TOMOGRAPHIC INVERSION OF NORMALIZED DATA - DOUBLE-TRACE TOMOGRAPHY ALGORITHMS

Tomography is widely used in geophysics as a technique for imaging geological structures by means of data that are line integrals of physical characteristics. In some transmission measurements, due to various kinds of normalization, the measured data are related to two (the current and the reference) raypaths and can be expressed as a function of differences between line integrals. This is the case, for example, in seismo-acoustic emission measurements, when (since the exact start time is unknown) only the differences between traveltimes (differences between line integrals of the slowness) can be determined. Similarly the use of normalized Fourier amplitudes results in data dependent upon the difference between line integrals of the absorption coefficient (computed along the actual and the reference raypaths). In order to invert these data the ordinary tomography algorithms should be modified. Some generalizations are presented for series expansion tomography methods in order to make them applicable to reconstruction problems in which the input data are differences between two line integrals. The conjugate gradient and the simultaneous iterative reconstruction technique (SIRT) methods were adapted and tested. It is shown that the modified tomography algorithms are stable and sufficiently accurate for practical use. In the reconstruction of noise-free difference data, the conjugate gradient algorithm is found to be faster and more accurate while, in the case of noisy difference data, the modified SIRT algorithm is more stable and insensitive to noise.