On ACH, or how reliable is regional teleseismic delay time tomography?

ACH (named after Aki et al., 1976, Bull. Seismol. Soc. Am., 66: 501-524; Aki et al., 1977, J. Geophys. Res., 82: 277-296) is a standard, widely used, method for three-dimensional seismic imaging of the Earth. The fundamental hypothesis which underlies the method is that the time residuals generated outside the given target volume (from the seismic source to the bottom of the modelled zone) are approximately constant across the seismic array. The main purpose of this study is to check this assumption. We computed travel times for a given station and event distribution using a three-dimensional global Earth model taken from seismic tomography. We found that the relative residuals generated outside the target volume are not negligible and that the fundamental hypothesis underlying ACH is thus not verified. These deviations are generated in the lower and/or upper mantle and the corresponding proportions are entirely dependent on the raypaths. The bias in the inverted model is statistically similar to the input model outside the target volume. We thus recommend caution in any interpretations involving ACH-generated models. A secondary, somewhat independent, outcome of this study is that Fermat's principle, used to linearise the inverse problem in ray theory based tomography, seems to be valid without any restrictions (given our input model is representative for the true Earth) for rays with turning points in the lower mantle. For rays with turning points in the upper mantle, the constant raypath approximation is probably not true. This applies to global tomography as well.