Linear inversion of a negative gravity anomaly in se Rio Grande cone: a graben on oceanic crust?

Linear inversion of a negative gravity anomaly in se Rio Grande cone: a graben on oceanic crust?

Emilson Pereira Leite^I; Naomi Ussami^II

^IDepartment of Geology and Natural Resources, Institute of Geosciences, State University of Campinas, 13083-970 Campinas, SP, Brazil. Postal box: 6152, Tel: [phone]; Fax: [phone] - E-mail: [e-mail]

^IIDepartment of Geophysics, Institute of Astronomy, Geophysics and Atmospheric Sciences, University of São Paulo, Rua do Matão, 1226 - 05508-900 São Paulo, SP, Brazil. Tel: [phone]; Fax: [phone] - E-mail: [e-mail]

ABSTRACT

We detect, for the first time, a negative free-air gravity anomaly of 23 mGal amplitude over a region in the South Atlantic Ocean centered at 48ºW and 35ºS. To this end, we used the integration of conventional shipborne gravity data and gravity data derived from GEOSAT/ERM satellite altimetry. The north bound of this anomaly coincides with the Chuí Lineament and the south bound indicates another lineament, which is the extension of the Meteor Fracture Zone. The anomaly trend is NE-SW, its width is 400 km and its length is 600 km. Two-dimensional linear inversion with relative and absolute equality constraints was used to calculate the density distribution along three profiles perpendicular to the main axis of the anomaly. The result suggests that the sediment thickness in the deepest part of the basin is at least 3.0 km where the ocean bathymetry is 4,800 m. This tectonic feature, an asymmetric half-graben formed between two lineaments, probably lies over an oceanic crust. The estimated volume of sediments in this basin is approximately 50% of the post-Miocene sediments volume deposited in the Rio Grande Cone where gas-hydrates were found.

Keywords: Potential Methods, Gravity Inversion, Rio Grande Cone, Oceanic Crust.

RESUMO

Uma anomalia ar-livre com amplitude negativa de 23 mGal em uma região no oceano Atlântico Sul, centrada em 48ºW e 35ºS, foi observada pela primeira vez devido à integração de dados de gravimetria marinha convencionais e dados de gravidade derivados de altimetria por satélite, adquiridos pela missão GEOSAT/ERM. O limite norte desta anomalia coincide com o Lineamento Chuí e o limite sul indica outro lineamento, que é uma extensão da Zona de Fratura Meteoro. A anomalia tem direção NE-SW, sua largura é de 400 km e seu comprimento é de 600 km. Foi utilizada uma metodologia de inversão linear bidimensional, com vínculos relativos e absolutos, para calcular a distribuição de densidades ao longo de três perfis paralelos ao eixo principal da anomalia. O resultado sugere que a espessura de sedimentos na parte mais profunda da bacia é de no mínimo 3,0 km onde a batimetria oceânica é de 4.800 m. Esta feição tectônica, um semi-gráben assimétrico formado entre dois lineamentos, provavelmente situa-se sobre uma crosta oceânica. O volume de sedimentos estimado para esta bacia é de cerca de 50% do volume de sedimentos pós-Mioceno depositados no Rio Grande Cone, onde hidratos de gás foram encontrados.

Palavras-chave: Métodos potenciais, Inversão gravimétrica, Cone do Rio Grande, Crosta oceânica.

INTRODUCTION

A free-air anomaly map in Southern Atlantic was obtained through integration of conventional shipborne gravity data and gravity data derived from GEOSAT/ERM satellite altimetry (Fig. 1), using the Least Squares Collocation technique (Leite et al., 1999). This technique assumes that a set of observations associated to any component of the Earth’s gravity field can be related to the anomalous gravitational potential through appropriate linear functionals. If the covariances between such components are known,then it is possible to estimate any other component of the Earth’s gravity field. This allows two or more components to be integrated, so that the output can be any one of them for a given study area. The errors associated with the observations and with the estimated quantities are taken into account rigorously in the Least Squares Collocation. Gravity free-air anomalies and height anomalies are the components of the Earth’s gravity field that were used in the estimation of the free-air anomalies used in this study.

The free-air anomaly map defined a negative gravity anomaly (Fig. 2) centered at 48ºW and 35ºS, on the southeast border of Rio Grande Cone (Fontana, 1992). Figure 2 also shows the main physiographic features in the region. To the authors knowledge, this anomaly has never been mapped before because it was used gravity datasets either from the conventional shipborne survey or derived from satellite altimetry (e.g. Andersen & Knudsen, 1995). This paper shows the advantage of using an integrated approach in mapping marine gravity anomalies. Figure 2 also shows the main physiographic features in the region, which are the São Paulo Plateau, the Rio Grande Rise, the Pelotas Basin, the Rio-Grandense Shield and the Rio Grande Cone.

Contrary to interactive forward modeling, an inversion method does not require a complete knowledge about the anomalous source. Rather, an inversion method requires few prior geologic constraints which must be mathematically incorporated by the method in an automatic way. This procedure is frequently adopted to obtain a unique and stable solution in gravity interpretation (Silva et al., 2002).

In this study, we have been working only with constrained linear inversion using the same idea described in Barbosa et al. (1997). The difference here is that we estimated the density contrast distribution that fits the observed anomaly within the measurement errors and represents smooth spatial density variations (Barbosa et al., 2002). So, a discrete density distribution is estimated by standard linear inversion stabilized by imposing smooth spatial density variations. The premise of a smooth spatial density distribution is justified by smooth spatial distributions of gravity values along selected gravity anomaly profiles, i.e. high wavenumber anomalies that could represent real anomalous sources within the crust are not detectable in these profiles.

In this paper, we estimate the discrete density distribution along three gravity profiles over the SE Rio Grande Cone by using an inverse technique which incorporates relative constraints and absolute equality constraints (Barbosa et al., 1997). In the inversions presented here, relative constraints are used to guarantee smooth spatial density variations, while equality constraints are used to set density values associated with specific cells which define the interpretation model.

As most of the geophysical data inversion techniques, the main issue in the proposed methodology is how to set the constraints. If one does not have a set of known density values provided by independent geophysical methods or if the knowledge about the geological setting in the study area is insufficient, this method may not be applied properly or else, the solution may not have any geological meaning.

RESIDUAL GRAVITY ANOMALY MODELING

The Earth’s Gravity Field is produced by a superposition of overlapping gravitational effects of many sources within the crust. Local gravity anomalies associated with near surface masses are referred as to residual anomalies and gravity anomalies due to larger and deeper geological features are referred as to regional anomalies.

In order to obtain the residual anomaly of the region shown in Figure 1, firstly we calculated the gravitational effect due tobending of the crust-mantle interface in response to sedimentary loads in order to check whether this component was important on the observed anomaly.

We also removed from the observed anomaly a polynomial flat surface, which is a regional field that represents sources deeper than about 10 km.

The following sections describe how the residual gravity anomaly was obtained.

Flexural Effect of Sedimentary Loads

Lithosphere and crust-mantle boundary is flexed due to sedimentary loads and this deformation produces long wavelengthcomponents on the gravity field. Thus, it is necessary to calculate the gravitational effect of this flexure and to remove it from the observed anomalies.

A sediment isopach map (Emery & Uchupi, 1984) based on reflection and refraction seismic, well stratigraphy, and DSDP (Deep Sea Drilling Project) data were digitized (Fig. 3).

Next to the Pelotas Basin it is possible to see a thick sedimentary layer centered at 48ºW and 32ºS with up to 7 km of sediments. In the southern continental margin of Uruguay there is also a 7 km wedge of sediment and a thick sedimentary layer in the Rio Grande Cone is also observed.

An algorithm developed by Shiraiwa (1994) was used to estimate the gravitational effect due to the flexure of the lithosphere caused by the sedimentary loading. In this algorithm, the lithosphere is approximated by a thin elastic plate, with a load on its top (Timoshenko & Goodier, 1970). The gravitational effect of the deformed crust-mantle boundary is calculated by Parker’s method (Parker, 1972). The parameters used to calculate gravitational effect of this deformation are: effective elastic thickness = 10 km; sediment density = 2.4 g/cm³; crust oceanic rocks density = 2.9 g/cm³; and mantle density = 3.3 g/cm³. Figure 4 shows that the gravitational effect due to flexure is less than 10^-1 mGal, therefore lower than the error in the free-air anomaly estimate.

Regional-Residual Separation

A deep source anomaly associated with variations in crust-mantle boundary and lower crust is observed and it should be removed in order to invert the anomalies associated with shallow sources.

For this purpose, a first degree polynomial surface was fitted to the original gravity data (Fig. 5) in order to estimate the regional gravity field. Figures 6 and 7 show the regional and residual anomalies, respectively. Gravity profiles were extracted from the residual anomaly shown in Figure 7.

LINEAR INVERSION METHODOLOGY

The solution of gravity data inversion is neither unique nor stable. Therefore it is an ill-posed problem (Hadamard, 1902). A way to reduce the instability and to guarantee the uniqueness of the solution is to introduce a priori information about unknown parameters.

Basically, gravity inversion problems can be subdivided into two groups: linear and nonlinear problems. The first group contains several methods to calculate physical properties, which generally is density, while body geometry is fixed. These methods are used to map lateral and subsurface density distribution (e.g. Braile et al., 1974; Bear et al., 1995). Nonlinear methods are used to calculate body geometry while physical propertiesare fixed and these methods are useful to calculate anomalous body’s position and orientation and layers depths (e.g., Richardson & MacInnes, 1989; Barbosa et al., 1997).

We have chosen the linear inversion because, more than the geometry of the anomalous body, we wanted to learn about the stratigraphy of the basin and how it was formed. This information should be reflected in the density distribution.

The inverse problem can be expressed as a linear system like

where G is a linear operator (usually called sensitivity matrix) that describes the relationship between unknown model parameters (Dr) and data (Dg). Matrix G will be defined using a forward method like that described in Talwani et al. (1959). To estimate Dr we assume that a set of M juxtaposed cells represents the medium beneath the N points where the data Dg was collected.

Let us define Dr as the M-dimensional density contrast vector to be estimated, and Dg as the N-dimensional gravity anomaly vector produced by the M cells. We can impose the fitting of gravity data by minimizing the functional

where ||·|| is the Euclidean norm. Estimating Dr from Dg is a linear problem in this case. We will describe a method to estimate Dr incorporating additional constraints.

Minimizing the functional below incorporates the relative equality constraints, namely the smooth density variation constraints

where f_r is a normalizing factor, R is a matrix L × M, where L is the number of a priori relationships between pairs of parameters. if we know that the density of the ith block is twice the density of the jth block, then the ith and jth elements of the specific row of R that corresponds to the constraint will take values 1 and 2, respectively, whereas the rest of the elements in this row will be zero, giving rise to the expression Dr_i - 2Dr_j@ 0 (Barbosa et al., 1997). Notice that it is possible to use different relationships in the same R matrix. For example, it can establish a linear relationship among the parameters forcing the increase of densities with depth.

Minimizing the functional below incorporates the absolute equality constraints

where A is an H × M matrix (H < M) whose rows contain only one non-null element, equal to unity (Barbosa et al., 1997), and h is an a priori specified H-dimensional vector for the densities. The term f_a is a normalizing factor. For instance, if the ith parameter is known and its value is 0.5, we just have to set 1.0 in the ith column and first row of the matrix A, whereas the rest of the elements are set to zero. Accordingly, the first element of h will be 0.5.

The terms f_a and f_r are given by

where ||·|| is the Euclidean norm.

Incorporating the constraints (3) and (4) to the problem can be done by minimizing the unconstrained functional in the least-squares sense

Its solution to the vector Dr is

The constants µ_a and µ_r are weights associated to each kind of constraints.

RESULTS OF DATA INVERSION

The proposed inversion methodology was applied to three gravity profiles shown in Figure 8: A-A’, B-B’ and C-C’. These profiles were extracted from the free-air anomaly residual map (Fig. 7). For each profile, the interpretative subsurface model consisted of 225 cells (15 ×15 cells with dimensions equal to 21 km and 0.35 km along x- and z- directions, respectively).

Absolute constraints were set as follows: the densities of the two top layers, at depths between 4.8 km and 5.5 km, were fixed with values of 2.4 g/cm³ based on seismic results given by Leyden et al. (1971). A background density of 3.0 g/cm³ was considered to represent the mean density of the crustal basement in the study area. Therefore, 0.6 g/cm³ was the density contrast value set into the h vector of Equation 7. The two bottom layers, at depths between 9.2 km and 10 km, had cells fixed with values of 2.9 g/cm³, which gives a density contrast of 0.1 g/cm³. Cells constrained with absolute values are shown in Figure 9 as gray cells. Absolute constraints also helps in order to limit the range of possible values associated with the free-cells, thus biasing the solution towards a set of geologically sound density values. The weight associated with the absolute constraints was set equal to µ_a = 1.0.

Relative constraints were used in order to impose an overall smoothness on the density distribution estimate, as described in the methodology section. The weight associated with the relative constraints was set equal to µ_r = 0.1. The combination of these two constraints provides a density distribution that is smooth and increases with depth, as was expected given the shapes of the anomalies together with the geological knowledge of the area.

Figures 10, 11 and 12 show the inversion results of the free-air anomalies profiles, A-A', B-B' and C-C', respectively. These results are consistent with a basin formation of evolution due to rifting and rapid initial subsidence. A uniform density distribution as shown in Figure 13, layer A, is expected if the first phase of sedimentation layer B refers to sedimentation well after rifting and oceanic lithosphere subsidence.

DISCUSSION

Sediment volume stored in this basin corresponds to approximately 50% of after-Miocene sediment volume stored in the Rio Grande Cone where gas-hydrates were found (Fontana, 1992).

LEPLAC seismic data are not available but Russo (1999) calculated an isopach map for the study area and its surroundings. This map shows a sedimentary thickness of 2.5 to 3 km, which is approximately equal to the inversion results, although there is no evidence in this map for the existence of a basin associated with the sedimentary layer.

Figure 14 shows the free-air anomaly overlapped by the tectonic map. We can see that the north limit of the negative free-air anomaly coincides with the Chuí Lineament, which extends to the Mid-Ocean Atlantic Ridge. The south limit of the anomaly appears to be another lineament and it is shown on the same figure, between the parallels -37º and -36.5º. This lineament may represent an extension of the Meteor Fracture Zone.

The graben-like structure of this basin may be associated with a rifting event that occurred in response to adjacent continental margin uplifting (Leite, 2000) in the Eocene. This process was responsible firstly to open the graben and secondly to store the sediment, due to erosion post-uplifting.

The results of inversion, synthesized in Figure 13, also suggests a rapid subsidence in the rifting phase resulting in a uniform sediment storing as we can see in layer A. Post-rifting sediment storing, represented by layer B, occurred in the after-Miocene as a slower process, which results in thinner sediment layers with density lower than that found in layer A.

CONCLUSIONS

We performed a regional-residual separation on an integrated gravity map, through a first-order polynomial fitting, after which we extracted three free-air anomaly profiles across the main axis of a negative 23 mGal amplitude anomaly from the residual map. This anomaly is centered at 48ºW and 35ºS on the South Atlantic Ocean. We then estimated density distributions using a constrained linear gravity inversion methodology.

Inversion results suggest that the thickness in the deepest part of the basin is at least 3.0 km where the ocean bathymetry is 4,800 m. At this bathymetric depth we would expect to find oceanic crust.

We proposed a mechanism to a graben formation in SE Rio Grande Cone, based on an integrated interpretation of the inversion results added to geological and other geophysical constraints at the adjacent continental margin. It is important to notice that the anomaly appears to be situated between two lineaments where crustal shearing may have taken place, thus generating a possible stress mechanism that was responsible for the formation of this sedimentary basin.

ACKNOWLEDGMENTS

We thank FAPESP for the financial support (Process number: 98/00107-8). The first author is specially thankful to the Institute of Astronomy, Geophysics and Atmospheric Sciences of the University of São Paulo, for all the computational, material and personal support during the time this work was carried out.We also thank Valéria Cristina F. Barbosa for her valuable comments, corrections and suggestions.

Recebido em 19 maio, 2006 / Aceito em 29 setembro, 2006

Received on May 19, 2006 / Accepted on September 29, 2006

NOTES ABOUT THE AUTHORS

Emilson Pereira Leite. Collaborator Researcher at the DGRN/IG-Unicamp. He received his Master's (2000) and Ph.D. (2005) degrees in Geophysics both from IAG/USP. His current research interests are in the area of spatial modeling and integration of geophysical and remotely sensed data and inversion methods in Geophysics.

Naomi Ussami. Associated Professor at the IAG/USP. She received her Ph.D. degree in Geophysics from Durham University, England (1986) and she did her post-doctorate at Cornell University (1995). Her current areas of research are Tectonophysics and Potential Methods in Geophysics.

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Publication Dates

• Publication in this collection
  11 Sept 2007
• Date of issue
  Sept 2006

History

• Accepted
  29 Sept 2006
• Received
  19 May 2006