Observed Gravity Data Research Articles

Gravity Anomaly Map over The Black Sea Using Corrected Sea Surface Heights from ERS1, ERS2 and Topex/Poseidon Satellite Altimetry Missions

Approximately nine-year data from ERS1, ERS2 and TOPEX/POSEIDON (T/P) satellite altimetry missions have been used for the recovery of gravity anomalies over the Black Sea. The Corrected Sea Surface Height product of Aviso/Altimetry has been proven to be homogeneous after a cross-over adjustment. The Least Squares Collocation method was applied in a so-called “remove-restore” procedure. The residual geoid heights, obtained by subtracting EGM96 geoid heights from cross-over adjusted sea surface heights, were inverted to recover residual gravity anomalies in a grid structure over the Black Sea. Finally, EGM96 free air gravity anomalies were added to the predicted residual gravity anomalies to obtain the free air gravity anomalies. In order to check the consistency with respect to an external source, these computed free air gravity anomalies were compared to ship gravity observations, and to alternative satellite altimetry derived gravity anomalies. Comparisons with the observed gravity data yielded that external consistency of the gravity anomalies computed in this study is about 3 mGal for individual ship tracks. Overall external consistency in the test area is 4.8 mGal. Comparison with other satellite altimetry derived gravity anomalies presented a good agreement.

Gravity evolution and earthquake activities of the northeastern edge of Qinghai-Xizang block

The relationship between temporal-spatial evolution of gravity and earthquake activity during 1992–2001 has been analyzed systematically by integrally adjusting the gravity observation data of the northeastern edge of Qinghai-Xizang (Qingzang) block. The result shows that the gravity observation data of the northeastern edge of Qingzang block obtained by using the uniform starting datum can completely reflect the precursory gravity information appearing during the seismogenic process. In the genesis stage of an earthquake, regional gravity anomaly appears in a large area, resulting in related local gravity anomaly. The dynamic image of gravity field can clearly reflect the orderly evolution and earthquake activity.

Ellipsoidal geoid computation

Modern geoid computation uses a global gravity model, such as EGM96, as a third component in a remove–restore process. The classical approach uses only two: the reference ellipsoid and a geometrical model representing the topography. The rationale for all three components is reviewed, drawing attention to the much smaller precision now needed when transforming residual gravity anomalies. It is shown that all ellipsoidal effects needed for geoid computation with millimetric accuracy are automatically included provided that the free air anomaly and geoid are calculated correctly from the global model. Both must be consistent with an ellipsoidal Earth and with the treatment of observed gravity data. Further ellipsoidal corrections are then negligible. Precise formulae are developed for the geoid height and the free air anomaly using a global gravity model, given as spherical harmonic coefficients. Although only linear in the anomalous potential, these formulae are otherwise exact for an ellipsoidal reference Earth—they involve closed analytical functions of the eccentricity (and the Earth’s spin rate), rather than a truncated power series in e2. They are evaluated using EGM96 and give ellipsoidal corrections to the conventional free air anomaly ranging from −0.84 to +1.14 mGal, both extremes occurring in Tibet. The geoid error corresponding to these differences is dominated by longer wavelengths, so extrema occur elsewhere, rising to +766 mm south of India and falling to −594 mm over New Guinea. At short wavelengths, the difference between ellipsoidal corrections based only on EGM96 and those derived from detailed local gravity data for the North Sea geoid GEONZ97 has a standard deviation of only 3.3 mm. However, the long-wavelength components missed by the local computation reach 300 mm and have a significant slope. In Australia, for example, such a slope would amount to a 600-mm rise from Perth to Cairns.

Power‐law scaling behavior of crustal density and gravity

The scale invariant nature of crustal heterogeneity has been established through direct measurements of rock properties and inferences from geophysical observations. We examine the behavior of crustal density variations over length scales from centimeters to hundreds of kilometers using well‐logs, surface rock samples and observed gravity data. The three data types support a simple model of an isotropic, scaling crust with density characterized by a power‐law spectral behavior.

Simulation of the Indonesian land gravity data using a digital terrain model data

The Indonesian gravity field is neither accurately nor comprehensively determined, especially due to inadequacy of land gravity data. This study deals with determination of Indonesian land gravity and proposes the solution to data unavailability by means of a simulation technique. The simulation was carried out by combining short wavelength topographic effects from GTOPO30 and long wavelength information from EGM96. The simulated result was then compared with the observed gravity data. Over Java, Sumatra and Sulawesi islands, using three methods commonly used on the computation of topographic effect; topography, isostatic and RTM (Residual Terrain Model), it was estimated that error propagation by the GTOPO30 into the simulated gravity is about 4.5 to 11.7 mgal, with the RTM method was affected less than others. It was also shown that the simulated gravity from the RTM method gave the best agreement with STD (Standard Deviation) differences of 17 to 42 mgal compared to the observed data. This result was achieved after applying optimal RTM parameters over the Indonesian area: a reference field of 25′–27.5′ and density of 2–2.2 gr/cm3. Compared to STD differences between EGM96 and observed data, that between the simulated gravity and observed data improved by 2.5–7 mgal, and gave more detailed gravity features, especially over areas of high topography.

A least‐squares derivatives analysis of gravity anomalies due to faulted thin slabs

This paper presents two different least‐squares approaches for determining the depth and amplitude coefficient (related to the density contrast and the thickness of a buried faulted thin slab from numerical first‐, second‐, third‐, and fourth‐horizontal derivative anomalies obtained from 2D gravity data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z) = 0. Knowing the depth and applying the least‐squares method, the amplitude coefficient is determined using a simple linear equation. In this way, the depth and amplitude coefficient are determined individually from all observed gravity data. The depths and the amplitude coefficients obtained from the first‐, second‐, third‐, and fourth‐ derivative anomaly values can be used to determine simultaneously the actual depth and amplitude coefficient of the buried fault structure and the optimum order of the regional gravity field along the profile. The method can be applied not only to residuals but also to the Bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local fault structure (shallow or deep) and a regional component represented by a polynomial of any order. The method is applied to theoretical data with and without random errors and is tested on a field example from Egypt.

Three least‐squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data

Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.

A least-squares derivative analysis of gravity data applied in Senegal, west Africa

A simple method to simultaneously determine the shape (shape factor or structural index) and the depth of a buried structure from second horizontal derivative anomalies obtained from gravity data using filters of successive window lengths has been developed. The method is similar to Euler deconvolution, but it solves for shape and depth independently. For a fixed window length, the depth is determined using the least-squares method for each shape factor. The computed depths are plotted against the shape factors representing a continuous window curve. The solution for the shape and depth of the buried structure is read at the common intersection of window curves. The method involves using simple models convolved with the same numerical horizontal second derivative filter as applied to observed gravity data. As a result, the method can be applied not only to true residuals but also to measured Bouguer data of a short profile length. Finally, the validity of the method is tested on theoretical examples with and without random errors and field data from Senegal, west Africa.

Gravity inversion by means of growing bodies

This paper presents a gravity inversion method for determining the volumes of bodies with pre‐established density contrasts. The method works step‐by‐step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities. The process is treated in a 3-D context; at the same time, it can determine a simple regional trend. Moreover, positive and negative density contrasts are simultaneously accepted. The solution is obtained by a double condition: (1) the 𝓁2-fitness to the observed gravity data (model fitness) and (2) the minimization of the total (weighted) anomalous mass (model smoothness). A positive parameter is used to balance the two minimization terms. The method is applied to a simulated example and also to a real example: the volcanic island of Gran Canaria (Canary Islands, Spain). In both cases, the results obtained show the possibilities of the method.

A finite element method for computation of the regional gravity anomaly

A regional gravity anomaly, based on element shape functions used in finite element analysis, is developed. The regional gravity is approximated by a weighted sum of discrete gravity values at eight stations coinciding with the eight nodes of a second‐order or at twelve stations coinciding with the twelve nodes of a third‐order isoparametric element superimposing the map space. The computations are carried out on a reference space with the shape functions acting as weighting factors, and subsequently translated to the real map space. In this technique, no observed gravity data lying inside the survey area enter into the regional computation. Tests on the gravity field in Harris County, Texas, a well known hydrocarbon prospect during the 1940s, and the Klamath Mountains and the Cascade Range in California confirmed the efficacy of this method.

A geodetic approach to gravity data reduction for geophysics

The currently adopted approach to reduce observed gravity data for geophysical purposes includes several approximations. These were originally used to reduce computational effort, but have remained standard practice, even though the required computing power is now readily available. In contrast, more precise gravity reductions are routinely employed in physical geodesy. The difference between simple Bouguer gravity anomalies derived using the geophysical and geodetic approaches can reach several tens of μm sec −2. The geodetic reductions include a more accurate calculation of normal gravity as a function of latitude, and a free air correction that accounts for the non-sphericity of the figure of the Earth. Also important, especially given the advent of Global Positioning System coordination of gravity surveys, is the need to ensure that the correct vertical and horizontal coordinate systems are used for the gravity reduction procedure. Errors associated with the use of non-geocentric horizontal coordinates and ellipsoidal heights are significant when compared with the accuracy of an individual gravity measurement. A generalised gravity reduction program and a coordinate transformation program are presented which can be employed to reduce geophysical data in a geodetic manner.

Computation of regional gravity anomaly — A novel approach

A new scheme is put forward based on the shape function concept of finite element approximation to compute regional gravity anomaly. The uniqueness of this approach is that excepting eight (or twelve) discrete gravity measurements coinciding with the eight (or twelve) nodes of a quadratic (or cubic) isoparametric element superimposing the map space, often very large, no other observed gravity data are invoked to compute the regional. Tests on two Bouguer gravity fields, an oil prospect and a rift valley confirmed better resolution by this approach. This technique is straight forward, uses simple mathematics to be easily automated and yields repeatable results.

Gravity anomaly and flexural model: constraints on the structure beneath the Peruvian Andes

Bouguer gravity data along the Nazca profile of Fukao et al. (1989), NE-SW striking across the Peruvian Andes, are used to investigate the flexure of the Brazilian Shield. Modeling of the observed gravity data indicates that the Brazilian Shield lithosphere is flexed downward and may extend beneath the Andes as far as 150 km. Assuming that the Brazilian Shield behaves elastically, flexural analysis shows that the isostatic gravity inequilibrium in the eastern Andes can be explained by deflection of the Moho due to the bending of an elastic plate beneath the Sub-Andes. The elastic thickness of the plate is estimated to be between 25 and 55 km, with corresponding flexural rigidity between 0.1 and 1.7 × 10 24 Nm. Many small to moderate-sized earthquakes that have focal depths of tens of kilometers are distributed over a broad area from the Eastern Cordillera to the Brazilian Shield. These events are located well above the subducted flat Nazca plate and very likely are associated with the underthrusting of the Brazilian Shield. A step-like gravity anomaly of 150 mGal on the eastern margin of the Eastern Cordillera cannot be fully explained by the flexure model alone and requires a sharp-edged mass deficit or discontinuous Moho beneath the Eastern Cordillera. Our gravity modeling shows that Bouguer gravity anomalies along the Nazca profile are best explained by a flexed Moho, which is deflected by the underthrusting of the Brazilian Shield beneath the Andes along with a wedge-shaped body of low-density material directly beneath the Eastern Cordillera.

Marine gravity surveying line system adjustment

The general theories and methods of marine surveying line system adjustment were introduced in Коугия (1979) and Tang (1991) . According to the characteristics of marine gravity measurement, this paper presents a new method of combined adjustment which takes into account both direct and indirect influence of position errors. The method is particularly suitable to be used in the post- processing of marine gravity observation data. With some practical applications, it is proved to be effective in improving the quality of marine gravity data.

Crustal and upper mantle contribution to the axial gravity anomaly at the southern East Pacific Rise

This paper reassesses the crustal and upper mantle contribution to the axial gravity anomaly and isostatic topography observed at two segments (14°S and 17°S) of the southern East Pacific Rise (SEPR) in order to determine what constraints these data place on the amount of melt present in the underlying mantle. Gravity effects due to seafloor topography and relief on the Moho (assuming a constant crustal thickness and density) overpredict the amplitude of the gravity high at the EPR by 8–10 mGal. About 70% of this mantle Bouguer anomaly (MBA) low (6–7 mGal) can be explained by a region of partial melt and elevated temperatures in the mid‐to‐lower crust beneath the rise axis. Compositional density reductions in the mantle due to melt extraction are shown to make a negligible contribution to the amplitude of the observed MBA. Temperature‐related mantle density variations predicted by a simple, plate‐driven, passive flow model with no melt retention can adequately account for the mantle contribution to the observed MBA within the experimental uncertainty (±1 mGal). However, the retention of a small amount of melt (≤1–2% at 14°S; ≤4% at 17°S) in a broad region (tens of kilometers wide) of upwelling mantle is also consistent with the observed gravity data given the uncertainty in crustal thermal models. The anomalous height of the narrow, topographic high at the EPR provides the strongest evidence for the existence of significant melt fractions in the underlying mantle. It is consistent with the presence of a narrow (∼10 km wide) partial melt conduit that extends to depths of 50–70 km with melt concentrations up to 2% higher than the surrounding mantle. Along‐axis variations in mantle melt fraction that might potentially indicate focused upwelling are only marginally resolvable in the gravity data due to uncertainties in crustal thermal models. The good correlation between along‐axis variations in depth, and changes in axial volume and gravity, argue against the mantle melt conduit as being the major source of this along‐axis variation. Instead, this variability can be adequately explained by a combination of along‐axis changes in crustal thermal structure and/or along‐axis crustal thickness changes of a few hundred meters.

Seismic reflection data and the internal structure of the Lake District batholith, Cumbria, northern England

SUMMARY Seismic reflection data across the western margin of the Lake District batholith reveal reflector-poor and reflector-rich areas within components of the intrusion. Synthetic seismograms generated from a series of velocity models have been used to interpret a representative panel of a seismic reflection profile across the western boundary of the batholith. Results indicate that the reflections bounding large, wedge-like reflector-rich zones may be associated with granite/country rock acoustic impedance boundaries. The reflector-rich zones are interpreted as bodies of country rock intruded by the granite and the reflection-poor areas as laccolithic granitic components of the batholith. Reflector-rich areas within the main body of the Lake District batholith may arise from either areas of included country rock, sills or fracture zones within the granite. The areal extent of the wedge-like zones of reflections suggests the intrusion hereabouts comprises a series of laccolithic bodies. It is interpreted that the subsurface western margin of the intrusion has a jagged, ‘cedar-tree’ profile, the intrusive envelope to which is steeper than previous gravity models imply for a ‘simple’ batholith margin. Such a configuration is compatible with observed gravity data.

A least‐squares minimization approach to depth determination from moving average residual gravity anomalies

We have developed a least‐squares minimization method to estimate the depth of a buried structure from moving average residual gravity anomalies. The method involves fitting simple models convolved with the same moving average filter as applied to the observed gravity data. As a result, our method can be applied not only to residuals but also to the Bouguer gravity data of a short profile length. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on two field examples from the United States and Senegal.

Internal structure of the Sierra Nevada batholith based on specific gravity and gravity measurements

About 6,000 specific‐gravity (SG) measurements of samples collected from nearly 200 granitic plutons comprising the central Sierra Nevada batholith yield a SG contour map across the batholith from 36.25° to 38° north latitude. With notable exceptions, SG decreases from values generally greater than 2.7 in the west to less than 2.6 over a few small areas of high‐silica, high‐potassium granites near the east edge. A good correlation between measured SG and analyzed weight percent SiO2 enables estimation of average silica variations across the batholith. The average SG is 2.69 corresponding to an average of 68 wt. % SiO2 for the 18,000 km² central part of the batholith.A 1‐km gridded version of the SG measurements has been used to generate a series of synthetic gravity maps, assuming that the SG of rocks at the surface extends unchanged to various depths. The synthetic map computed for a depth of 10 km shows the best correspondence with the isostatic residual gravity map indicating that variations in the observed gravity residuals are largely caused by SG variations of the plutonic rocks exposed at the surface that apparently extend downward to an average depth of about 10 km.Although the 10‐km synthetic gravity map gives the best overall fit to the observed gravity data, comparison of individual anomalies indicates that the bottoms of the plutons as defined by SG variations at the surface are generally shallower along the west edge of the Sierra Nevada (7±2 km) and deeper in the younger and more felsic eastern part (12±3 km). These depths do not necessarily represent a distinct base of the Sierra Nevada batholith. They may indicate the depth below which density homogenization occurs, either by igneous, or possibly, structural processes.

Monitoring the Bulalo geothermal reservoir, Philippines, using precision gravity data

Precision gravity monitoring of the Bulalo geothermal field began in 1980 to estimate the natural mass recharge to the reservoir. Between 1980 and 1991, gravity decreases exceeding 2.5 × 10 −6 N/kg (250 microgals) were observed in response to fluid withdrawals. A maximum rate of −26 microgals per year was observed near the production center. Mass discharges predicted by recent reservoir simulation modeling generally match those inferred from the observed gravity data. According to simulation studies, no recharge occurred between 1980 and 1984. The mass recharge between 1984 and 1991 was estimated to be 30% of net fluid withdrawal during the same period, equivalent to an average rate of 175 kg/s (630 metric tons per hour).

A Comparison of Regional - Residual Separation Techniques for Gravity Surveys

Tasmania lies on a triangular extension of the Australian continental crust, surrounded on two sides by deep ocean basins. Strong regional effects from these features obscure much of the short wavelength character in the observed gravity data. Interpretation of the data requires reliable separation of the residual and regional components of the gravity field. Bouguer gravity data covering onshore and offshore Tasmania have been used to test a variety of methods of regional ? residual separation, including trend surfaces, filtering, upward continuation and forward modelling. Forward modelling was used to calculate a regional field from a three-dimensional model for Tasmania consisting of continental crust, oceanic crust, water and the mantle. The main advantage of modelling is that it enables the incorporation of geological and geophysical constraints into the regional field. Automated separation techniques are simple, fast and purely numerical but do not allow the incorporation of geological constraints. Quantitative interpretation of the resultant residual maps is difficult and uncertain. All automated methods tested produce undefined dc shifts which limit the usefulness of the residuals. Of the automated methods, trend surfaces produce residual maps which show the best correlation with known geology. The preferred method of regional ? residual separation is forward modelling, although it is both time consuming and subjective. Quantitative interpretation of residuals from modelling can be carried out with a greater degree of confidence since the regional field has a well-defined geological basis.