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.     

Parabolic density function in sedimentary basin modelling

For modelling sedimentary basins of large thickness from their gravity anomalies, the concept of parabolic density function which explains the variation of true density contrast of the sediments with depth in such basins is introduced inBott's (1960) procedure. The analytical expression the gravity anomaly of a two-dimensional vertical prism with parabolic density contrast needed to estimate the gravity effect of the basin in modelling procedure is derived in a closed form. Two profiles of gravity anomalies, one across San Jacinto Graben, California and the other across Tucson basin, Arizona where the density of sediments is found to vary with depth are interpreted.     

On the calculation of magnetic anomalies of irregular two-dimensional bodies

Summary An easy method of calculating the magnetic anomalies of two-dimensional irregular bodies is presented. The body under consideration is replaced by a set of line doublets with a pole strength equal to the intensity of magnetisation and parallel to its direction. The magnetic effects of some of the equally spaced doublets are obtained, added and multiplied by the distance between them to yield the magnetic anomaly. The expressions involved here are simpler than those existing in geophysical literature.     

盆地基底岩性的综合地球物理预测方法——以松辽盆地滨北地区基底岩性预测为例

预测盆地基岩岩性不仅对于研究盆地的深部地质结构及盆地的形成演化具有重要的意义,而且也对基岩风化壳油气藏的勘探具有一定的指导作用.本文通过对盆地重、磁异常成因的综合分析,提出了一系列盆地基底岩性综合预测研究的综合地球物理资料处理解释方法技术.指出在地震构造界面的约束下采用重力剥皮技术可以较为可靠地获取基底岩性重力异常并分...     

Gravity and magnetic signatures of volcanic plugs related to Deccan volcanism in Saurashtra, India and their physical and geochemical properties

The Bouguer anomaly and the total intensity magnetic maps of Saurashtra have delineated six circular gravity highs and magnetic anomalies of 40-60 mGal (10⁻⁵m/s²) and 800-1000 nT, respectively. Three of them in western Saurashtra coincide with known volcanic plugs associated with Deccan Volcanic Province (DVP), while the other three in SE Saurashtra coincide with rather concealed plugs exposed partially. The DVP represents different phases of eruption during 65.5±2.5 Ma from the Reunion plume. The geochemical data of the exposed rock samples from these plugs exhibit a wide variation in source composition, which varies from ultramafic/mafic to felsic composition of volcanic plugs in western Saurashtra and an alkaline composition for those in SE Saurashtra. Detailed studies of granophyres and alkaline rocks from these volcanic plugs reveal a calc-alkaline differentiation trend and a continental tectonic setting of emplacement. The alkaline plugs of SE Saurashtra are associated with NE-SW oriented structural trends, related to the Gulf of Cambay and the Cambay rift basin along the track of the Reunion plume. This indicates a deeper source for these plugs compared to those in the western part and may represent the primary source magma. The Junagadh plug with well differentiated ring complexes in western Saurashtra shows well defined centers of magnetic anomaly while the magnetic anomalies due to other plugs are diffused though of the same amplitude. This implies that other plugs are also associated with mafic/ultramafic components, which may not be differentiated and may be present at subsurface levels. Paleomagnetic measurements on surface rock samples from DVP in Saurashtra suggest a susceptibility of 5.5×10⁻² SI units with an average Koenigsberger ratio (Q_n) of almost one and average direction of remanent magnetization of D=147.4° and I=+56.1°. The virtual geomagnetic pole (VGP) position computed from the mean direction of magnetization for the volcanic plugs and Deccan basalt of Saurashtra is 30°N and 74°W, which is close to the VGP position corresponding to the early phases of Deccan eruption. Modeling of gravity and magnetic anomalies along two representative profiles across Junagadh and Barda volcanic plugs suggest a bulk density of 2900 and 2880 kg/m³, respectively and susceptibility of 3.14×10⁻² SI units with a Q_n ratio of 0.56 which are within the range of their values obtained from laboratory measurements on exposed rock samples. The same order of gravity and magnetic anomalies observed over the volcanic plugs of Saurashtra indicates almost similar bulk physical properties for them. The inferred directions of magnetization from magnetic anomalies, however, are D=337° and 340° and I=−38° and −50° which represent the bulk direction of magnetization and also indicate a reversal of the magnetic field during the eruption of these plugs. Some of these plugs are associated with seismic activities of magnitude ≤4 at their contacts. Based on this analysis, other circular/semi-circular gravity highs of NW India can be qualitatively attributed to similar subsurface volcanic plugs.     

Crustal model based on aeromagnetic profiles,gravity studies and wave velocities in rocks and crust

Summary Regional airborne magnetic profiles from India and U.S.A. are analyzed. Profiles are i) 130 km offshore Manglore to 60 km offshore Madras (India) along 13th parallel; ii) Washington to San Francisco (U.S.A.): iii) Brownsville (Texas) to Guatemala City (Mexico). Depth to the sources of magnetic anomalies along Manglore-Madras profile and Washington-San Francisco profiles is calculated either by elementary approximation ofSmellie or Prism model method ofVacquier et al. It is significant that depth values for some of the anomalies obtained by these methods are in very good agreement with those based on drilling data. The magnetic pictures along these profiles are compared with Bouguer gravity anomaly maps and it is shown that in almost all cases where magnetic bodies lie below 5 km (approximately) from sea level they are not reflected in gravity maps whereas all the magnetic bodies which are above 5 km (approximately) produce a markable feature in Bouguer gravity anomaly. This indicates that density of material below this level is almost equal to that of normal basic rocks (2.80 gm/cm³) and those above 5 km have a density less than this. Based on these results the top most layer in crust is considered to be metasedimentary including intrusive rocks and below this it is tentatively taken as Quartz-diorite accounting for the quartz rich Archean formations. Curves representing the variation of compressional wave velocity in i) granite; ii) quartz-diorite; iii) gabbro and iv) dunite, with pressure and temperature as reported from measurements in laboratory, are studied in the light of the general variation of P-wave velocity in the earth's crust reported from seismic sounding studies. It is found that a change in composition from metasedimentary zone to quartz diorite at about 5 km below sea level is supported by this study. It is found that further increase in compressional wave velocity in earth's crust can be explained by a compositional change from quartz diorite to gabbro. At certain places an unusual high velocity for compressional wave at the base of the crust is reported. This can be explained by considering that gabbro merges to Dunite in those areas. Based on this crustal model a probable explanation for the origin of granite masses is attempted.     

The zero-line method of interpreting total field magnetic anomalies of spherical ore-bodies

Summary A method called the zero-line method for interpreting the total field magnetic anomalies of spherical bodies is described. The contour of zero-anomaly is controlled by a linear equation of the typeAx ² +By ² +Cxy +Dx +Ey +F = 0, where the coefficientsA toF are related to the depth of the sphere and the parameters relating to its position and magnetisation. From the coordinates (x, y) of the various points lying on the zero-contour, five normal equations for the above equation are set and solved for the various coefficients. The various parameters relating to the position and magnetisation of the sphere are then determined from these coefficients. It is expected that similar methods can be developed for interpreting magnetic anomalies of other three dimensional bodies also.     

Interpretation of gravity anomalies of dykes by pseudo-magnetic transformation

Summary A simple transformation called pseudo-magnetic transformation is introduced in which the horizontal derivatives of the observed gravity anomalies of any body will be calculated. These horizontal derivatives, called the pseudo-magnetic anomalies, are proportional to the vertical magnetic anomalies of the same body assumed to be polarised horizontally. It is shown that the interpretation of gravity anomalies of dykes is not unique except by computing the pseudo-magnetic anomalies, which will be interpreted by the logarithmic curve fitting technique indicated earlier [5]²).     

Global Crust-Mantle Density Contrast Estimated from EGM2008, DTM2008, CRUST2.0, and ICE-5G

We compute globally the consolidated crust-stripped gravity disturbances/anomalies. These refined gravity field quantities are obtained from the EGM2008 gravity data after applying the topographic and crust density contrasts stripping corrections computed using the global topography/bathymetry model DTM2006.0, the global continental ice-thickness data ICE-5G, and the global crustal model CRUST2.0. All crust components density contrasts are defined relative to the reference crustal density of 2,670 kg/m³. We demonstrate that the consolidated crust-stripped gravity data have the strongest correlation with the crustal thickness. Therefore, they are the most suitable gravity data type for the recovery of the Moho density interface by means of the gravimetric modelling or inversion. The consolidated crust-stripped gravity data and the CRUST2.0 crust-thickness data are used to estimate the global average value of the crust-mantle density contrast. This is done by minimising the correlation between these refined gravity and crust-thickness data by adding the crust-mantle density contrast to the original reference crustal density of 2,670?kg/m³. The estimated values of 485 kg/m³ (for the refined gravity disturbances) and 481?kg/m³ (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480?kg/m³, which is adopted in the definition of the Preliminary Reference Earth Model (PREM). This agreement is more likely due to the fact that our results of the gravimetric forward modelling are significantly constrained by the CRUST2.0 model density structure and crust-thickness data derived purely based on methods of seismic refraction.     

A gradational density model for gravity anomalies over oceanic ridges

The long-wavelength gravity anomalies observed over oceanic ridges have been interpreted in terms of horizontal slabs with lateral variation of density. The location of such a slab in the earth's interior is estimated to be between the depths of 350 and 430 km, which defines the boundaries of the upper phase-transition zone of the mantle. A total density contrast, between the end planes of the horizontal slab, of 0.3 g/cm³ appears to be satisfactory for the interpretation. This remarkable coincidence in depth and density contrast associated with the pyroxene-garnet transformation process is considered to suggest that this process may possibly be: (1) taking place laterally; and (2) generating the gradational density contact which is reflected in the gravity anomalies. In turn, the mechanism for this lateral phase transformation may ultimately be attributable to the convection currents in the asthenosphere.     

A gravity and magnetic study of the volcanic island of Ischia, Naples (Italy)

Gravity and magnetic data for the volcanic island of Ischia, Naples, Italy, have been analyzed and interpreted in light of recent geological and volcanological data to define a model of the island's shallow and deep structures. From the interpretation of the gravity data it appears that the shallow structures consist of pyroclastic material (p=2.0 g/cm³). Within these pyroclastics there are domes and lava flows of higher density and eruptive centres filled with lower density material. The basement is a “horst” with the shallowest depth at about 1.0 km, south of the centre of the island, if we assign a density contrast of 0.5 g/cm³ relative to the above pyroclastics.Interpretation of magnetic data measured at 725 stations showed that the basement derived from the gravity interpretation is magnetized. Moreover, this basement is less magnetized on the western side of Ischia which may be caused by the anomalous thermal state of the area, as indicated by surface fumaroles, hot springs etc. and temperature measurements in deep drillings.     

Gravity and magnetic investigation on the distribution of volcanic rocks in the Qinggelidi area,north‐eastern Junggar Basin (north‐west China)

A detailed investigation on the location of magmatic intrusions in the Carboniferous strata of the Qinggelidi area, north‐eastern Junggar Basin, is presented based on the interpretation of gravity and magnetic data constrained by petrophysical data, seismics and surface geology. The wavelet multi‐resolution analysis based on the discrete wavelet transform is adopted to the regional‐residual separation of gravity and magnetic anomalies. A power spectrum analysis is applied to estimate the source depths corresponding to different scales. A comparative analysis on the characteristics of local gravity and magnetic anomalies improved our understanding of volcanic rock distribution in the Carboniferous strata. Generally speaking, in total 75 anomalies are recognized, among which 23 are inferred to be the responses of basalts, diabases and andesites with high density and strong magnetization. Twelve anomalies are assumed to be caused by andesites, rhyolites and volcanic breccias with medium‐low density and high magnetization. There are still five anomalies that are believed to be generated by volcanic tuffs with low density and weak magnetization. Lastly, four cross‐sections in 3D gravity and magnetic modelling are displayed to provide a more thorough image of volcanic rocks in our study area.     

Preliminary Results from Paleomagnetic Records on Lake Sediments from South America

The preliminary results of paleomagnetic and radiocarbon dating of late pleistocene-holocene sediments from two lakes of south-western Argentina (41°S, 71.5°W) are presented. The magnetic susceptibility, intensity and direction of the natural remanent magnetisation were measured. The stability of the natural remanent magnetisation was investigated by alternating field demagnetisation. The magnetic parameters allowed the cores within each lake to be correlated. ¹³ C analysis, total organic content measurements and C ¹⁴ dating were carried out. A model of sedimentation is suggested. Using this model and the correlation, curves of variations of magnetic inclination and declination in time are shown.     

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)…     

Easy method of interpreting dyke anomalies

Summary An entirely new procedure is proposed in this paper for interpreting anomalies of dykes. This reduces the ambiguity in magnetic interpretation. Measurements of the first vertical derivative simplifies the problem of interpretation and also supplies additional information concerning the parameters of a dyke. The first vertical derivative profile cuts the distance axis at two points whose separation is related to the depth and direction of magnetisation of a dyke.     

三度体（均质模型）位场波谱的正演计算

本文给出任意指向的均质直线段、多边形面和多面体的重磁异常谱的解析表达式。利用它们可以进行不规则三度体的重磁异常谱的数值计算。此外,尚导出任意指向的斜平行六面体重磁异常谱的解析表达式。这些表达式结构简单,易于计算,用作位场的正演反演计算都十分方便。     

Some applications of the linear programming within gravimetry

Summary The paper presents some mathematic patterns by using the linear programming. These patterns are making up a simple method of gravimetric data transformation, solvable with the help of digital computers. Some methods of differentiating the regional and local anomalies, of effectuating the calculus of some gravity derivatives and of establishing the shape of bidimensional bodies, are shown. This work was aimed to enlarge the field of the linear programming appliableness within geophysics. Former studies on the scope were undertaken byShalaev [7]³), [8], as well as byDougerty andSmith [3].     

非均匀物性条件下多尺度窗口修正法换算磁源重力异常及在寻找DSO的应用

DSO(Direct Shipping Ore,直运块矿)是一种高品位的富铁矿.在加拿大拉布拉多(Labrador)地槽谢菲尔威利(Schefferville)铁矿成矿带,含铁建造苏克曼(Sokoman)组地层全铁含量低、具高密度、强磁性,能够引起高重力异常与高磁异常;而风化淋滤后富集的赤铁矿和针铁矿等(也称DSO)全铁含量高,具高密度、无磁性,仅能够引起高重力异常.采用一般的滤波方法不能提取DSO的重、磁异常.本文采用基于泊松(Poisson)公式的磁场换算磁源重力异常(pseudo-gravity anomaly)方法,由磁场换算磁源重力异常,再与实测重力异常对比,得到纯粹由高密度、无磁性的DSO产生的剩余重力异常,对剩余重力异常采用密度成像与2.5D反演方法解释DSO.泊松公式虽然提出时间很长,但迄今为止仅仅用在资料解释中的定性分析,本文推导并实现了密度磁性非均匀条件下经典泊松公式的形式与实现过程,提出了多尺度窗口滑动线性回归修正的磁场换算磁源重力异常方法,使该公式的数学原理能够对重、磁异常的反演解释定量化.最后本文将多尺度窗口滑动线性回归修正的换算磁源重力异常方法用于加拿大拉布拉多地槽谢菲尔威利铁矿成矿带铁矿勘探,较好地解决了寻找高密度、无磁性DSO的问题.     

A geophysical approach to the granite batholith under the eastern Southern Uplands,Scotland

From our interpretation of the Bouguer gravity and aeromagnetic anomalies in south-east Scotland, we conclude that a massive granite batholith underlies the greater part of the eastern Southern Uplands. The granite model which we computed earlier from gravity anomalies in the Tweeddale area fits the observed magnetic anomalies closely, if a normal magnetization of 0.095 A m^–1 is assigned, similar to values found for exposed local granites. Further gravity modelling shows that, apart from the Tweeddale boss, the granite shallows to less than 1 km near Lammer Law in East Lothian and extends north of the Lammermuir Fault. A model for the East Lothian volcanics was computed from their aeromagnetic anomalies, then their gravitational effect was combined with that estimated for the Devonian and Carboniferous sediments and the result stripped off the observed gravity field. The residual gravity anomalies were used to generate a two-dimensional model for the granite north of the Lammermuir Fault. The expected tectonic consequences of a massive granite batholith in the eastern Southern Uplands are compared with the known development of faults and sedimentary basins around its margins.     

Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts

During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of \(\lambda =ax^m+by^n+cz^t\), where m, n, t are nonnegative integers and a, b, c are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of \(m\le 1\), \(n\le 1\), \(t\le 1\), and an analytic formula of the gravity potential in the case of \(m=n=t=2\). For a rectangular prism, we derive an analytic formula of the gravity potential for \(m\le 3\), \(n\le 3\) and \(t\le 3\) and closed forms of the gravity field are presented for \(m\le 1\), \(n\le 1\) and \(t\le 4\). Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.