ASA 127th Meeting M.I.T. 1994 June 6-10

3aUW19. Time reversal transformation in linear acoustics and application in a cross borehole prospect.

Shoumian Yu

Tian Yu

Depts. of Phys. and Electron., Shandong Univ. Jinan, Shandong 250100, People's Republic of China

Yinbin Liu

Inst. of Tectonics, Univ. of California, Santa Cruz, CA 95064

A time reversal transformation transforms a process into its inverse, and is stated mathematically by the transformation of time t->t'=-t. The velocity potential (Phi)(r,t) and its Fourier transform (phi)(r,(omega)) are transformed into (Phi)'(r,t')=-(phi)(r,-t) and (phi)'(r,(omega))=-(phi)*(r,(omega)), respectively. It is proved that the time reversal of a source is a receiver and vise versa. The signal received by a receiver at r[sub 2] in the field (phi)(r,r[sub 1];(omega)) produced by a source at r[sub 1] is defined by (phi)(r[sub 2],r[sub 1];(omega))=(double contour integral)ds(centered dot)(phi)(r,r,(omega))(cursive beta)(phi)'(r,r[sub 2](omega)), where the surface integral is taken around the receiver. Here, (phi) is proportional to the power absorbed by the receiver. This theory leads to an important assertion that for a reducible transducer, if the frequency spectrum is f((omega)) and the directional factor is D((theta),(cursive phi)) when it is used as a source, then the frequency response and directional factor when it is used as a receiver must be f*((omega)) and D*((theta),(cursive phi)), respectively. The theory is applied to a cross borehole prospect. The radiation pattern produced by a source borehole and that received by a distant receiving borehole are obtained and plotted for comparison. [Work supported by NSFC.]

Standard Committee S2 on Mechanical Vibration and Shock. Working group chairs will present reports of their recent progress on writing and processing various shock and vibration standards. There will be a report on the interface of S2 activities with those of ISO/TC 108 (the Technical Advisory Group for ISO/TC 108 consists of members of S2, S3, and other persons not necessarily members of those committees) including a report on the current activities of ISO/TC 108, and plans for the next meeting (September 1994).SCOPE OF S2: Standards, specifications, methods of measurement and test, and terminology in the fields of mechanical vibration and shock, and condition monitoring and diagnostics of machines, but excluding those aspects which pertain to biological safety, tolerance, and comfort.