THE △- TRANSFORM IN SEISMIC TOMOGRAPHY

Based on Radon transform, the △- transform for seismic travel-time inversion is proposed in this paper. We define the linear relationship of model coordinates (x, z), source position △ and seismic ray slope by an equation x = △ + z. The theoretical equations of forward and inverse △- transforms are given, then therelationship between the △- and Fourier transforms is discussed. It is shown in theory that a unique solution can be derived with continuous △- transform.For an incomplete tomographic image reconstruction in seismology, in order to avoid the artificiality and to increase the resolution so as to improve the image quality, the authors give a detailed discussion about the resolution of reconstructed image. Finaly, the influnce of observational system and filter approach upon the reconstruction is discussed through numerical computation.