基于Lp范数(0＜p＜0.5)约束的裂陷盆地基底非线性重力反演

利用重力反演沉积盆地基底起伏是油气重力勘探研究的一个重要方面.随着地质目标勘探难度逐渐增大,亟需提高重力反演盆地基底的精细程度.本文研究了基于Lp范数约束的非线性重力反演方法,反演结果能更好地符合裂陷盆地基底起伏特征.反演时假设沉积盆地基底和沉积层均为单一岩性,即沉积层与基底的密度差为常数.将基底之上的沉积层剖分为垂直并置的棱柱体,用棱柱体底面深度近似沉积盆地基底深度,其为待反演的参数.利用Ekblom范数近似Lp范数的表达式,并建立Lp范数意义下的参数向量函数,将其与重力误差函数结合得到非线性反演的目标函数.利用二维裂陷盆地模型进行试算,结果表明当p取0.2时能较准确的反演裂陷盆地基底起伏形态,其应用效果优于基于L0范数和L1范数的约束反演方法.将本文方法应用于南海珠江口盆地实际重力资料反演,将反演的基底深度与地震剖面解释结果进行对比,结果表明该反演方法具有较好的实用性.     

南祁连盆地重力异常特征及其地质意义

南祁连盆地具有丰富的油气资源,盆地内部坳陷边界、基底深度及内部构造控制着油气资源的分布.为落实南祁连盆地内部坳陷及构造分布,笔者充分利用多年来在研究区及周缘完成的各类勘探资料,以南祁连盆地的重力数据为主,结合相关资料,开展重力数据处理和综合反演解释,分析提取反映深大断裂的重力异常信息,并基于重力异常完成主要坳陷的密度界面深度反演和剖面2.5维反演,推断南祁连主要沉积盆地和坳陷的基底深度及起伏变化,进而综合讨论研究区主要坳陷的油气远景,为南祁连盆地油气资源战略调查和进一步勘探选区提供了依据.     

基于Lp范数正则化的V字型密度界面重力反演

V字型密度界面是一类常见的密度界面,如海沟、半地堑以及俯冲带之下的莫霍面,利用重力数据刻画此类密度界面形态对于区域构造研究、油气勘探以及物理海洋学等都具有重要意义.本文首先建立了L_p-范数形式的模型约束函数,并利用正则化原理将其与重力数据误差函数和已知深度约束函数结合形成V字型密度界面反演的目标函数,推导了目标函数的梯度表达式,并以非线性共轭梯度法为核心给出了反演流程.二维简单模型试算结果表明p=5时该方法能准确地刻画V字型密度界面起伏特征,且亦能准确地应用于二维复杂密度界面和三维界面的反演.最后将反演方法应用于挑战者深渊及邻区的实际资料处理之中,利用研究区海底地形数据和沉积层厚度数据对自由空间重力异常逐层剥离而得到莫霍面引起的重力异常,用本文方法对此重力异常进行反演,结果呈现了板块俯冲作用引起的V字型莫霍面起伏特征.     

考虑沉积层重力改正的中国西部Moho面深度反演

首先研究了大型沉积盆地对地表重力异常的影响,然后基于Parker-Oldenburg迭代算法,利用经过沉积层改正的布格重力异常数据反演了中国西部的Moho面深度。结果表明,地壳浅层密度异常对地表重力异常和Moho面深度结果的影响较大,利用简化的三层沉积层模型,计算出的中国西部沉积盆地的重力异常改正最大可达25 m Gal,由此引起的Moho面深度可达2.2 km,Moho面深度最终计算结果与区域最新研究成果相符合,因此,利用重力异常反演Moho面深度时,应考虑沉积层的影响以提高反演精度。     

约束变密度界面反演方法

三维密度界面反演具有严重的多解性,已有方法较少利用已知信息约束反演过程,导致界面反演结果可信度降低.本文在反演过程中,利用已有地质信息作为约束条件,有效提高了三维界面反演结果的准确性.该方法具有如下特点:1)利用指数变密度模型,通过已知密度分布计算模型参数,使其更加接近实际密度分布;2)引入已知深度点约束,提高了反演结果的准确性;3)引入深度加权函数,纠正界面畸变,使其适用于界面起伏较大的情况;4)频率域正演与空间域迭代反演相结合,在提高计算速度的同时保证反演收敛.通过模型检验,证实了方法的有效性,并将该方法应用于中蒙边境地区东段莫霍面深度反演中,效果良好.     

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.     

基于深度学习U-net网络的重力数据界面反演方法

重力数据的密度界面反演是位场数据解释中的一项主要工作,在区域构造演化、深部莫霍面确定等领域的研究中发挥重要作用.近年来,数据驱动的深度学习方法广泛地应用在地球物理数据处理与反演中,本文提出一种基于深度学习U-net网络的重力数据密度界面反演方法.首先,对半椭球体界面模型进行随机抽取和组合进而形成地下起伏界面数据集,并基于Parker正演理论对界面数据集进行重力异常正演计算,为深度学习网络模型的训练提供特征完备的数据源;其次,设计了基于U-net网络模型的深度学习界面反演算法,在传统的损失函数基础上增加光滑损失项和过拟合抑制项,提高重力界面反演结果的光滑性和收敛效率;最后通过测试样本集进行反演预测,验证建立深度学习网络模型的泛化性.本文通过理论模型和实际数据试验分析了本文方法在密度界面反演中的有效性和实用性,基于改进损失函数约束的深度学习界面反演方法有效地提高了密度界面反演的收敛效率和计算稳定性.     

改进的约束变密度界面反演策略及其应用

计算密度分界面的起伏变化在区域地质构造研究和石油矿产资源勘探中具有重要意义.已有密度界面反演方法更多侧重约束变密度界面反演算法,而对约束信息的准确性、研究区横向密度变化往往考虑不足,影响了最终反演结果的可信度.本文在变密度界面正反演算法基础之上,结合实际需求,提出已知深度信息约束下的变密度界面反演策略.该策略主要包括变密度约束反演算法、已知深度约束信息校验和分区变密度模型三个方面.其中反演算法提供了带已知深度约束信息的密度界面迭代反演方法;约束信息校验用于评估约束信息精度,通过调差降低约束信息的系统误差;在反演过程中引入水平密度分区以应对不同构造背景密度界面模型,提高反演结果的可信度.最后将本策略应用于南海莫霍面深度反演计算中,结果显示借助已知约束信息,利用分区密度模型能够获得更为可信的深度反演结果,验证了该策略的正确性.     

南海重力异常的沉积层密度改正及其对区域构造特征分析的意义

南海位于太平洋板块、印澳板块和欧亚板块交汇处,自晚中生代以来历经张裂作用、海底扩张以及印藏碰撞、菲律宾海板块西向运动等构造事件的叠加改造,不仅形成了复杂多样的构造格局,而且堆积了厚薄不均的沉积层.为了考察沉积层密度改正对利用重力资料分析南海不同尺度构造特征的影响,本文利用南海各区域不同深度沉积层的地震波速度及钻孔密度等数据,建立了沉积层与沉积基底密度差随深度变化的二次函数关系式,并基于该关系式,计算了南海沉积层相对基底密度低而产生的重力异常值.结果显示,南海沉积层的重力异常值在海盆区介于-40~-60 mGal,而在堆积巨厚沉积物的莺歌海盆地可达到-135 mGal;相对于空间重力异常、布格重力异常,经沉积层重力异常改正后的地壳布格重力异常更能突出深部不同尺度的密度结构和莫霍面的起伏特征,其总水平导数模更突显了南海西北部红河断裂带的海上延伸;利用谱分析技术估算岩石圈强度时,经沉积层重力异常改正的地壳布格重力异常数据获得的岩石圈有效弹性厚度值更为符合地质实际,特别是在长条形的巨厚沉积区如莺歌海盆地和马来盆地.分析表明,重力异常的沉积层密度改正对揭示南海构造特征具有重要的意义.     

中国南海地区重力剥离对莫霍面反演的影响分析

确定更为精细的中国南海地区莫霍面对认识该地区内部结构、形成机制及相关动力学问题具有重要意义.重力剥离的精度直接影响莫霍面反演结果的质量.本文将由XGM2019e解算的自由空气重力扰动进行地形水深、沉积层、固体地壳密度异常和岩石圈热膨胀重力剥离,提取出莫霍面重力扰动,结合线性回归法和地震资料估计反演参数,并采用直接迭代法反演南海莫霍面模型,最后利用地震资料对反演结果进行精度评定.研究结果表明：仅顾及地形水深重力剥离的莫霍面反演结果整体精度较高,为1.94 km;在沉积物较厚的陆坡盆地,忽略沉积层的影响可使莫霍面最大加深6.30 km,但在沉积物较薄的南海海盆,考虑沉积层重力剥离会降低反演精度;利用CRUST1.0进行固体地壳重力剥离会使反演结果的精度降低0.22 km,表明CRUST1.0在南海地区并不准确;热膨胀重力剥离对反演精度的影响不大,但若忽略该效应,可能会高估洋壳区的莫霍面深度．针对南海重力莫霍面研究,笔者建议:若无精细地壳资料,忽略固体地壳重力剥离;若主要关注南海海盆可忽略沉积层的影响,但应考虑热膨胀重力剥离;若研究区覆盖沉积盆地,则应考虑沉积层重力剥离,并仔细选取密度-深度...     

Determination of Sedimentary Basin Basement Depth: A Space Domain Based Gravity Inversion using Exponential Density Function

An automatic inversion using ridge regression algorithm is developed in the space domain to analyze the gravity anomalies of sedimentary basins, among which the density contrast decreases with depth following a prescribed exponential function. A stack of vertical prisms having equal widths, whose depths become the unknown parameters to be estimated, describes the geometry of a sedimentary basin above the basement complex. Because no closed form analytical equation can be derivable in the space domain using the exponential density-depth function, a combination of analytical and numerical approaches is used to realize forward gravity modeling. The depth estimates of sediment-basement interface are initiated and subsequently improved iteratively by minimizing the objective function between the observed and modeled gravity anomalies within the specified convergence criteria. Two gravity anomaly profiles, one synthetic and a real, are interpreted using the proposed technique to demonstrate its applicability.     

Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods

Based on the line integral (LI) and maximum difference reduction (MDR) methods, an automated iterative forward modelling scheme (LI‐MDR algorithm) is developed for the inversion of 2D bedrock topography from a gravity anomaly profile for heterogeneous sedimentary basins. The unknown basin topography can be smooth as for intracratonic basins or discontinuous as for rift and strike‐slip basins. In case studies using synthetic data, the new algorithm can invert the sedimentary basins bedrock depth within a mean accuracy better than 5% when the gravity anomaly data have an accuracy of better than 0.5 mGal. The main characteristics of the inversion algorithm include: (1) the density contrast of sedimentary basins can be constant or vary horizontally and/or vertically in a very broad but a priori known manner; (2) three inputs are required: the measured gravity anomaly, accuracy level and the density contrast function, (3) the simplification that each gravity station has only one bedrock depth leads to an approach to perform rapid inversions using the forward modelling calculated by LI. The inversion process stops when the residual anomalies (the observed minus the calculated) falls within an ‘error envelope’ whose amplitude is the input accuracy level. The inversion algorithm offers in many cases the possibility of performing an agile 2D gravity inversion on basins with heterogeneous sediments. Both smooth and discontinuous bedrock topography with steep spatial gradients can be well recovered. Limitations include: (1) for each station position, there is only one corresponding point vertically down at the basement; and (2) the largest error in inverting bedrock topography occurs at the deepest points.     

Three-dimensional structure of the Laguna Salada Basin and its thermal regime

A comprehensive reinterpretation of the available gravity, magnetic, geothermal, geological and borehole information has been made of the Laguna Salada Basin to establish a 3D model of the basement and sedimentary infill. According to statistical spectral analysis, the residual gravity anomaly is due to sources with a mean regional depth of 2.8 km. The topography of the basement was obtained from a three‐dimensional inversion carried out in the wavenumber domain using an iterative scheme. The maximum density contrast of ?300 kg/m³ estimated from previous studies and the mean depth of 2.5 km finally constrained this inversion. The resulting model indicated that the sedimentary infill is up to 4.2 km thick at its deepest point. According to the gravity‐derived basement topography, the basin presents an asymmetry (i.e. it is of the half‐graben type). It is deeper to the east, where it is delimited from the Sierra Cucapah by a step fault. By contrast, the limit with the Sierra de Juarez is a gently sloping fault (i.e. a listric fault). The basement is not even, but it comprises a series of structural highs and lows. N–S to NW–SE and E–W to NE–SW faults delimit these structural units. The magnetic modelling was constrained by (i) the gravity‐derived basement topography; (ii) a Curie isotherm assumed to be between 7 km and 10 km; (iii) assuming induced magnetization only; (iv) the available geological and borehole information. The magnetic anomalies were interpreted successfully using the gravity‐derived basement/sedimentary interface as the top of the magnetic bodies (i.e. the magnetic modelling supports the gravity basement topography). An elongated N–S to NW–SE trending highly magnetized body running from south to north along the basin is observed to the west of the basin. This magnetic anomaly has no gravity signature. Such a feature can be interpreted as an intrusive body emplaced along a fault running through the Laguna Salada Basin. Treatment of the gravity and magnetic information (and of their horizontal gradients) with satellite image processing techniques highlighted lineaments on the basement gravity topography correlating with mapped faults. Based on all this information, we derived detailed geological models along four selected profiles to simulate numerically the heat and fluid flow in the basin. We used a finite‐difference scheme to solve the coupled Darcy and Fourier differential equations. According to our results, we have fluid flow in the sedimentary layers and a redistribution of heat flow from the basin axis toward its rims (Sierra de Juárez and Sierra Cucapah). Our model temperatures agree within an error of 4% with the observed temperature profiles measured at boreholes. Our heat‐flow determinations agree within an error of ±15% with extrapolated observations. The numerical and chemical analyses support the hypothesis of fluid circulation between the clay–lutite layer and the fractured granitic basement. Thermal modelling shows low heat‐flow values along the Laguna Salada Basin. Deep fluid circulation patterns were observed that redistribute such flow at depth. Two patterns were distinguished. One displays the heat flow increasing from the basin axis towards its borders (temperature increase of 20°C). The second pattern shows an increasing heat flow from south to north of the basin. Such behaviour is confirmed by the temperature measurements in the thermometric boreholes.     

内蒙古河套断陷带及其邻区地壳磁性构造特征

本文依据航磁资料和频率域磁性单界反演方法，计算了河套断陷带及其邻区的基底磁性界埋深；依据三维磁性层反演方法求取了该区磁性层下界面，即居里界面的埋深；分析了磁性层上下界面的定量特征，并结合重力、地热、地形变诸方面的研究成果，讨论讨论了该区的地壳结构特征及地震成因。     

Gravity-geoelectric joint inversion over the Potiguar rift basin, NE Brazil

A joint inversion of gravity and geoelectrical data has been performed along a 100 km long profile across the oil-bearing Potiguar rift basin in NE Brazil. The integrated approach is based on the connection between density and resistivity of a sedimentary sequence through the porosity. Seventy-one gravity stations and twenty-nine vertical electrical soundings were carried out across the central part of the Early Cretaceous basin in the Precambrian Borborema Province to apply the proposed joint inversion. Both the physical properties and geometry of the multilayer deep model were well constrained by a wide set of prior information obtained by surface mapping, geophysical logs and seismic sections. The results reveal a rift architecture formed by a 5000 m thick half-graben structure separated by an intervening basement high and an extensive adjacent platform with a sedimentary infill of about 300 m thick. The calculated model shows geometries for the sedimentary density/resistivity interfaces in agreement with the seismostratigraphic sequences revealed by seismic section, representing a substantial improvement in comparison with previously published gravity models.     

Gravity interpretation of nonoutcropping sedimentary basins in which the density contrast decreases parabolically with depth

The decrease in density contrast of sedimentary rocks with depth in many sedimentary basins can be approximated by a parabolic density function. Analytical gravity expression of an outcropping two-dimensional vertical step along which the density contrast decreases parabolically with depth is derived in the space domain. A modification ofBott's (1960) method of gravity interpretation is proposed by considering two outcropping vertical steps on either side of the first and last observation points in addition toN outcropping vertical prisms in order to interpret the gravity anomalies of nonoutcropping basins. The thicknesses of the two outcropping vertical steps are made equal to the thicknesses of the two outcropping vertical prisms placed below the first and last observation points. The initial depth estimates of the sedimentary basin are calculated by the infinite slab formula ofVisweswara Rao et al. (1993). The gravity effects of theN outcropping prisms and the two outcropping vertical steps are calculated at each anomaly point and the depth to the floor of the basin are adjusted based on the differences between the observed and calculated anomalies. A gravity anomaly profile of Los Angeles basin, California is interpreted.     

THREE-DIMENSIONAL INTERPRETATION OF GRAVITY DATA FROM SEDIMENTARY BASINS USING AN EXPONENTIAL DENSITY-DEPTH FUNCTION*

In mapping the topography of the basement of deep sedimentary basins by gravity modelling, the accuracy can be improved by incorporating an exponential increase in density with depth. For calculating the gravity effect of a three-dimensional (3D) structure with such an exponential density-depth relation a frequency-domain forward algorithm based on series expansion is presented, the numerical evaluation of which can be performed efficiently by fast Fourier transform. The algorithm can be applied in a recursive procedure to give the inverse solution in terms of basement relief. The inversion procedure is satisfactorily tested on a 2D synthetic example and a 3D field example of gravity data from the western margin of the Pannonian Basin in eastern Austria, where up to 2.2 km of Tertiary sediments overlie an igneous or metamorphic basement. The results are confirmed by basement intersections in several wells.     

基于接收函数约束的川滇地区莫霍面深度反演研究

本文利用川滇地区宽频地震接收函数结果和WGM2012全球布格重力场模型数据,采用正则化参数和接收函数结果交叉验证得到最优莫霍面参考深度和上下界面密度差,使用基于球坐标系下的快速非线性重力反演方法建立川滇地区莫霍面深度模型.研究结果显示,川滇地区整体莫霍面深度介于30～69km,青藏高原内部地区莫霍面深度大于50km;四川盆地莫霍面深度在36～38km;攀枝花地区莫霍面出现明显的隆起和下凹,变化范围在42～48km;川滇菱形地块莫霍面深度在40～50km;滇西和滇南地块莫霍面深度由南向北逐渐变深,变化范围在38～44km.本文反演莫霍面深度与接收函数结果平均误差为0.18km,与该区域天然地震层析成像、人工地震探测以及重力数据反演结果基本一致,但细节更加丰富,进一步确认了莫霍面在攀西裂谷地区存在隆起,小江断裂带下方存在下凹的特征.该结果可作为精细化川滇地区地壳密度界面模型,为研究该地区岩石圈结构和地质构造演化提供参考.     

Magnetic Basement Depth Inversion in the Space Domain

We present a total-field anomaly inversion method to determine both the basement relief and the magnetization direction (inclination and declination) of a 2D sedimentary basin presuming negligible sediment magnetization. Our method assumes that the magnetic intensity contrast is constant and known. We use a nonspectral approach based on approximating the vertical cross section of the sedimentary basin by a polygon, whose uppermost vertices are forced to coincide with the basin outcrop, which are presumably known. For fixed values of the x coordinates our method estimates the z coordinates of the unknown polygon vertices. To obtain the magnetization direction we assume that besides the total-field anomaly, information about the basement’s outcrops at the basin borders and the basement depths at a few points is available. To obtain stable depth-to-basement estimates we impose overall smoothness and positivity constraints on the parameter estimates. Tests on synthetic data showed that the simultaneous estimation of the irregular basement relief and the magnetization direction yields good estimates for the relief despite the mild instability in the magnetization direction. The inversion of aeromagnetic data from the onshore Almada Basin, Brazil, revealed a shallow, eastward-dipping basement basin.