An unsynchronized acoustic or radio-frequency (RF) computed tomography (CT) imaging system with matched, but independent, continuous wave (CW) transmitters and receivers configured to radiate acoustic or RF transmissions in a plurality of vector paths through solid geologic material. A computer calculates and displays tomographic images constructed from individual acoustic or RF path signal travel time or attenuation measurements logged from registered locations from the CW transmitters and receivers after their being shuttled amongst a number of different transmitter and receiver perspectives available around said geologic material to generate data necessary for computed tomography. Each of the transmitters and receivers include independent unsynchronized crystal oscillators rated at 10-ppm or better frequency uncertainty to produce and to detect CW radio frequency (RF) transmissions.