2 EFFICIENT ALGORITHMS FOR ITERATIVE LINEARIZED INVERSION OF SEISMIC WAVE-FORM DATA

We present two equivalent algorithms for iterative linearized waveform inversion for 3-D Earth structure with respect to an arbitrary 3-D st arting model; one is a matrix formulation, and the second is a wavefie ld formulation. Both algorithms require the computation of accurate sy nthetic seismograms, but neither requires that any particular method b e used to compute the synthetics. The matrix formulation is equivalent to our previously published algorithm (Hara, Tsuboi & Geller 1991), b ut requires less than 10 per cent of the CPU time of the previous algo rithm. The wavefield algorithm is equivalent to that of Tarantola (198 6) and Mora (1987), but appears to be substantially more efficient.