INVERSION WITH A GRAIN OF SALT

In conducting a sensitivity analysis of least-squares inverse solutions, confidence limits can be placed on parameter estimates by use of Jackson's edgehog and most-squares methods. These techniques, which evaluate the 'degree of uniqueness' in a least-squares inversion, require only the information computed in a singular value decomposition solution. While the 'edgehog' and 'most squares' techniques are mathematically similar, the 'most squares' estimate is the simpler to compute. Both methods show that the credibility of an inversion depends on both the specified error criterion as well as on the properties of the Jacobian matrix associated with the least-squares solution. The similar performance of these two closely related methods is demonstrated with the traveltime inversion of both synthetic and real vertical seismic profiles. The sensitivity analysis of this inversion problem provides a quantitative measure of solution reliability.