PAPER MM

ACOUSTIC RADIATION PATTERNS FOR BOREHOLE SOURCES

Michael Fehler, Geophysics Group, Oregon State University

Chris Pearson, Los Alamos National Laboratory

ABSTRACT

Amplitudes of S and P waves from commercial borehole acoustic logging tools depend on the angle between the borehole axis and the direction of propagation as well as the distance between source and receiver. Knowledge of the angular dependence, or radiation pattern, is necessary to properly measure the attenuation of waves traveling between two boreholes. In this paper we show that the S-wave amplitude is proportional to

 1/R sinf cosf  exp{-pfR/Q_v}

and the P-wave amplitude is proportional to

1/R (2-cos²f) exp{-pfR/Q_v}

where f is the angle between the propagation direction and wellbore axis, R is the source-receiver distance, f is the signal frequency, and Q and V are the S or P-wave quality factor and velocities, respectively. Experimental work in relatively homogeneous granite suggests that this relationship adequately describes the radiation pattern for both explosive sources and for acoustic transducers placed in fluid filled boreholes.

Using the above functional expressions for the S and P-wave amplitudes we have developed a technique to estimate Q and locate discrete fractures in crystalline rock that compose the Hot Dry Rock Geothermal Reservoir at Fenton Hill, New Mexico.