedure is utilized to determine the Moho depths globally. The gravimetric result is presented and compared with the seismic Moho model. Our gravimetric result has a relatively good agreement with the CRUST2.0 Moho model by means of the RMS of differences (of 3.5 km). However, the gravimetric solution has a systematic bias. We explain this bias between the gravimetric and seismic Moho models by the unmodelled mantle heterogeneities and uncertainties in the CRUST2.0 global crustal model.     

The gravity and isostatic Moho undulations in Qinghai–Tibet plateau

It is our interest to study the Moho depths in the Qinghai–Tibet. An iterative hybrid spectral–classical methodology is applied to invert the gravity data and obtain the 3D variation in Moho depth. The gravity inversion is constrained by results from deep seismic sounding and seismological investigations. The Moho is found between 70 and 75 km depth over most of Tibet. Maximum depths of up to 80 km are found along the margins of the plateau, and shallower depths of 65 km correlate with an important suture running along central Tibet (Bangong Nujiang). At Moho level most of Tibet is isostatically compensated at 90–110%, according to the Airy isostatic model. The Qaidam basin in North-Eastern Tibet and the Tarim basin to the North-West are found to be over-compensated.     

东北地区重力均衡异常特征的初步研究

本文利用地面实测重力资料和地形高程资料,采用普拉特-海福特(Pratt-ttayford)重力均衡理论模型,取1°×1°方格网,通过使用现成改正表格查取改正值与个别计算点用理论公式计算作校核的方法,计算了我国东北地区75个计算点的均衡重力异常值;并对局部第四系覆盖较厚地区作了第四系密度改正;在此基础上,构制了我国东北N39°—49°,E121°—131°大部分地区的均衡重力异常图;结合区域布格重力异常和区域空间重力异常特征以及莫霍界面的起伏特点作了对比分析和讨论     

南北地震带南段地壳厚度重震联合最优化反演

重力反演方法是研究地壳结构和物性界面起伏的有效地球物理手段之一.本文收集了南北地震带南段67个已有的固定台站接收函数反演的Moho面深度结果,并使用基于EGM2008重力异常模型计算的布格重力异常,验证了本文提出的重震联合密度界面反演方法的有效性.利用接收函数对台站下方Moho面深度估计作为先验约束,定义了一类评价函数,通过对重力反演算法中尺度因子,平移因子和稳定性因子的最优选择,最小化重力反演结果与接收函数模型之间的差异.结果表明,本文提出的方法,可以有效地同化不同地球物理方法获得的反演模型,且通过重震联合反演可以改进由于对空间分布不均匀的接收函数结果插值可能而引起的误差.本文还通过引入Crust1.0的Moho面深度为初值,同时考虑地壳密度的横向不均匀分布,通过模型之间的联合反演有效改善了地球物理反演模型间的不一致性问题.本文反演得到的最优化Moho面深度模型与已知67个台站位置接收函数模型之间的标准差约1.9km,小于Crust1.0与接收函数结果模型之间标准差为3.73km的统计结果.本文研究结果对于同化重震反演结果、精化地壳密度界面模型,都具有十分重要的参考意义.     

优化滤波方法及其在中国大陆布格重力异常数据处理中的应用

在优选延拓法的理论基础上,研究提出基于格林等效层概念和维纳滤波器的优化滤波法,用于对重力异常数据进行去噪和分离.与传统向上延拓法和优选延拓法相比,优化滤波法分离异常与延拓高度无关,不需要已知延拓高度,具有一定的优势.理论重力模型数据的去噪和异常分离试验表明优化滤波法有效,异常分离效果优于传统向上延拓法和带通滤波法.利用优化滤波法对中国大陆重力异常数据去噪和异常分离,得到有效的布格重力异常和区域重力异常.以中国大陆深地震探测推断的莫霍面深度信息为约束,对区域重力异常数据进行密度界面约束反演,得到中国大陆莫霍面深度分布.本文方法为中国大陆深部探测和区域构造研究提供一定的技术支撑.     

Inversion of gravity and topography data for the crust thickness of China and its adjacent region

Introduction Since the middle of the century, gravitational isostasy has been a fundamental hypothesis for inverting the gravity data to find the crust thickness. Geophysicists have done a lot of researches on using gravity data to investigate the depth of Moho discontinuity. Since 1980, the International Lithosphere Program emphasized the importance of investigating the Moho depth variation. Thereafter a lot of results have been published in the world (Braitenberg et al, 2000; Kaban et al,…     

Spatial and Spectral Analysis of Refined Gravity Data for Modelling the Crust–Mantle Interface and Mantle-Lithosphere Structure

We analyse spatial and spectral characteristics of various refined gravity data used for modelling and gravimetric interpretation of the crust–mantle interface and the mantle-lithosphere structure. Depending on the purpose of the study, refined gravity data have either a strong or weak correlation with the Moho depths (Moho geometry). The compilation of the refined gravity data is purely based on available information on the crustal density structure obtained from seismic surveys without adopting any isostatic hypothesis. We demonstrate that the crust-stripped relative-to-mantle gravity data have a weak correlation with the CRUST2.0 Moho depths of about 0.02. Since gravitational signals due to the crustal density structure and the Moho geometry are subtracted from gravity field, these refined gravity data comprise mainly the information on the mantle lithosphere and sub-lithospheric mantle. On the other hand, the consolidated crust-stripped gravity data, obtained from the gravity field after applying the crust density contrast stripping corrections, comprise mainly the gravitational signal of the Moho geometry, although they also contain the gravitational signal due to anomalous mass density structures within the mantle. In the absence of global models of the mantle structure, the best possible option of computing refined gravity data, suitable for the recovery/refinement of the Moho interface, is to subtract the complete crust-corrected gravity data from the consolidated crust-stripped gravity data. These refined gravity data, that is, the homogenous crust gravity data, have a strong absolute correlation of about 0.99 with the CRUST2.0 Moho depths due to removing a gravitational signal of inhomogeneous density structures within the crust and mantle. Results of the spectral signal decomposition and the subsequent correlation analysis reveal that the correlation of the homogenous crust gravity data with the Moho depths is larger than 0.9 over the investigated harmonic spectrum up to harmonic degree 90. The crust-stripped relative-to-mantle gravity data correlate substantially with the Moho depths above harmonic degree 50 where the correlation exceeds 0.5.     

龙门山及其邻区地球物理场与地震的关系

龙门山及其邻区地处青藏高原东缘，地质构造上处于不同构造单元的交汇地区。龙门山断裂带由多条大型推覆构造组成，利用重力资料对该区深部构造进行了研究。计算中采用Ｐａｒｋｅｒ－Ｏｌｃｌｅｎｂｕｒｇ三维位场反演方法。根据反演结果，综合其它地球物理和区域地质资料，研究了该区的地球物理场和地震的关系。     

Correction to the crustal thickness of the northwestern China using the data of seis-mic tomography

Introduction The gravity anomaly is an indicator of the density distribution of the underground material. Therefore the gravity anomalies have been important data used for studying the deep crustal struc-ture for a long time. Many people have made detailed researches on the regional crustal structure inverted by Bouguer anomalies. In particular some empirical formulae and practical algorithms about the crustal thickness were brought forward, and a series of results were obtained (MENG, 1996)…     

Crustal structure of northeastern margin of the Tibetan Plateau by receiver function inversion

Using seismic data of about one year recorded by 18 broadband stations of ASCENT project,we obtained 2547 receiver functions in the northeastern Tibetan Plateau.The Moho depths under 14 stations were calculated by applying the H-κ domain search algorithm.The Moho depths under the stations with lower signal-noise ratio(SNR) were estimated by the time delay of the PS conversion.Results show that the Moho depth varies in a range of ~40–60 km.The Moho near the Haiyuan fault is vague,and its depth is larger than those on its two sides.In the Qinling-Qilian Block,the Moho becomes shallower gradually from west to east.To the east of 105°E,the average depth of the Moho is 45 km,whereas the west is 50 km or even deeper.Combining our results with surface wave research,we suggest a boundary between the Qinling and the Qilian Mountains at around 105°E.S wave velocities beneath 15 stations have been obtained through a linear inversion by using Crust2.0 as an initial model,and the crustal thickness that was derived by H-κ domain search algorithm was also taken into account.The results are very similar to the results of previous active source studies.The resulting figure indicates that low velocity layers developed in the middle and lower crust beneath the transition zone of the Tibet Block and western Qinling,which may be related to regional faults and deep earth dynamics.The velocity of the middle and lower crust increases from the Songpan Block to the northeastern margin of Tibetan Plateau.Based on the velocity of the crust,the distribution of the low velocity zone and the composition of the curst(Poisson's ratio),we infer that the crust thickening results from the crust shortening along the direction of compression.     

南海海盆三维重力约束反演莫霍面深度及其特征

利用南海海盆及周边最新的重力,经过海底地形、沉积层的重力效应改正,并采用岩石圈减薄模型的温度场公式,校正了从张裂边缘到扩张海盆的热扰动重力效应.通过研究区的地震剖面和少量声呐数据得到的莫霍面深度点作为约束,采用基于"起伏界面初始模型"的深度修正量反演迭代公式,反演、计算了研究区的莫霍面深度及地壳厚度.结果表明,海盆区莫霍面深度在8~14 km之间,地壳厚度在3~9 km之间;东部海盆和西南海盆残留扩张中心沿NNE向展布向西南延伸至112°E,莫霍面深度超过12 km,地壳厚度在6 km以上,而西北海盆没有明显的增厚扩张中心;在西南海盆北缘的中沙地块南侧,存在一个近EW向地壳减薄带,地壳厚度在9~10 km;莫霍面深度14 km的等深线和地壳厚度9 km的等值线可指示洋陆边界位置.     

Construction of regional geophysical models based on the joint interpretation of gravitaty and seismic data

The technique of solving the inverse structural gravity problem based on the joint interpretation of gravity and seismic data is described in this paper. The method of solving is based on the method of local corrections, but involves some modifications described in the paper. An area of the northeastern part of the Urals and West Siberia (60°-65°N, 54°-72°E) was studied with the use of this technology and the spatial position of the boundaries of the crystalline crust of the Earth (its roof K₀ and base M) were determined from seismic and gravity data.     

Geodynamics of the Baikal-Stanovoy seismic belt

The convection generated tensional stress field in the Earth, as inferred from satellite gravity data, reveals an anomalous lens of upwelling mantle rocks under the Baikal rift zone. The point of no strain at 56°N 116°E forms a seismic gap along the Baikal-Stanovoy seismic belt. East of this point, the stress field changes from extension to compression. Therefore, the position of no strain at the eastern termination of the rift accounts for the dying-out of the rift zone and for the appearance of a compressive structure in the Stanovoy Range.     

Geodynamical basis for crustal deformation under the Tibetan Plateau

This paper uses plate tectonics and satellite-derived gravity data to further discussion of crustal deformation under the Tibetan Plateau. The first of our three contributions is a spherical harmonic analysis of the global plate boundary system. A distribution of 470 Dirac delta functions is applied to describe the generating forces according to the rates of crustal creation and destruction on the plate boundaries. Analysis of the extensional and compressional forces in the spreading and subducting zones shows that the present global plate motion causes compressional stresses in the N-S direction under the Tibetan Plateau. The second contribution is the calculation of the crustal stresses in Tibet as inferred from satellite gravity data. By applying solutions to the problem of the spherical shells, the satellite-determined stresses indicate that the up-welling mantle material under Tibet induce N-S and E-W extension. Finally, a superimposed stress system is constructed. This stress system shows that the present crustal deformation in Tibet does not produce N-S shortening but generates E-W extension.The results of this paper have provided geodynamical explanations for geological field observations in Tibet and fault plane solutions of earthquakes in the Tibetan side of the India-Eurasia collision. The stress patterns reveal that the cold downwelling mantle convection flow beneath southern Tibet pulls the Indian plate down but applies a bending moment on the end of the plate to uplift and support the mass of the Himalayas.