Surface waves and discontinuities

BOOK

371

REVIEWS

every geophysician will be looking forward to its continuation. LUDMILA

KUBACKOVA

(Bratislava,

CSSR.)

Waues and ~~~co~ti~uitie~. P. Malischewsky. Developments in Solid Earth Geophysics, 16. Elsevier, Amsterdam, 1987, vi f 229 pp, price: Dfl 175.00 (hardback), ISBN 0-44498959-5.

Surface

Of all observable physical phenomena, seismic waves provide by far the best insight into the structure of the Earth’s interior. For shallow investigations that reach not much deeper than the crust, we apply artificial sources to generate these waves. When we are interested in the deeper structure of our planet, or when financial considerations preclude the use of expensive equipment and manpower, we must rely on earthquakes as the most powerful natural sources available to us. In regions of high seismic activity, densely covered with seismic observatories, we may use the arrival times of P waves to invert for the seismic structure of the crust and upper mantle, a technique now known as ‘seismic tomography’. Such regions are rare, however; the oceans and the aseismic platforms especially are regions where such seismic tomography will not work because the few P waves that ever cross here do not provide sufficient resolution. Seismic surface waves do provide resolution in aseismic areas. Whereas seismic body waves arise from a very simple asymptotic solution of the elastic wave equations, surface waves are dispersive and more difficult to analyze and observe. The classical theory of seismic surface waves has been developed for ho~ontally layered media. If we wish to use surface waves to analyze the real Earth, we must know what happens to these waves when they cross heterogeneous regions. This field of research is of a very theoretical nature, using mathematics techniques that do not belong to the standard luggage of the average seismologist. Malichewsky’s book is an attempt to review these mathematical techniques. From the outset, he isolates the problem by placing the heterogene-

in a very simple Earth model (usually a halfspace or a closed waveguide) and by restricting the attention to Love waves in two-dimensional structures so that the differential equations remain scalar. To allow Love waves to exist in the halfspace, the free surface boundary condition is replaced by a finite impedance. The book begins by setting up the basic theory, explores the nature of the the spectrum and investigates the completeness of the Hilbert space of eigenvectors. Chapter 3 investigates the analytical solutions for the Love waves in closed and open waveguides. The heart of the book is formed by Chapter 4, where the scattering of modes at a vertical discontinuity is investigated. Matching the boundary conditions at the discontinuity leads to a system of linear equations that is essentially infinite. Various methods pass in review to solve this system, using perturbation theory, simple truncation or least squares criteria, and are compared. Some other methods from the litterature are discussed. Chapter 5 studies the exact solution for the propagation of a wave in a halfspace with an impedance jump, using the Wiener-Hopf technique. This gives a useful solution for comparison with the approximate methods of the previous chapter, but the physical model on which this is tested is far from realistic and I do not think the technique will ever be used in practical applications. The book is concluded with a brief chapter discussing the application to more realistic Earth models and Rayleigh waves. Normal modes in a spherical Earth are not discussed. The book obviously aims at the theoretical readership. The use of very simple models to illustrate the techniques makes it possible to analyse the solutions in great detail, and acquire some feeling for what happens to surface waves in the real Earth. But the abundance of detailed solutions for simple models makes the book also somewhat confusing to read a times, and this may not appeal to a more experimentally minded seismologist. Personally, I missed a short chapter with a compa~son of the basic principles involved in a concise and abstract notation. On the whole Malichewsky has done a remarkable job in writing this monograph on such a complicated subject. Unfortunately, the same can-

ity

BOOK

372

not be said of the Publisher. not recommend making quality

the common

notes in the margin:

For this book scientific

it is printed

paper that tends to disintegrate

I do

practice

of

on low

when using

only

flaw being

information commendable

GUUST

NOLET (La Jolla. Calif., U.S.A.)

feature 3 discusses

River

Nile.

Rock-types

jacent

Areas.

Greiling

Belt of Northeast Samir

(Editors).

El-Gaby

Africa and Ad-

and Reinhard

Vieweg, Braunschweig,

0. 1988,

the Nile with respect metamorphism, available

The concept

of a Pan-African

thermo-tectonic

early

outcropping

of the

west of the

to lithology,

structure

and

age data outcrops

are

are, in

in age. Schandelmier

and his

quote new Nd model ages to suggest an

to middle

Saharan

west

from those exposed east of

to prove that the western

colleagues

for the ex-

crust

but no radiometric

fact, pre-Pan-African

xiii + 379 pp., price: DM. 136.00 (hardback).

refer-

each chapter. the evidence

of a pre-Pan-African

Nile differ significantly The Pan-African

is the comprehensive

ence list that accompanies istence

explanatory

in one or two of the figures. Another

Chapter

a simple pencil eraser on it.

a lack of sufficient

REVIEWS

craton.

Proterozoic

protolith

in the east

It is to be regretted

that figs. 5

event was introduced by W.Q. Kennedy following his recognition of the widespread distribution of

and 6 in this chapter

radiometric ages of - 600 Ma in the late Proterozoic in Africa. The evidence then available led

captions that reduce their value. Typographical errors are uncommon throughout the volume, so it

him to believe that this event reflected reactivation of much of the continent resulting in the genera-

is surprising

tion of mobile belts. The Damara-Katanga appeared to be an exception to this concept.

The next chapter by Krbner and his co-authors carries the debate about the existence of a pre-

volume current

belt The

under review presents an overview of the status of the Pan-African event in Egypt,

northern Sudan and adjacent areas. It soon becomes clear to the reader that, despite the concerted efforts of earth scientists form several nations, controversy and uncertainties still prevail. This excellent

volume

in twelve chapters

that

presents

different

are arranged

under

views four

have omissions

to find the symbol

Pan-African

basement

into the Eastern

Chapter African Eastern

and

northern Sudan comprises five chapters. The first of these is a first-class overview of the geology, evolution and metallogenesis of the Pan-African in Egypt. The chapter is liberally illustrated with clear figures. The figures throughout the book are, with few exceptions, of extremely high quality, the

of

2 where

it is contended

that

pre-Pan-

gneisses do underlie large areas of the Desert. Krbner and his co-authors con-

crust in parts of the Eastern

great help to the non-specialist reader. The section on the Pan-African of Egypt

Desert

the Eastern Desert. This conclusion differs from the views expressed by El-Gaby and others in

of the Arabian-Nubian geophysics. A short

part of the Pan-African domain into its continental setting and indicates the broad areas covered by the succeeding chapters. This illustration is a

omitted

Egypt. They decide that there is no conclusive proof for the existence of basement of this age in

cede with

editors sets the scene for the more detailed accounts that follow. This chapter contains a particularly useful figure that places the northeastern

for epsilon

from the text in this chapter.

main headings, namely; the Pan-African of Egypt and northern Sudan; ophiolites and the evolution shield; metallogenesis; and introductory chapter by the

from their

that available isotopic data are consistent the incorporation of some old continental Desert.

The apparently conflicting structural data from the Eastern Desert is discussed in Chapter 5 and emphasizes the extreme complexity of this area, which is not an uncommon domains

elsewhere.

The

feature of Pan-African authors

(Greiling

and

others) present a balanced discussion and attempt to draw the facts together into an internally consistent model while recognizing some data (e.g. direction

of nappe

transport)

is still equivocal.

The impressive dyke swarms in eastern Egypt are the subject of Chapter 6. These swarms reflect unequivocal crustal extension, the mafic dykes being feeders to the Dokhan volcanics, whereas the felsic dykes are regarded as feeders to tabular granitoid intrusions. The authors emphasize that