By measuring the acoustic profile of lightning-generated thunder at several locations simultaneously, it is possible to reconstruct the lightning channel geometry. The technique allows a ground-based study of the lightning channel structure inside thunderstorm clouds. The maximum spatial resolution at a range of 5 km is + 50 meters, except for the vertical direction where the error is + 200 meters. The maximum range is 5 - 25 km, determined by atmospheric attenuation losses and the degree to which refraction of sound away from the array is observed. These limits apply only to a single station deployment of microphones - multi-station arrays greatly increase effective range and data statistics. At least three microphones are deployed in an equilateral triangular shaped array 100 meters on a side. The acoustic pressure profile of thunder events is recorded on magnetic tape and the time lags between similar events are calculated through a cross-correlation analysis. These time lags, taken from the microphone data, are then used to calculate the incident wave vector of the plane wave at the microphone array. A model atmosphere is chosen and the incident wave vector is tracked back in time through the atmosphere to its source location. However, interference phenomena due to sources extended in both space and time introduce random, non-stationary effects into the thunder data, we show how to identify these sources of variability in the data. in many cases, we show how to extract this variability from the data to produce more meaningful results, although approximately 60% of the cross-correlations must be disregarded because of the absence of well-defined peaks in the correlograms. By effectively digitizing the lightning source into a "point” source 50 meters in extent, we are usually able to generate 20 to 40 sets of space coordinates that we use to map the lightning channels. Data taken near Tucson, Arizona in August 1970, with photographic support provided by the University of Arizona, is presented in which we match acoustic reconstructions to photographs of the source lightning events.