Twin Vertical-Seismic-Profile (VSP) Simulation of Crosswell Seismic Tomography

Researchers in crosswell seismic tomography attempt to image interwell velocity fields by using traveltimes of transmitted waves generated by a downhole source and recorded by downhole receivers. These traveltimes are governed by subsurface velocities along their travel paths, which in turn provide the basis for adjusting an initial-velocity model such that the traveltimes predicted by ray tracing best-match observed traveltimes. Twin-vertical-seismic-profile simulation of crosswell (TVSC) tomography uses the first-arrival timesfrom wavefields generated by a number of surface sources positioned inline with two receiver wells. The differential traveltimes between receiver wells are used to estimate interwell velocities. As a result, TVSC tomography is theoretically independent of subsurface velocities outside the interwell space, although the vertical seismic profile (VSP) wavefields traveled through these parts of the subsurface. TVSC tomography is evaluated on synthetic and real data. The velocity model is parameterized by cubic B-splines, and adjustments to the initial-velocity model are obtained by means of a least-squares solution. A model covariance matrix designed to minimize variations in spatial derivatives of the velocity updates is incorporated into the inverse problem. The synthetic examples have differential traveltimes between receiver wells on the order of 70 to 80 ms. Velocities can be recovered from noise-free data having local errors as large as 2 percent and an associated data misfit of [plus or minus] 1 ms. Use of the model covariance matrix illustrates the trade-off between data fit and model reasonableness. Examples having Gaussian random noise as large as plus or minus 6 ms added to the differential traveltimes show local velocity errors as large as 5 percent, 95 percent of the data being predicted to within plus or minus 5 ms. Field data were acquired at Texaco's Borehole Test Site located near Humble, Texas. Wavefields from four offset surface-source locations were recorded by six-element hydrophone arrays (10-ft receiver spacing, 50-ft maximum recording aperture) in two receiver wells over a depth interval of 2,550 to 1,540 ft. Three-component geophone data recorded in a third well over a depth interval of 1,500 to 50 ft provide information on the common shot statics (plus or minus 3 ms) and overall shot reproducibility. VSP data quality is quite variable. Overall signal-to-noise ratio ranges from 15.5 to 4.8 decibels (root-mean-square amplitude). The differential traveltimes (between receiver wells) are roughly 50 to 60 ms. Noise in the first-arrival times produced by tube waves and timing inconsistencies that occurred during data acquisition is on the order of plus or minus 5 ms. TVSC tomography predicts the measured first arrival times to within plus or minus 5 ms. Inversion results obtained assuming low and high noise levels in the data illustrate the trade-off between data fit and model reasonableness. The resulting velocity estimate indicates an overall increase in velocity from 6,800 ft/s at 1,540-ft depth to 7,600 ft/s at 2,550-ft depth, with a sharp increase at 2,100 ft. Surface-source to downhole-receiver traveltime inversion reproduces data to within plus or minus 3 ms, and it is less sensitive to noise than is the TVSC inversion. Velocity models estimated by TVSC and surface tomography inversions are similar.