Full-wavefield seismic inversion ͑FWI͒ estimates a subsurface elastic model by iteratively minimizing the difference between observed and simulated data. This process is extremely computationally intensive, with a cost comparable to at least hundreds of prestack reverse-time depth migrations. When FWI is applied using explicit time-domain or frequency-domain iterative-solver-based methods, the seismic simulations are performed for each seismic-source configuration individually. Therefore, the cost of FWI is proportional to the number of sources. We have found that the cost of FWI for fixed-spread data can be significantly reduced by applying it to data formed by encoding and summing data from individual sources. The encoding step forms a single gather from many input source gathers. This gather represents data that would have been acquired from a spatially distributed set of sources operating simultaneously with different source signatures. The computational cost of FWI using encoded simultaneous-source gathers is reduced by a factor roughly equal to the number of sources. Further, this efficiency is gained without significantly reducing the accuracy of the final inverted model. The efficiency gain depends on subsurface complexity and seismic-acquisition parameters. There is potential for even larger improvements of processing speed.

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ŽThe effect of water shear on the stability of infinitesimal perturbations in . the form of side bands to a finite-amplitude gravity wave is investigated both numerically and analytically. The shear is modeled by a piecewiselinear velocity profile. Nonlinear cubic Schrodinger equation for the wavë envelope of a slowly varying wave train is derived. It is shown that depending Ž . on the direction of propagation along or against the shear of the finiteamplitude waves, the effect of shear on the stability is substantially different. In most cases, however, the shear strength increase first enhances, but later suppresses, the instability.

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