Electromagnetic reverberation at VHF on wires in uncased water-ﬁlled boreholes I.M. Mason, J.H. Cloete, W. van Brakel and J.E. Hargreaves Guided electromagnetic wave pulses were excited on long, thin conducting wires in water-ﬁlled, uncased boreholes by a VHF mono- static borehole radar. Reverberations were recorded at the excitation point. Spectral warping focused the dispersed echoes in space-time. Echo patterns are correlated with geological and geotechnical struc- tures, e.g. bedding plane intersections. Introduction: There is signiﬁcant interest, in geophysics, in mapping interfaces and faults in strata through which boreholes pass. In this Letter, we report observations of HF-VHF wire-guided waves that were launched onto thin wires in boreholes, reﬂected at geological discontinuities, and recorded at the launch point by a monostatic downhole radar transceiver. The propagation mode observed is related to those described by Sommerfeld [1], by Goubau [2] on lossy and coated metal cylinders, and by Barlow [3] in his studies of a coaxial cable, stripped of its outer sheath. In the classiﬁcation of Schelkunoff [4] the axial ‘wireline wave’ supported by a wire in a borehole is a ‘cylindrical trapped surface wave’. Ellefsen et al. [5] and Nusberger et al. [6] have studied Goubau- style wave generation on tubes in boreholes and dielectric sheathed rods driven into soil. Experimental method: A 32 mm diameter, 1.75 m-long monostatic bore- hole radar transceiver ﬁred a train of 400 V steps at 11 kHz PRF into a broadband (10–125 MHz) dipole. One dipole arm was resistively loaded; the other, formed from a metre-long copper tube, housed the electronics and battery. A duplexer protected the receiver during ﬁring. Echoes, ampliﬁed, were fed to a 250 MS=s 8 bit analogue-to-digital converter (ADC), controlled by a ﬁeld programmable gate array (FPGA). Stacking in the FPGA raised dynamic range to 11–12 bits (70 dB). Traces accumulated in an on-board ﬂash memory were downloaded when the transceiver returned to surface. 200 mm diameter borehole in granite: The monostatic radar was hung on an insulating cord in a 200 mm diameter water-ﬁlled bore- hole, drilled into granite. A 2 mm-thick steel wire, 10 m long, was stretched along the cord, with its lower-most end set 1.8 m above the top of the radar, in order to proximity couple to a wire-guided TM0 cylindrical wave mode. Fig. 1a shows a typical 2 ms-long trace s(t) recorded downhole in a uniform section of the granite host. The trace starts with crosstalk through the duplexer. The borehole behaves as an electromagnetic duct in which group delay depends strongly on frequency. ‘Chirping’ obscures round-trip reﬂections. Fortunately, spectral warping can recompress echoes from targets that are embedded at very different ranges in dispersive ducts. 0 10 20 30 40 echoes dispersed st S () ( ) ﬁ w recompressed s S () ( ) ‹ t W ~375 ns E1 E2 E3 |( )| S W |( )| S w recompressed 0 0.5 1.0 1.5 2.0 time, s m 0 0.5 1.0 1.5 2.0 frequency, MHz spectral warping Fig. 1 Reverberations on isolated 10 m thin wire in 200 mm-diameter, uncased, water-ﬁlled borehole, dispersed by ducting and then recom- pressed, numerically, by spectral warping First described by Booer et al. [7], warping involves the fast Fourier transformation of s(t) into the frequency domain S(o), projecting the spectrum into S(O) space; and inverse transforming to secure s(t). Consider: if H(o, Z) is the transfer function of a length Z of a waveguide and if the signal spectrum Sðo; ZÞ¼ Sðo; 0Þ H ðo; ZÞ ¼ Sðo; 0Þ exp i F 0 þ F 1 o  o p c p þ F 2 o  o p c p  ! 2 2 4 3 5 Z 8 < : 9 = ; Then dispersive recompression can be achieved, for all Z, by substituting  F 1 2F 2 1  ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 þ 4O  F 2 F 1 s  ! for o  o p c p  ! to get H ðO; ZÞ¼ expfiðF 0 þ F 1 OÞZg H(O, Z ) yields a linear phase roll with O, i.e a simple delay proportional to Z. Spectral warping is illustrated in Fig. 1. It reconverted the FM of each echo E1, E2, E3 in s(t) back to a replica of the original amplitude modulated driving pulse in s(t). The group velocity is 54 m=ms near the centre of the 10–35 MHz band. 75 mm diameter borehole in faulted dolomite: The time section in Fig. 2a was recorded in a 75 mm diameter, 300 m-deep, slanting water-ﬁlled borehole as the monostatic radar dropped downhole at 10 m=min on a thin wire rope. Axially guided pulses, travel up the wire at 75 m=ms, reﬂect from impedance discontinuities at faults, washouts, bedding plane intersections, and travel back downwards at 75 m=ms to the transceiver. Some complete a ‘second transit’ between transceiver and geological reﬂector. 60 80 100 120 140 160 180 200 220 240 depth, m borehole fault echoes a 60 80 100 120 140 160 180 200 220 240 0.2 0.4 0.6 0.8 1.8 1.2 1.4 time, s m 60 80 100 120 140 160 180 200 220 240 depth, m diatreme flank echoes b 60 80 100 120 140 160 180 200 220 240 0.2 0.4 0.6 0.8 1.8 1.2 1.4 time, s m depth, m de p th, m Fig. 2 Traces recorded by monostatic borehole radar over 200 m-long section of 75 mm borehole, drilled in dolomite past ﬂank of diatreme Radar suspended a On 2 mm-diameter wire rope b On 2 mm dielectric cord Narrow boreholes launch proportionately more energy into 3-D spreading waves. Normal radar arrivals lie beneath the wire-guided arrivals in Fig. 2a. These can be enhanced, and the wire-guided mode can be extinguished, as we illustrate in Fig. 2b by replacing the thin wire rope with a dielectric cord. Conclusion: When deployed using conducting wireline in a water- ﬁlled borehole, a monostatic radar can excite and detect both the conventional radiation mode (broadside, approximately TM01 sphe- rical wave) and the axial wireline mode (wire-guided TM0 cylindrical wave mode). The latter is a tightly bound slow wave which propagates ELECTRONICS LETTERS 2nd March 2006 Vol. 42 No. 5