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An łterath/e method for obtalnlng the nor mai modes of a laterally heterogeneous body [220] has beeo studied. Normal modę ełgenfrequencies and eigen-functions of an Earth wlth laterally variable anełas-tfcity have been investlgated (221); the transient response of juch an Earth to eerthquakes has been determined. Equations of torsional oscillatlons of Earth have been studied (222), as has the motlon of gravłtating bodłeś subject to large Initial hydro-statłc stresses In a lineer approximation. Analysis of the ylbrational behavior of the Earth when two modes occur at neeriy the same frequency and at similar ampłltudes has been dlscussed [223]. Expres-słons for the kinetlc, potential. and gravitatlonal potentlal energles for spheroldal oscillatlons of a spherlcally symmetrlc. self-gravltatlng Earth model have been consldered [224].

The origin of aperiodic slgnals during excitation of free oscillatlons In a nonelastic Earth has been studied [225]; excitatlon of torsional oscillatlons Ina homo-geneous Earth was consldered. An Earth havlng both radial and lateral varlations In seismic properties has been modeled [226] uslng flnite eiements; numerical algorlthms are produced that yield efflclent estima* tions of norvdegenerate eigenfunctlons and eiger.-frequencles of this laterally nonhomogeneous spher-old. The ełgenperlods of torsional o9clllation of the Earth have been lnverted into shear wave velocity, denslty, and Q structures on the constralnts for the mass and moment of Inertla of Earth [227]. Shear modulus and denslty proflles of a layered Earth have been determined [228] by torsional stress and displacement on Its surface at two frequencles. The sheer veloclty structure from free osclllation data for an Earth model [229] wlth vełocity dlscontinu-ities has been obtained. Variations in Q-values for two large eerthquakes from damped terrestrial elgenvlbrations [230] and In period and Q of free oscillatlons due to modę overlap [231] have been consldered. An analogy In the algebraic structure between terrestrial spectra of whole Earth free oscillatlons belonglng to dlfferent Earth models and electron energy levels of some quantum me-chanical systems [232] has been dlscussed.

The coupllng coefflcłent can be represented as J-square; this meesure of the physical coupllng of the normal modes of a vibratlng system can be used for computlng long-period eigenfunctlons of reelistic Earth models [233]. The effect of variations in the angular veloc!ty of the Earth'$ rotation on the ratę of change of the pulsar period [234] has been ana-lyzed. The problem of secular variatlons of the Earth's rotational veiocity has been reviewed [235]. The motlon of the Earth's axis of inertla has been consldered [236]. The inertla! reference axls has an apparent wandering motion wlthin the deformable Earth.

The Earth's polar motion contains a free component called the Chandler wobble [237]. Liouville equa-tions have been used to study Chandler and nearly diurnal eigenfrequencies [238]. The mean wobble power excited by earthquakes is only a tiny fraction of the total power of the Chandler wobble [239]. High frequency longitudinał and transverse waves and the Chandler wobble have been discussed [240].

SEISMIC PROSPECTING

Seismic reflectlon prospecting is slmple echo-sound-ing. Basic principles and methods for geophysical prospecting have been studied [241]. The history of the reflection seismograph exploration industry has been considered; and the reflection method. from Its origin to the present day and into the futurę, has been described [242]. A brief overview of the appli-cation of wave theory in seismic exploration has been presented [243]. Seismic methods have been used to prospect for oil and natural gas deposltes [244]; methods for producing a seismic pulse elther in the sea or in the crust were developed to detect and record returned sounds. Seismic exploration by the reflected wave method has been explained [245], and a technique to study reflection prospecting for oil and gas has been described [246]. Some aspects of the application of blasting cord as an energy source In seismic prospecting [247] have been discussed.

The 222r₀ concentration in ground close to the Earth's surface provides a sensitive signal for recog-nizing subterranean flow of fluids. Such flows can indicate the existence of regions of enriched 222p_n and hence the presence of uranium ore [248]. Mee-surements of the concentration of the radioactive gas radon at shalłow ground depths are belng used [249] In explorations for geothermal resources.

The presence of large accumulations of natural gas hydrates in cooled zones of Earth's crust has been