Seismic location of tunnels or voids with a cross‐borehole survey is examined with field data and theory. The field data were taken at a site with a 2.2-m high by 2.7-m wide, roughly rectangular cross‐section tunnel, using a newly developed 1 to 5 kHz system employing a P‐wave sparker source. The synthetic records were obtained using a 2.5-D boundary‐valued solution for an explosive point source near a cylindrical void, and the solution was evaluated with the method of steepest descent. The synthetic waveforms compared well to the field data; both showed a maximum reduction of amplitude in the tunnel shadow of 8 dB and a maximum first arrival delay of 0.1 ms. Additional theoretical modeling was used to examine the variations of the received signals with tunnel size and frequency and showed amplitude reduction increased with frequency and tunnel size. Calculations showed that S‐waves scattered from the tunnel are more than 20 dB smaller than the primary P‐wave on hydrophones and more than 12 dB smaller on particle velocity sensors and so could be difficult to see in field data. The close comparison of synthetic waveforms to the field data indicate that the cylindrical model can be used to model data for roughly square cross‐section tunnels or voids, as well as for circular cross‐section tunnels, and thus is useful for data interpretation and survey planning.
Crosshole tomography requires solution of a mixed‐determined inverse problem and addition of a priori information in the form of auxiliary constraints to achieve a stable solution. Composite distribution inversion (CDI) constraints are developed by assuming parameters are drawn from a composite distribution consisting of both normally and uniformly distributed parameters. Nonanomalous parameter estimates are assumed to be Gaussian while anomalous parameters are assumed uniform. The resulting constraints are sensitive to anomaly volume and are an alternative to the usual constraints of minimizing [Formula: see text] solution length or some measure of roughness. Damped least‐squares inversion, which minimizes solution length, distributes anomalous signal through poorly resolved areas to produce in attenuated and smoothed anomalies. Similar regularization methods, such as smoothness or flatness constraints, also degrade small spatial wavelength features and produce diffuse images of distinct anomalies. CDI constraints preserve small spatial wavelength features by encouraging small amplitude anomalies to assume the value of the reference model and by allowing truly anomalous parameter estimates to assume whatever value minimizes prediction error without incurring additional penalty. CDI tomograms are characterized by nearly ideal point‐spread functions, suggesting the possibility of better quantitative parameter estimates than are produced using most existing methods. CDI tomograms of both synthetic and field data are shown to produce less diffuse images with more accurate anomaly amplitude estimates than damped least‐squares methods. The CDI algorithm is potentially applicable to nontomographic inversion problems.
For tomographic investigations of shallow subsurface features of limited lateral extent, a high‐frequency, low‐cost borehole seismic source would be highly desirable, particularly for investigators with limited budgets. We constructed a simple, arc‐discharge seismic source from off‐the‐shelf items. This source consists of a salt water filled bottle containing exposed conductors of a coaxial cable, across which 100 to 300 joules of electrical power were discharged. This source produced a seismic pulse with a dominant frequency in the neighborhood of 1.5 kHz and a half‐power bandwidth in excess of 1 kHz. Repeatability of seismic signatures in a variety of environmental settings was excellent. Sufficient power was generated to observe seismic signals with at least a 35 dB signal‐to‐noise ratio at horizontal borehole separations of 100 m. For a borehole separation of 33.2 m, signals with at least a 35 dB signal‐to‐noise ratio were observed at angular ranges in the vertical plane to 68 degrees. The hydrostatic head limit for this source was determined to be approximately 430 m.
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