Читать книгу Muography - Группа авторов - Страница 36

This chapter introduces two mathematical methods to reconstruct three‐dimensional density images from multi‐directional muographic images. One method is a linear inversion, while the other is a filtered back projection. Linear joint inversion has been studied in recent years to effectively incorporate both gravity and muon flux, which are density‐sensitive observables, as well as other a priori information. Since it can be also applied to multi‐directional muography, the basic theory of this method is described. The filtered back projection method is widely common in the medical field; however, intensity, angle of the beam, and number of detectors are considerably different in observation of large structures such as volcanoes. In order to resolve these differences and to make filtered back projection applicable to volcanic observations, we have introduced an improved geometric approximation and a method to estimate the error due to the statistics of muons. We also evaluate the performance of these two methods with a forward simulation and describe future research avenues.