Two efficient algorithms for iterative linearized inversion of seismic waveform data

We present two equivalent algorithms for iterative linearized waveform inversion for 3-D Earth structure with respect to an arbitrary 3-D starting model; one is a matrix formulation, and the second is a wavefield formulation. Both algorithms require the computation of accurate synthetic seismograms, but neither requires that any particular method be used to compute the synthetics. The matrix formulation is equivalent to our previously published algorithm (Hara, Tsuboi & Geller 1991), but requires less than 10 per cent of the CPU time of the previous algorithm. The wavefield algorithm is equivalent to that of Tarantola (1986) and Mora (1987), but appears to be substantially more efficient.