System Identification for Three-dimensional AE-Tomography with Kalman Filter

Three-dimensional AE-Tomography computes source locations of AE and reconstructs elastic wave velocity distribution simultaneously from arrival times of AE at receivers. Its algorithm is summarized that elastic wave velocity distribution is updated by using estimated travel times with conventional elastic wave velocity tomography technique. The estimated travel time is obtained as a difference between the arrival time and an estimated occurrence time at an estimated source location. The estimated occurrence time and source location are computed by using a source location technique that was proposed by the authors on presumed elastic wave velocity distribution. This fact implies that the reconstruction is executed with less boundary conditions than the conventional elastic wave velocity tomography because the travel times already involve “estimation” prior to the reconstruction. Hence, the accuracy of the reconstruction would be improved if observed travel times are added as its observations. Although the authors had adopted Simultaneous Iterative Reconstruction Technique (SIRT) for the reconstruction, this technique does not consider importance of each observation. Hence, less influence of an observation is consequently exerted on result of reconstruction even if the observation should play important role if large number of observations exist. Thus, in this paper, kalman filter is adopted as the reconstruction technique to properly control the weight of observations for reflecting its importance on the resultant elastic wave velocity distribution. The proposed method is verified by numerical investigations, and its applicability will be discussed.