Seismic tomographic mapping of the Earth's interior — Back to basics revisiting the ACH inversion

It is now more than 35 years since our original work on seismic tomography commenced in June 1974 upon Keiiti Aki's arrival at Kjeller near Oslo. It was published by Aki et al. (1977) and has found wide-spread applications in numerous studies of the Earth's interior from crust to core and in addition triggered many theoretical ones as well. In those times, computer technologies were rather crude and this hampered our tomographic research. In particular, we were somewhat unhappy about both our Generalized Inverse (GI) and the Stochastic Inverse (SI) solutions because of the former being too bumpy and the latter involving vertical smoothing. These problems remain in evidence also in recent studies as will be demonstrated in this review work. We start with re-examining the ACH-original work and then introduce Gauss–Markov (GM) filtering offsetting the defects of both the generalized and stochastic inverses. We highlight the relative merits of our novel inversion method by real tests on the original Norsar P-residuals and the corresponding 5 layered lithosphere model using synthetic velocity anomalies. Then we repeated the original inversion experiment adding the GM solution. The outcome was that the original SI solution was useless; GI too bumpy while the GM solution was appealing both computationally and in the context of geotectonic interpretation. We found that alternative inversion procedures like those forwarded by Backus and Gilbert (1968) and by Pijpers and Thompson (1992), the latter for helioseismology, were not applicable. The reason is that our unknowns are relative velocity anomalies within separate model layers and thus violate basic assumptions in the mentioned procedures. We also discuss source and structure parameter separation and the recent ‘double difference’ approach in tomography based on local earthquake data.