Commercialization of atom interferometers for borehole gravity gradiometry. Quarterly report, January--March 1993

Abstract

Naturally, as higher resolution and/or range is specified the reconstruction accuracy deteriorates. With too fine a resolution and/or at to great a range, the reconstructed density acquires sufficiently large error as to be meaningless. For a specified instrument accuracy we thereby determined the range and resolution limits of our instrument. Not surprisingly, as the instrumental accuracy improves, greater range and/or resolution is fostered.In a given ring surrounding a single borehole, by using data from that hole alone, one can determine only the lowest Fourier coefficients of its azimuthal mass distribution. If a single mass anomaly is localized somewhere on that ring, then its range, bearing, elevation and mass can be determined. However, an ambiguity remains as to whether it is a positive mass in the specified direction or a negative one in the antipodal direction. With ideal instruments and correlated measurements taken from two adjacent holes it is possible to have very high azimuthal resolution. However, minuscule instrumental error quickly reduces this enhancement to essentially a determination of no more than information regarding the second Fourier component of the azimuthal resolution. Thus with data from two holes, two independent localized mass anomalies can be located. Presumably, the use of correlatedmore » data from N holes can, in turn locate N localized mass anomalies, although a direct calculation to prove this conjecture was beyond the scope of the current project and computer power. By limiting the range and number of points considered for the one hole problem, the accuracy and resolution of the one and two hole solutions was found comparable with that of the two hole solution, but with the latter exhibiting twice the azimuthal accuracy w.r.t the former. Depth and range resolution deteriorate with increasing range from the hole, and simultaneously with increasing instrumental error.« less