This paper demonstrates some results obtained using state-variable models and techniques on problems for which solutions either cannot be or are not easily obtained via more conventional input-output techniques. After a brief introduction to state-variable notions, the following seven problem areas are discussed: modeling seismic source wavelets, simultaneous deconvolution and correction for spherical divergence, simultaneous wavelet estimation and deconvolution, well log processing, design of recursive Wiener filters, Bremmer series decomposition of a seismogram (including suppression of multiples and vertical seismic profiling), and estimating reflection coefficients and traveltimes.

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