Method and apparatus for logging the characteristics of materials forming the walls of a borehole

A method of displaying acoustic reflection signals obtained from a borehole wherein acoustic energy pulses are transmitted by a transducer assembly located in the borehole and rotated at an offset position from the borehole axis and reflections of such acoustic energy pulses from formations surrounding the borehole are received by said transducer, said reflection signals being amplitude modulated in accordance with the varying oblique angles of incidence of said reflection signals with the borehole wall as the transducer assembly is rotated at said offset position within the borehole, comprising the steps of:

• (a) visually displaying signals representative of the reflections received by said transducer assembly so that amplitude variations in said signals can be contrasted visually, and
• (b) compensating the amplitude modulation of said reflection signals that have oblique angles of incidence with the borehole wall due to the offset of said transducer assembly from the borehole axis so that the entire 360.degree. of the wall of said borehole is delineated visually, said compensation being carried out in accordance with the following steps:
• (i) determining the offset of said transducer,
• (ii) adding said offset to the reflection signals as follows:
• f.sub.1 (k,l)=f(k,l)+1.0
• for k=1, . . . , k;
• l=1, . . . , L,
• (iii) applying a natural log function to the reflection signals f.sub.1 (k,l) from the step (ii) to convert frequency multiplicative noise to low frequency additive noise as follows:
• f.sub.2 (k,l)=Ln[f.sub.1 (k,l)]
• for k=1, . . . , K;
• 1=1, . . . , L,
• (iv) transforming the reflection signals f.sub.2 (k,l) from step (iii) from a spatial domain to a spatial frequency domain by applying a two-dimensional fast Fourier transform, 2DFFT, as follows:
• ##STR3## (V) removing low frequency noise from the reflection signals, F.sub.2 (U,V) from step (iv) by complex multiplication of F.sub.2 (U,V) with a high-pass filter mask H(U,V) as follows:
• F.sub.3 (U,V)=F.sub.2 (U,V).multidot.H(U,V),
• where H(U,V)=exp[-Do/D(U,V)].sup.N with Do being a constant which determines cut of frequency chosen from 0 to 10 depending on frequency and amplitude of the modulation that is compensated, and N being a constant which determines the slope of the filter from the range 1 to 4, and
• D(U,V)=(U.sup.2 +V.sup.2).sup.1/2, with
• U=1, . . . , (K/2+1), and
• V=1, . . . , (L/2+1),
• (vi) transforming the reflection signals F.sub.3 (U,V) from step (v) from a spatial frequency domain to a spatial domain by applying a two-dimensional inverse fast Fourier transform, 2 DIFT, as follows:
• ##STR4## (vii) applying an antilog function to the reflection signals f.sub.3 (k,l) from step (vi) as follows:
• f.sub.4 (k,l)=exp [f.sub.3 (k,l)]
• for k=1, . . . , K;
• 1=1, . . . ,L and
• (viii) subtracting said offset from the reflection signals f.sub.4 (k,l) from step (vii) as follows:
• f.sub.5 (k,l)=f.sub.4 (k,l)-1.0
• for k=1, . . . ,K;
• 1=1, . . . , L.