In his paper, Fajklewicz discusses the improvement of vertical gravity gradient measurements arising from a very stable tower apparently not affected by wind gust vibration and climatic changes. Further, the lower plate where the gravity meter is resting can be changed in position to avoid possible disturbances from surface and near‐surface variation, and new methods for correcting and interpreting observed gradients over the vertical interval of about 3 m are presented. Some 1000 field stations were observed, including research work and industrial application.
The utility of combining geoid, gravity, and vertical gravity gradient measurements for delineation of causative mass anomalies is explained and compared with spatial and spectral methods for depth estimation. Depth rules for various source geometries are reviewed and new rules developed for geoid, gravity, and vertical gravity‐gradient data. Both spatial and frequency‐domain methods are discussed. Simple ratios of single observations of different data types (e.g., geoid, gravity, or vertical gravity gradient) are shown to provide information comparable to the traditional spatial and frequency analyses of one data type alone.
For some purposes it may be desirable to work with the gravity force g rather than its vertical gradient g′. A simple method has been tested by which measurements of g′ on a plane surface can be integrated to produce values of g anywhere in space above the plane of measurement. The method appears to show promising results.
We study the feasibility of imaging density variations away from boreholes using gravity gradient measurements in a single borehole. The objective is to develop numerical interpretation tools and to understand the utility and limitations of borehole gravity gradiometry in anticipation of the development of such instruments for the exploration and production of minerals, oil, and gas. We develop an analytic solution for directly locating discrete off-hole mass anomalies and apply a generalized inverse approach to image anomalous density distribution. In the analytic approach, we solve for the distance and direction angles to a point source using the multiple components of the gravity gradient tensor from a set of observations in a single borehole; and then apply this approach to the scenarios of prismatic sources. In the generalized inverse approach, we invert multiple gradient tensor components to construct 3D density contrast distributions around the borehole. As few as two independent gravity gradient components in a single borehole can be used to locate and image isolated anomalous density bodies.
SUMMARY
We present a new approach that allows for the inversion of quantities derived from the observed data using non-diagonal data covariance matrices. For example, we can invert approximations of apparent resistivity and phase instead of magnetotelluric impedance using this methodology. Compared to the direct inversion of these derived quantities, the proposed methodology has two advantages: (i) If an inversion algorithm allows for the specification of a full data covariance matrix, users can invert for arbitrary derived quantities by specifying the appropriate covariance matrix instead of having to rely on the inversion code to have implemented this feature. (ii) It is fully compatible with the assumptions of least-squares optimization and thus avoids potential issues with bias when inverting quantities that are nonlinear functions of the original data, We discuss the theory of this approach and show an example using magnetotelluric data. However, the same method can be applied to other types of geophysical data, for example gravity gradient measurements.
Validation of GOCE time-wise gravity field models using GPS-levelling, gravity, vertical deflections and gravity gradient measurements in Hungary
