METHOD FOR TOMOGRAPHIC INVERSION BY MATRIX TRANSFORMATION

摘要

METHOD FOR REDUCING INSTABILITY AND INCREASING COMPUTATIONAL EFFICIENCY IN TOMOGRAPHIC INVERSION FOR VELOCITY MODEL BUILDING. A SYSTEM OF TOMOGRAPHIC EQUATIONS IS DEVELOPED FOR A UNIFORM GRID. A NON-UNIFORM PARAMETERIZATION (BLOCK 30) IS FOUND FOR WHICH A LINEAR MAPPING EXISTS BETWEEN THE SPACE OF THE UNIFORM GRID AND THE SPACE OF THE NON-UNIFORM GRID. THE MATRIX THAT RELATES VELOCITY TO THE TOMOGRAPHIC DATA IN THE NONUNIFORM REPRESENTATION IS THEN GIVEN BY THE MATRIX PRODUCT OF THE CORRESPONDING MATRIX IN THE UNIFORM GRID REPRESENTATION AND THE MAPPING MATRIX. INVERSION CAN THEN BE PERFORMED FOR THE NON-UNIFORM PARAMETERIZATION ON A SMALLER, MORE STABLE MATRIX (BLOCK 60).