Laser seismo-acoustic antenna array

Abstract

The determination problem of wide band wave field parameters in continuous mechanical media is considered. The problem is solved by means of the accurate measurements of displacements and strain of the certain number of medium elements together with subsequent numeric development and data processing.The oscillations which are excited by the source of any physical nature in the continuous mechanical medium can be presented as some superposition of relative spatial displacements of medium particles. These displacements cause the variations of pressure or tension in the medium depending on their mechanical properties.The simple problem of the acoustic wave tests in the liquid or gas medium is usually solved by measurements of the temporal pressure variations dp ( t ) at some point x within this medium. In the threedimensional case, the space-time distribution of the scalar pressure field is the function of four variables:where t is time.pressed as follows:The equation of such a medium motion is ex-where: v is the velocity vector of the particle spatial displacements <k (uk = a& / a t : k = 1,&3); p is the scalar pressure; w is the frequency ofthe complex amplitudes of wave field, i = One pressure sensor can measure the intensity of the wave oscillations. For determination of the spatial wave field parameters (the direction to a source of oscillations and its localization), the acoustic array of N sensors has to be used [I]:. p,, = p,,(t), n = 2,3 ,..., N Another situation occurs when the wave field distribution is probed in the elastic continuous medium. The basic equation of motion in such a medium is expressed as [2]: P a'G 1 at2 = h: a'c!,, I ax,ax,,, + a% 1 ax; (2) The left part of this equation includes the temporal derivations of particle displacement vector CA. : C: = C . ( x , t ) , k , m = 1,2,3, whereas the right one represents the combinations of the spatial displacement derivations in some given plain x1 = 0 : K and q are the combinations of Lame's constants, which determine the elastic medium properties. This kind of media motions usually are detected by three-component accelerometers, which measure every component of the acceleration A three-component accelerometer alone, in addi-tion to the wave intensity, is able to determine the direction to the oscillations source. The source localization is defined when using the velocities difference of refining longitudinal and transversal components of the elastic waves (the so called primary and secondary seismic waves). One can see that the amount of information has been increased here in comparison with the above acoustic methods ( I ) of the wave field parameters determination.We resort to the next approach of the elastic wave detection improvement in continuous media. It is based on application of the precise laser interferometers for measurements of the medium strains in the wave field distribution to be studied. This technique deals with the values in the right part of equation (2). which actually relate to the strain tensor Pk., of the tested medium. Th...

Detection of solid Earth excitations by laser seismo-acoustic antenna array

“…The developed antenna array technique [1] implies as well as ability of phase-difference measurements: dΦ kn , k = 1,2,3 , n = 2,…, N-1…”

“…The antenna array containing the number of precise laser interferometers with the spatially distanced measuring arms has been recently introduced for the solid Earth exploration [1,2]. Some new examples of the developed technique application for seismic and acoustic monitoring are presented in this paper.…”

“…Nevertheless in contrast to temporal the spatial parameters are more informative because of their relation with the elastic medium characteristics: the combinations of Lame's constants tightly connect the spatial derivations themselves in the equations mentioned above [1]. For example, the next relation of medium strain and particle displacement velocity can be found from these equations [5]:…”