基于时空域混合法利用Kaula正则化精确和快速解算GOCE地球重力场

为了研究卫星重力梯度技术对中高频地球重力场反演精度的影响,本文基于时空域混合法,利用Kaula正则化反演了250阶GOCE地球重力场.模拟结果表明:第一,时空域混合法是精确和快速求解高阶地球重力场的有效方法;第二,Kaula正则化是降低正规阵病态性的重要方法;第三,基于改进的预处理共轭梯度迭代法可快速求解大型线性方程组...     

新疆精河6.6级地震周边地区密度构造、均衡异常以及岩石圈挠曲机理

依据EIGEN-6C4重力模型和ETOPO1高程模型数据,围绕新疆精河6.6级地震展开岩石圈均衡与挠曲机理研究,得到如下结论：（1）震中附近的布格与自由空气重力异常分别为-221和-92mGal(10~(-5 )m·s~(-2)）,震中位于重力异常高梯度带上;（2）震中周边地区地壳厚度约为50km,密度结构总体变化平缓,东西方向地壳厚度变化较小,但自南向北地壳厚度逐渐变薄,精河6.6级地震初始破裂发生在上中地壳分界面附近;（3）震中附近岩石圈承载的垂向构造应力为20MPa左右,震中位于岩石圈垂向构造应力极大值附近的高梯度带上;（4）地震周边地区岩石圈有效弹性厚度最优解为26km,加载比最优解为F_1=1,F_2=F_3=0,表明该区域岩石圈相对坚硬,且导致岩石圈变形的初始加载全部来自地表．     

南极洲东部普里兹湾海域重磁场特征及地壳结构

普里兹湾位于南极洲东部大陆边缘,其深部地壳结构特征对认识白垩纪冈瓦纳古陆裂解和新生代大陆边缘形成具有重要意义.本文利用重磁、多道反射地震、声纳浮标折射地震和ODP钻井数据对普里兹湾海域的深部地壳结构进行了研究.研究结果显示,普里兹凹陷表现为典型的盆地负重力异常特征,其沉积基底较深,而在四夫人浅滩为高幅重力正异常,其沉积基底普遍抬升.在大陆架中部存在SW-NE向条带状基底的抬升,且呈朝NE向逐渐变深的趋势.在中大陆架外侧,均衡残余重力异常呈V字形负异常条带状分布,其两翼分别与四夫人浅滩和弗拉姆浅滩外的大陆坡相连.该异常带在大陆架中部向陆的偏移可能是由于古大陆架边缘的地形影响,推测其与普里兹冲积扇同属于洋陆过渡带向陆的部分,在重力模拟剖面表现为地壳向海逐渐减薄.普里兹冲积扇的地壳厚度较薄,平均为6 km,最薄处可达4.6 km,并且根据洋陆过渡带向海端的位置,推测可能属于接近洋壳厚度的过渡壳.重力异常分区的走向与兰伯特地堑在普里兹湾的构造走向基本一致,可能主要反映了二叠纪-三叠纪超级地幔柱对普里兹湾的裂谷作用的影响.该区域的自由空间重力异常和均衡残余异常均表现为超过100×10^-5m/s²的高幅正异常特征,可能由位于大陆架边缘的巨厚沉积体负载在高强度岩石圈之上的区域挠曲均衡作用所导致,可能与该区域第二期裂谷期之后的沉积间断以及快速进积加厚的演化过程有关.普里兹湾磁力异常的走向与重力异常明显不同,大致可分为东北高幅正异常区和西南低幅异常区.重磁异常在走向上的差异反映高磁异常主要来源于岩浆作用形成的铁镁质火成岩的影响,并且岩浆作用的时代不同于基底隆升的时代,而可能形成于前寒武纪或者南极洲和印度板块裂谷期间(白垩纪).     

基于GRACE Follow-On卫星重力梯度法精确反演地球重力场

由于GRACE Follow-On双星系统等效于基线长为星间距离的一维水平重力梯度仪,因此本文基于GRACE Follow-On卫星重力梯度法开展了精确和快速反演下一代地球重力场的可行性论证研究. 研究结果表明：第一,基于GRACE Follow-On卫星重力梯度法（GFO-SGGM）,利用卫星轨道参数（轨道高度250 km、星间距离50 km、轨道倾角89°、轨道离心率0.001）、关键载荷测量精度（星间距离10^-6 m、星间速度10^-7 m·s^-1、星间加速度10^-10 m·s^-2、轨道位置10^-3 m、轨道速度10^-6 m·s^-1、非保守力10^-11 m·s^-2）、观测时间30天和采样间隔10 s反演了120阶地球重力场,在120阶处累计大地水准面精度为9.331×10^-4 m. 第二,在120阶内,利用将来GRACE Follow-On双星反演地球重力场精度较现有GRACE双星平均提高61倍,因此GRACE Follow-On卫星重力梯度法是进一步提高地球重力场反演精度的优选方法. 第三,下一代GRACE Follow-On计划较当前GRACE计划的优点如下：轨道高度更低（200~300 km）、载荷精度更高（10^-7 ~10^-9 m·s^-1）和星间距离更短（50~100 km）.     

CHARACTERISTICS OF SATELLITE GRAVITY FIELD AND SEISMOGENIC MECHANISM IN THE LONGMENSHAN FAULT ZONE

Longmenshan fault zone is a famous orogenic belt and seismic zone in the southeastern Tibetan plateau of China. The Wenchuan M_S8.0 earthquake on May 12, 2008 and the Ya'an M_S7.0 earthquake on April 20, 2013 occurred in the central-southern part of Longmenshan fault zone. Because of its complex geological structures, frequent earthquakes and special geographical locations, it has attracted the attention of many scholars around the world. Satellite gravity field has advantages in studying gravity field and gravity anomaly changes before and after earthquake. It covers wide range, can be updated regularly, without difficulty in terms of geographical restrictions, and is not affected by environmental factors such as weather, terrain and traffic. Therefore, the use of high-precision Earth satellite gravity field data inversion and interpretation of seismic phenomena has become a hot topic in earth science research. In order to understand satellite gravity field characteristics of the Longmenshan earthquake zone in the southeastern Tibetan plateau and its seismogenic mechanism of earthquake disasters, the satellite gravity data was used to present the terrain information of the study area. Then, by solving the regional gravity anomaly of the Moho surface, the crustal thickness of the study area was inverted, and the GPS velocity field data was used to detect the crustal deformation rate and direction of the study area. Combining the tectonic setting of the Longmenshan fault zone and the existing deep seismic sounding results of the previous researchers, the dynamic characteristics of the gravity time-varying field after the earthquake in the Longmenshan earthquake zone was analyzed and the mechanism of the earthquake was explored. The results show that the eastward flow of deep materials in the eastern Tibetan plateau is strongly blocked at the Longmenshan fault zone. The continuous collision and extrusion process result in a "deep drop zone" in the Moho surface, and the long-term stress effect is conducive to the formation of thrust-nappe and strike-slip structures. The Longmenshan earthquake zone was in the large-scale gradient zone of gravity change before the earthquake, the deep plastic fluid material transport velocity differed greatly, the fluid pressure was enhanced, and the rock mechanical strength in the seismic source region was weakened, which contributed to the intrusion of crustal fluid and the upwelling of the asthenosphere. As a result, the continuous accumulation of material and energy eventually led to continuous stress imbalance in the deep part and shear rupture of the deep weak structure, causing the occurrence of the thrust-nappe and strike-slip earthquake.     

应用卫星重力信息对横断山系地区布格重力异常特异分布的纠正

在云南省西部,跨越中、缅两国交界的横断山系地区（97°E~102°E,24°N~30°N）有近一半的面积尚没有重力测点、即重力数据空白区和重力测点稀少的普查级测区.以前的有关文献、图集中所给出对此地区的重力场都是十分模糊的结果与图件.因此应用这些资料无法详细地研究该地区重力场特征与深部地壳结构（构造）.本文应用卫星重力异常资料作为“近似空间重力异常”,经中间层改正后给出的“计算布格重力异常”,其分布特征与该地区的地形高程呈很好的镜像相关.对相应山脉、河谷以及断裂构造都有所反映.特别是在横断山系地区该布格重力异常呈现为近南北的走向.为此,据该“计算布格重力异常”,并选定对该区有代表性的一条重力异常剖面作正反演计算,以得到其地壳深部结构剖面.结果表明,在横断山脉地区的地壳厚度在51~56 km间起伏变化;滇西北云岭山系以及玉龙山区的地壳厚度约在60 km以上. 最后,对所得结果与图件进行了讨论,并提出了几点认识和纠正的建议.     

维西—贵阳剖面重力异常与地壳密度结构特征

维西—贵阳剖面位于青藏高原东南缘,为青藏高原物质往东南逃逸、东构造结侧向挤压及华南地块北西西向推挤作用的重要地段.利用剖面观测的重力与GPS定位数据,结合区域背景重力场、地质构造及深部地球物理成果,反演研究剖面较为细化的地壳密度结构特征.观测研究表明:剖面布格重力异常总幅差变化达190×10-5 m·s-2,具"斜N"分段变化特征,从西往东呈上升(维西至攀枝花,水平梯变大)—下降(攀枝花至会泽,水平梯变较大)—上升(会泽至贵阳,水平梯变较小)态势;高程与布格重力异常比值的趋势性转折部位为康滇地轴核心和小江断裂带东侧,可能与先存构造或新生构造发育有关;剖面地壳密度结构可分上、中和下三层结构,各层底界面平均埋深分别约20km、35km和51km,金沙江—红河断裂带和鲜水河—小江断裂带为地壳结构相对简单与复杂的过渡带;地壳厚度西深东浅,可能是东构造结的侧向挤压所致;下地壳厚度变化相对较大,可能对地壳增厚起主要作用;华坪—攀枝花附近的Moho面隆起和上地壳高密度体的存在暗示上地幔往上底侵作用,对青藏高原物质向南东逃逸和东构造结的侧向挤压均起到一定阻挡作用;中地壳下伏有限低密度薄层有利于其上物质的南东逃逸和顺时针旋转,有利于其下物质受喜马拉雅东构造结作用下往东向运移.     

Variation of crustal thickness in the Philippine Sea deduced from three-dimensional gravity modeling

Abstract   Crustal thickness of the northern to central Philippine Sea was gravimetrically determined on the simple assumption of four layers: seawater, sediments, crust and lithospheric mantle, with densities of 1030, 2300, 2800 and 3300 kg/m³, respectively. As for the correction of the regional gravity variation, a 15 km difference of the lithospheric thickness with a density difference of 50 kg/m³ against the asthenosphere below between both sides of the Kyushu-Palau Ridge was taken into consideration. Mantle Bouguer anomalies were calculated on the assumption of constant crustal thickness of 6 km, and then the crustal thickness was obtained by three-dimensional gravity inversion method. The results show occurrence of thin crust areas with a thickness of approximately 5 km in the southern part and at the western margin of the Shikoku Basin and also of thick crust areas in the northwestern and northeastern parts of the Parece Vela Basin. We suggest that these are because of the variation of magma supply at the time of sea floor spreading in the Shikoku and Parece Vela Basins, which is possibly related to the variation of spreading rate and enhanced magmatism near the past arc volcanic fronts. The results further show the occurrence of crust thinner than 5 km in the northeastern part of the West Philippine Basin, of crust thicker than 15 km in the Amami Plateau, the Daito and Oki-Daito Ridges, and also in the northern part of Kyushu-Palau Ridge, whereas the southern part of the Kyushu-Palau Ridge the crust is thicker than 10 km. It was also inferred that small basins in the Daito Ridge province have the thinnest oceanic crust of less than 5 km in the Kita-Daito Basin.     

基于重磁震资料的南海新生代盆地分布综合研究

作为西太平洋最大的边缘海,南海分布有30多个新生代沉积盆地,其蕴含着丰富的油气资源.但由于资料的限制,南海存在不同区域盆地研究程度不同,不同区域盆地面积差别较大,部分盆地只是坳陷而没有达到盆地的级别以及盆地外围可能存在凹陷等问题.南海新生代盆地分布问题制约了其油气分布规律、储量等基础地质问题的研究.本文以地震剖面数据为约束,以重力资料为主、辅以磁力资料,研究了南海新生代盆地分布及构造区划.通过提取新生代盆地及其构造单元引起的重力异常,结合地震剖面等资料反演了新生界底界面深度及新生界厚度.在充分调研已有盆地和构造单元划分方案的基础上,根据南海的地质及地球物理特征,确定了盆地及构造单元划分标准.以新生界厚度为基础并结合重、磁、震、地质等资料,进行地质-重磁震联合解释,将南海原有的36个盆地重新划分为24个盆地,盆地总面积扩大了约15万km².研究表明,南海新生代盆地沉积层厚度在1.5~16 km之间,有6个北东东/北东向沉积坳陷带、2个近南北向沉积坳陷带以及1个三角沉积坳陷区;盆地展布方向主要为北东和北东东向,其次为北西和近南北向,呈现"南三北三"的分布特征.     

南海及邻区莫霍面深度分布特征及其与各构造单元的关系

为了研究南海及邻区莫霍面分布特征及其与边缘海盆、海沟、岛弧、新生代沉积盆地的关系等构造单元的关系,本文通过对研究区的空间重力异常数据进行全布格改正,得到研究区内的布格重力异常,并以近年来的声纳浮标探测与海底地震仪探测剖面所得到的莫霍面深度资料为控制点采用三维带控制点界面反演方法得到了研究区的莫霍面深度图和地壳厚度图.本...     

The Alpha Ridge: Gravity, seismic and magnetic evidence for a homogenous, mafic crust

Gravity and bathymetric results from the 1983 Canadian Expedition to Study the Alpha Ridge (CESAR) have outlined positive free-air anomalies centred on the continental break off Ellesmere Island characteristic of normal Atlantic-type passive margins. These data confirm implications derived from depth-to-magnetic basement calculations that the ridge may not be structurally connected to the continent. Across the Alpha Ridge magnetic and gravity anomalies mimic the bathymetry. The magnetic anomalies apparently are not caused, to any great extent, by internal structures or magnetic reversals, but rather seem to result simply from variations in depths to a homogenous magnetic structure. The gravity anomalies across a 500 km wide section of the Alpha Ridge can be almost completely accounted for by topography, shallow sedimentary fill and a simple two-tier crustal model. This implies an extraordinary lateral density homogeneity unknown in continental structures of comparable size. Gravity models show the crustal thickness to increase gradually from 20 km at the Marvin Spur to 38 km at the ridge crest. A comparison of this model with a gravity model of the continental-type Lomonosov Ridge, which has a thickness of about 25 km, indicates that, at the same thickness of 25 km, the average crustal density of the Alpha Ridge is 0.08 Mg/m³ greater. These gravity constraints, the unusually homogenous seismic velocity structure revealed by the CESAR studies, the homogeneous magnetic structure, and the extraordinary high intensity satellite magnetic anomaly associated with the Alpha Ridge, indicate that the ridge may be composed of a large pile of mafic rock, possibly unique on this planet.     

华北地区重力场变化特征与孕震模型研究

本文采用基于贝叶斯原理的重力平差方法对华北地区2009—2017年的16期陆地流动重力观测资料进行了统一处理,结合研究区内2009年以来4次M≥4.5 地震活动,分析区域重力场动态演化特征。基于华北地区均衡重力异常、布格重力异常、沉积层重力异常和莫霍面重力异常,研究华北地区三维密度结构特征,分析区域重力场变化与深部密度结构之间的关系。结果表明:研究区内近年来M≥4.5地震均位于区域差分重力场和累积重力场“零值”等值线附近、异常变化剧烈的梯度带及梯度带转弯部位,以及深部结构中理论均衡厚度与实际地壳厚度存在差异的非均衡区和三维密度结构的高低密度过渡带内。      

Spectral expressions for modelling the gravitational field of the Earth’s crust density structure

We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm⁻³. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure.     

基于下一代三向车轮双星编队改善地球重力场空间分辨率研究

由于当前GRACE(Gravity Recovery and Climate Experiment)串行式编队存在"南北向条带误差"等缺陷,因此本文基于星间速度插值法开展了利用下一代三向车轮双星编队ACR(Along-Cross-Radial)-Cartwheel提高地球重力场空间分辨率的可行性研究论证.第一,采用GRACE卫星轨道参数和关键载荷精度,利用三向车轮双星编队ACR-Cartwheel-A/B反演了120阶地球重力场.结果表明:基于ACR-Cartwheel-A/B双星编队反演地球重力场的模拟精度较德国波茨坦地学研究中心(GFZ)公布的EIGEN-GRACE02S地球重力场模型的实测精度平均提高2.6倍,从而检验了基于下一代三向车轮双星编队ACR-Cartwheel-A/B反演地球重力场精度优于当前GRACE串行式双星编队的可行性.第二,通过星间速度插值法,采用卫星轨道参数(初始轨道高度350km、平均星间距离100km、初始轨道倾角89°、初始轨道离心率0.0046)、卫星关键载荷精度指标(星间速度10-7 m·s-1、轨道位置10-3 m、轨道速度10-6 m·s-1、非保守力10-11 m·s-2)、观测时间30天和采样间隔10s,基于经向车轮双星编队Lo-AR(Longitudinal-Along-Radial)-Cartwheel-A/B、纬向车轮双星编队La-AR(Latitudinal-Along-Radial)-Cartwheel-A/B和三向车轮双星编队ACR-Cartwheel-A/B,分别反演了120阶地球重力场;在120阶处,累计大地水准面精度分别为5.115×10-4 m、4.923×10-4 m和3.488×10-4 m.结果表明:(1)由于La-AR-Cartwheel-A/B编队的轨道稳定性优于Lo-AR-Cartwheel-A/B编队,因此基于La-AR-Cartwheel-A/B编队反演重力场精度高于Lo-AR-CartwheelA/B编队;(2)由于ACR-Cartwheel-A/B编队可以同时获得轨向、垂向和径向的重力场信息,卫星观测数据具有各向同性优点,因此ACR-Cartwheel-A/B编队是建立下一代高精度和高空间分辨地球重力场模型的优化选择.     

Contribution of satellite altimetry data in the geophysical investigation of the Red Sea Region, Egypt

Successful development of geodetic satellite missions has aroused new interest in determining global and regional gravity field based on satellite data. Satellite altimetry data enable direct determination of the geoid over sea regions. In Egypt, where land and marine geophysical data are inadequate because of rough topography and economic reasons, the use of satellite altimetry data is of special importance. The northern Red Sea region has been selected as a site for case study of the current research, after applying spectral analysis to reveal near-surface structure, the residual geoid of the studied region shows a good correlation with the known geologic features. Moreover, satellite-based gravity data enhance small-scale features and agrees well with land and marine gravity data. Thus, geoid undulation and satellite gravity data can be a complementary source of data to determine near-surface and deep structures.     

基于OBS数据的南黄海沉积地层速度结构特征

南黄海盆地是在前古生代变质基底及中-古生代海相沉积基底之上发育起来的中-新生代陆相叠合盆地.本文基于南黄海深部地学探测的主动源地震数据(OBS2013测线),通过多尺度层析成像方法利用初至波走时反演得到测线下方沉积层的纵波速度结构,结合多道地震、重、磁等资料,综合分析南黄海盆地北部沉积地层的特征.结果表明,OBS2013测线下方的地层纵、横向上有多个速度分界面,纵向上以印支面为界,下部挤压与上部伸展地层速度分别呈现高、低速特征;横向上表现为众多断裂,断裂控制了盆地发育,个别断裂发生走滑.断裂将速度剖面划分为四个纵波低速区和五个高速区,6km深度以内纵波速度的低值区(<4.5km·s-1)是中-新生代沉积地层;而高值区(>5km·s-1)归属于不同的形成机制:北部高速区对应千里岩隆起区的变质岩,中部高速区是被挤压的海相沉积地层,南部高速区属于中部隆起,为埋藏较浅、但厚度较大的中、古生代海相地层,部分位置可能含有火成岩.北部坳陷的中、南部区域,在陆相中-新生代沉积盆地之下的海相地层中发育砂岩,该区域(埋深不超过6km)的砂岩沉积分布于约2km厚度的地层中.     

喜马拉雅地区与天山地区地壳强地震的孕震因素探讨

利用哈佛大学GCMT数据中心和前人积累的历史地震资料(1962~2016年M W>4.0地震)以及Crust2.0地壳结构统计分析了喜马拉雅地区、天山地区的地壳区域构造与地震活动间的相关性。此外,利用GFZ地学研究中心提供的静态卫星重力模型GGM03S/EGM2008和地形模型Topo计算了2个地区的各类重力异常场,同时还模拟了不同地壳弹性参数下的重力异常场,结果表明喜马拉雅地区重力异常场在水平、垂直方向的梯度特征远大于天山地区的异常特征,且喜马拉雅地区的有效弹性板厚度Te(6~15km)小于天山地区的有效弹性板厚度Te(20~30km)。最后,利用喜马拉雅地区与天山地区的GPS震间三维形变场约束了断层运动模型,结果显示两者主前缘断裂的断层闭锁深度及应力积累状态存在较大的差异。因此认为,造成青藏高原及邻区的边界地壳区域地震活动性差异的动力学因素,与地壳有效弹性板厚度、孕震断层参数及区域应力积累状态等密切相关。     

一种新型重力测量卫星系统确定全球重力场的性能分析

本文设计了一种高-低卫星跟踪卫星、低-低卫星跟踪卫星和卫星重力梯度测量相结合的新型重力测量卫星系统,其可在一定程度上发挥卫星重力梯度和低低卫星跟踪卫星两种测量模式各自的优势.基于重力卫星系统指标设计的半解析法,深入分析了不同重力测量卫星系统配置和不同观测量及其不同白噪声水平情况下,新型卫星重力测量模式反演重力场模型的能力.数值模拟分析结果表明：在观测值精度和星间距离相同的条件下,轨道高度是影响重力场反演精度的关键因素;随着星间距离的增大,高频重力场信号反演精度会先提高后降低,轨道高度在200~350 km之间时,星间距离在150~180 km之间时反演精度最优;星间距离变率和卫星重力梯度两类观测值仅在某些精度配置时可达到优势互补,如果某一类观测值精度很高,则另一类观测值在联合解算时贡献非常小或者没有贡献.在300 km轨道高度,若以GRACE和GOCE任务的设计指标1 μm·s^-1/√Hz和5 mE/√Hz来配置新型重力测量卫星系统中星间距离变率和引力梯度观测值的精度,联合两类观测值解算200阶次模型大地水准面的精度比独立解算分别提高1.2倍和2.8倍.如果以实现100 km空间分辨率1~2 cm精度大地水准面为科学目标,考虑卫星在轨寿命,建议轨道高度选择300 km,星间距离变率和卫星重力梯度的精度分别为0.1 μm·s^-1/√Hz和1 mE/√Hz.本文的研究成果可为中国研制自主的重力测量卫星系统提供参考依据.     

Mechanical and thermal isostatic response of the Del Cano Rise and Crozet Bank (southern Indian Ocean) from altimetry data

An analysis of the relationship between the bathymetry and the gravity field has been carried out both in the frequency domain (admittance technique) and in the space domain over the Del Cano Rise and the Crozet Bank (southern Indian Ocean). A bathymetric map, contoured from original shipboard data and a geoid anomaly map, computed from a merged set of SEASAT and GEOS3 data were used. The inversion of admittances for water depth, crustal thickness, crustal density and elastic plate thickness shows that the isostatic response of the lithosphere supporting the Del Cano Rise differs very much from that of the one situated beneath the Crozet Bank. The Del Cano Rise appears to have been formed near the active Southwest Indian Ridge before Early Eocene and is locally supported by a thickened crust. Shallow thermal processes contribute to the present topography of the Crozet Bank, emplaced further away from the Southeast Indian Ridge on older crust.     

An algorithm to calculate the gravity anomaly of sedimentary basins with exponential density-depth relationships

We derive wavenumber domain expressions to calculate the gravity anomaly of a body with irregular bounding surfaces and an exponential density‐depth relationship. We apply the method to sedimentary basins, which commonly have this type of geometry and density distribution. The mathematical formulation also allows the exponential density‐depth relationship to be measured from an arbitrary irregular surface rather than the top surface. Using this arrangement, the gravity anomaly of exhumed sedimentary basins can be predicted if the amount of eroded section can be estimated. The corresponding inverse algorithms are also derived. Examples of the use of the forward algorithms, from the Galicia Interior Basin and the Central Irish Sea Basin, are used to illustrate these methods.