This research is to develop theoretical perturbation methods towards inversion of seismograms for 3-D earth structure. Improved realism in theoretical methods is a field which promises to yield major new results on earth structure. An important application will be to the dramatically improved new data sets such as those which the NSF-supported PASSCAL instrumentation will produce. Perturbation methods will be applied to the calculation of functional derivatives for seismic inversion. The ultimate goal is the simultaneous inversion of both travel-time and amplitude for velocity, attenuation and interface parameters. Because this work will provide basic theoretical analysis techniques for a wide range of seismic investigations including those anticipated for determination of earthquake-related crustal structures, it is a contribution to the basic research of the National Earthquake Hazard Reduction Program.