Schemes for seismic mapping of reflectors in the presence of an arbitrary velocity model, dipping and curved reflectors, diffractions, ghosts, surface elevation variations, and multiple reflections are reviewed and reduced to a single formula involving up and downgoing waves. The mapping formula may be implemented without undue complexity by means of difference approximations to the relativistic Schroedinger equation.

A direct (noniterative) method is presented to determine an acoustic layered medium from the seismogram due to a time‐limited plane wave incident from the lower halfspace. It is shown that one side of the autocorrelation of the seismogram due to an impulsive source at depth is the seismogram due to an impulsive source on the surface. This transforms the problem to the acoustic reflections problem as solved by Kunetz. Both the deep source time function and the layering can be determined from a surface seismogram.

An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infinite blunders along with the data will hardly affect the solution to an otherwise well‐posed problem. An example of this great stability is seen when an average is, determined by using the median rather than the arithmetic mean. Algorithms for absolute error minimization are often approximately as costly as least‐squares algorithms; however, unlike least‐squares, they naturally lend themselves to inequality or bounding constraints on models.

Book reviews 217 of the chapters discuss different aspects of this problem. D. Moos presents an interesting case study of VSP in fractured crystalline rock. The importance of both scattering and anelasticity is emphasized. M. Simaan and P. L. Love discuss the synthesis of VSP including the effects of absorption, dispersion and frequency-dependent reflection coefficients. E. Strick in a significant chapter occupying almost a third of the book provides a thorough review of anelasticity and P-wave distortion. In comparing well log sonic data and VSPs it is essential that dispersion and distortion are accounted for properly. In this excellent article, Strick considers the various mathematical models for attenuation and dispersion and compares the predicted waveforms with observations. It might be argued that too much emphasis is placed on analytic models. Mathematical methods and final results are often sensitive to analytic details not necessarily required by the data nor predicted by physics. Perhaps a more general, numerical approach would be preferable and more flexible as available data expand. Nevertheless, this article is to be highly recommended.Three chapters in the book consider synthetic VSP data. The article by Simaan and Love in which the normal recursive transfer model is used connecting up-and downgoing wave in successive layers, has already been mentioned. J. M. Mendel extends this method using the so-called 'state variable' models. The Bremmer series decomposition is used to separate primaries and multiple seismograms. These two chapters are restricted to plane wave seismograms. In the other chapter on modelling, D. Khosla and G . H. F. Gardner use both scale laboratory models and finite difference solutions to model realistic structures. Unfortunately, the book contains no mention of modelling techniques intermediate between plane wave and finite difference methods. The final chapter of the book by E. R. Kanasewich, D. Bingham and C. Gold is outside the main scope of the book as its title suggests: 'Continuous monitoringof rnicrotremors using a digital seismic nrray'. mis book natLlraily suffers fronl the rapid growth of its subject. The main emphasis is on near-offset VSP data while many recent developments have been with far-offset and hole-tohole tomography. Most seismologists will be happy to use library copies of this book rather than buy their own. Nevertheless, much is useful as introductory reading for VSP techniques and the chapter by E. Strick is highly recommended. Scientific Publications, OxJi,rd, I985 274 pp., .~ 242.00The interpretative techniques that are being used in the seismic exploration industry have changed considerably in the past, and continue t o d o so a t present. A major breakthrough occurred around 1970 when Claerbout introduced wavc equation migration with finite difference met.hods, soon to he followed by Kirchhoff summation and a variety of methods,

No abstract