abstract

The time-term method of interpreting seismic refraction data is analyzed to examine inadequacies in the chosen time-term model by relating observational errors to the solution variance. The results obtained from data that has been simulated for various structures are investigated. This is done quantitatively for simple structures and semi-quantitatively for more complex cases. Velocity and topographic variations of the refractor are considered as signals having dominant wavelengths. It is found that the response of the time-term method to these structural variations depends on the relationship of the structural wavelength to the dimensions of the experiment and the critical distance. For all but the simplest structures, the standard error estimates that can be obtained from a time-term solution are likely to be completely inadequate as estimates of the true error. It is demonstrated that if the refractor is anything other than uniform, the effects of a complicated velocity structure may be absorbed into the time terms. Similarly it is argued that in situations in which the refractor is not horizontal, erroneous values for complex velocity coefficients (e.g., gradient, anisotropy, etc.) can be obtained if these coefficients are included in the chosen time-term model. Finally, it is indicated that reduced travel times can be used in a way that removes the “stirring pot” aspect of time-term analysis, and to determine if a data set is suitable for examination by the time-term method.

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