Theory and Practice of Geophysical Data Inversion pp 335-360 | Cite as

# Empirical Covariance Functions between Seismic, Density and Gravity Data — an Important Constraint in 3D Gravimetric-Seismic Stochastic Inversion

## Abstract

In gravity field approximation it is possible to describe the gravity field by a stationary stochastic process. This approach is used in gravity field modeling by Least Squares Collocation (LSC). The purpose of this paper is to include seismic and density information within the framework of the LSC approach. This is done by estimating (and later modeling) covariances between the involved quantities.

In this paper, 41 density and sonic logs were used together with gravity information, to obtain the empirical covariance functions between the involved residual quantities. The area of investigation lies in the North Sea, the horizontal dimensions are 3°x6° and the log data span from 200 m to 5000 m in depth. Regional reference models for density, reciprocal seismic velocity and gravity are modeled and subtracted from the data. A reference model relating the density and the reciprocal seismic velocity is also computed. The correlation coefficient between the density and the reciprocal seismic velocity is -0.66.

The results of this investigation show the characteristic correlation lengths, the variances and the correlation coefficients for the involved residual quantities. The peaks in the variation of the characteristic parameters with depth are related to the geology in the area. The data show a strong correlation between the residual densities both horizontally and vertically. The correlation between the residual reciprocal seismic velocities is not as strong as for the residual density distribution, which indicates that this parameter varies much more than the density distribution. The correlation coefficients between the residual density and the residual reciprocal seismic velocity are large, both positive and negative. There is no correlation between the residual gravity and the residual density and between the residual gravity and the residual reciprocal seismic velocity. This may be due to the constructed reference model for gravity. The residual gravity may still contain strong signal generated from depths which are not covered by the log data.

The covariance functions presented in this paper are probably characteristic only for the area of investigation. They contain however ‘large scale’ information about the distribution of the involved physical parameters within the sedimentary bassin and thus perhaps about the bassin evolution (e. g. compaction, tectonics).

## Keywords

Covariance Function Reference Model Gravity Field Gravity Data Seismic Velocity## Preview

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