### 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.