Frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments

Abstract

Analyses of synthetic frequency-domain acoustic waveform data provide new insights into the design and imaging capability of crosshole surveys. The full complex Fourier spectral data offer significantly more information than other data representations such as the amplitude, phase, or Hartley spectrum. Extensive eigenvalue analyses are used for further inspection of the information content offered by the seismic data. The goodness of different experimental configurations is investigated by varying the choice of (1) the frequencies, (2) the source and receiver spacings along the boreholes, and (3) the borehole separation. With only a few carefully chosen frequencies, a similar amount of information can be extracted from the seismic data as can be extracted with a much larger suite of equally spaced frequencies. Optimized data sets should include at least one very low frequencycomponent. The remaining frequencies should be chosen fromthe upper end of the spectrum available. This strategy proved to be applicable to a simple homogeneous and a very complex velocity model. Further tests are required, but it appears on the available evidence to be model independent. Source and receiver spacings also have an effect on the goodness of an experimental setup, but there are only minor benefits to denser sampling when the increment is much smaller than the shortest wavelength included in a data set. If the borehole separation becomes unfavorably large, the information content of the data is degraded, even when many frequencies and small source and receiver spacings are considered. The findings are based on eigenvalue analyses using the true velocity models. Because under realistic conditions the true model is not known, it is shown that the optimized data sets are sufficiently robust to allow the iterative inversion schemes to converge to the global minimum. This is demonstrated by means of tomographic inversions of several optimized data sets.