Potential and limits of double-difference tomographic methods

Double-difference tomographic methods use directly accurate time delays computed between similar signals. Such methods are designed to image very heterogeneous media, such as volcanoes or fault zones. In seismological applications, similar signals are recorded at a given station from earthquakes sharing similar and close-by sources. In seismic exploration experiments, similar signals are often recorded at neighbouring receivers. After a brief presentation of the tomographic algorithm used, a seismological application is summarized. The potential and limits of double-difference tomographic methods are explored using various numerical experiments. They show that two effects are competing in double-difference tomography: (i) the degradation of the stability of the inversion due to the geometrical proximity of the rays used in the differentiation and (ii) the decrease in modelling error, which allows improving the stability of the inversion and using smaller quantities of a priori information when data are sufficiently accurate. The best resolution is obtained for an optimal value of the inter-source or inter-receiver distance. For optimal values of these distances and a priori information, tomography using traveltime differences provides significantly better resolved results than using traveltimes.