oa Non-uniqueness with Refraction Inversion – A Syncline Model Study

Non-uniqueness occurs with the 1D parameterization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of nonuniqueness is the inversion algorithm used to generate the starting model. This study generates tomograms with wavepath eikonal traveltime (WET) tomography from starting models obtained with a smooth velocity gradient, the tau-p algorithm and the generalized reciprocal method (GRM) to traveltime data for a syncline (2D) model.

The seismic velocity at the region of maximum gradient, taken to be refractor interface, was both ambiguous and anomously low for the smooth velocity gradient and the tau-p starting tomograms. These starting models also produced an artefact with a high seismic velocity in the main refractor. The GRM tomograms accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than, as well as the true seismic velocities.

It is concluded that inversion algorithms, which explicitly identify forward and reverse traveltime data, such as those of the GRM, are required to generate useful starting models in the near-surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model, or with a priori information, such as head wave amplitudes.

The determination of vertical velocity functions within individual layers is also subject to non-uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The GRM average vertical velocity provides a more accurate measure of depth estimates, where it can be derived.

Non-uniqueness is a fundamental reality with the inversion of all near-surface seismic refraction data. Unless specific measures are taken to explicitly address non-uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either “correct” or even the most probable.