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ACOUSTIC RADIATIONS FROM LIGHTNING 57 these measurements are in closer agreement, with the exception of those events containing other lower-frequency acoustic sources. There are a number of experiments that could and should be done to evaluate the propagation effects. Using thunder as the acoustic source, several widely separated arrays of microphones could compare signals from the same source at several distances. If carefully executed this experiment could quantify some of the propagation effects. Another approach would be to employ a combination of active and passive experiments such as point-source explosions inside clouds from either balloons or rockets. This experiment provides an additional controllable factor that can yield more precise data; it also involves greater cost and hazard. Acoustic Reconstruction of Lightning Channels In the section on refraction we mentioned the utility of ray-tracing computer programs that could accurately calculate the curved path of an acoustic ray from its source to a receiver; the accuracy is limited to the precision with which we are able to define the atmosphere. An obvious application of thunder measurements is to invert this process; one measures thunder then traces it backward from the point of observation along the appropriate ray to its position at the time of the flash. Few (1970) showed that by performing this reverse-ray propagation for many sources in a thunder record it was possible to reconstruct in three dimensions the lightning channel producing the thunder signal. The sources in this case were defined by dividing the thunder record into short (~ 1/2sec) intervals and associating the acoustics in a given time interval with a source on the channel. Within each time interval the direction of propagation of the acoustic rays are found by cross correlating the signals recorded by an array of microphones. The position of the peak in the cross-correlation fraction gives the difference in time of arrival of the wave fronts at the microphones; from this and the geometry of teh array, one calculates the direction of propagation. At least three noncollinear microphones are required. Close spacing of the microphones produces higher correlations and shorted intervals thus more sources; however, the pointing accuracy of a small array is less than that of a large array. Based on experiences with several array shapes and sizes, 50 m2 has been adopted as the optimum by the Rice University Group (see Few, 1947a). The reconstruction of lightning channels by ray tracing was described by Few (1970) and Nakano (1973). A discussion of the accuracy and problems of the technique is given in Few and Teer (1974) in which acoustically reconstructed channels were found to agree closely with photographs of the channels below the clouds. The point is dramatically made in these comparisons that the visual part of the lightning channel is merely the ''tip of the iceberg." Nakano (1973) reconstructed, with only a few points per channel, 14 events from a single storm. Teer and Few (1974) reconstructed all events during an active period of a thunderstorm cell. MacGorman et al. (1981) similarly performed whole-storm analyses by acoustic channel reconstruction and compared statistics from several different storm systems. Reconstructed lightning channels by ray tracing have been used to support other electric observations of thunderstorms at the Langmuir Laboratory by Weber et al. (1982) and Winn et al. (1978). A second technique for reconstructing lightning channels has been developed that is called thunder ranging. This technique was developed to provide a quick coarse view of channels (within minutes after lightning if necessary) as opposed to the ray-tracing technique, which is slow and time consuming. Thunder ranging requires thunder data from at least three noncollinear microphones separated distances on the order of kilometers. Experience with cross- correlation analysis of thunder signals has shown that the signals become spatially incoherent at separations greater than 100 m owing to differences in perspective and propagation path. However, the envelope of the thunder signals and the gross features such as claps remain coherent for distances on the order of kilometers. As discussed earlier these gross features are produced by the large-scale tortuous sections of the lightning channel. Thunder ranging works as follows: (1) The investigator identifies features in the signals (such as claps) that are common to three thunder signatures on an oscillograph. (2) The time lags between the flash and the arrival of each thunder feature at each measurement point are determined. (3) The ranges to the lightning channel segments producing each thunder feature are computed. (4) The three ranges from the three separated observation points for each thunder feature define three spheres, which should have a unique point in space that is common to all of them. (5) The set of points gives the locations of the channel segments producing the thunder features (see Few, 1974b; Uman et al., 1978). The basic criticism of the thunder-ranging technique is that the selection of thunder features is the subjective judgment of the researcher; for many features the selection is unambiguous; other features, which are close together, may appear separated at one location and merged at another. The program developed by Bohannon (1978) included these uncertainties in the estima