Physical model for the downhole orbital vibrator (DOV) - II. Rotary correlation wavelets and time-lapse seismics (2005)

The downhole orbital vibrator (DOV) acts as a rotating acoustic point force coupled to the borehole fluid. Operated as a Vibroseis source modulated over rotational frequencies 50-350 Hz, the DOV can generate crosswell seismic signals at well separations up to 800 m in oilfield sediments. Source-wavelet stability and crosswell seismic traveltime resolution are estimated from an ensemble of 13 000 wavelets recorded at a crosswell seismic facility with 300 m source-sensor separation. DOV auto-correlation source wavelets Si cross-correlated against the ensemble mean wavelet Smn give correlation coefficients γi=Si★Smn having mean γmn≈ 99.97 per cent and standard deviation γrms≈ 0.03 per cent. S wavelets give observed traveltimes τi with normalized standard deviation Δτrms/τmn≈ 0.03 per cent. This level of seismic monitoring source stability and crosswell traveltime resolution offers considerable promise for accurate, cost-effective time-lapse seismic imaging of active geofluid reservoirs. Application of stable DOV waveform production to time-lapse seismic imaging is, however, affected by the dual-wavelet nature of rotary motion cross-correlations. In general, DOV cross-correlation signals mix time-symmetric (even) wavelets χcc(t) ≅ cos(ω(t)t) ★ cos(ω(t)t) ≅χcc(−t) and time-antisymmetric (odd) wavelets χcs(t) ≅ cos(ω(t)t) ★ sin(ω(t)t) ≅−χcs(−t), where ★ denotes correlation, ω(t) describes the modulation of rotational frequency, and time-reversal t↔−t equates to interchanging clockwise/counter-clockwise (cw/ccw) DOV rotations. Cross-correlating sensor motion along source-sensor axis x with source motion along axis g mixes wavelet symmetries as χg(t) ≅ cos φχcc(t) + sin φχcs(t) where cos φ=g·x and angle φ orients the DOV relative to the source-sensor axis. DOV orientation uncertainty Δφ affects the sensor wavelet apparent traveltime as Δτ≈ 1.3(Δφ/2π)Tmin, Tmin the period of peak modulation frequency. Since source orientation uncertainty can generate apparent traveltime uncertainty as large as 1-2 ms, time-lapse seismics cannot effectively ignore DOV orientation. Traveltime resolution can be improved to order 0.1 ms without knowing DOV orientation if traveltimes are computed using even/odd wavelets composed by summing/differencing cw/ccw wavelets. Prospects for time-lapse resolution improve if observers can orient the DOV. A DOV equipped with a collar of rotation-phase point detectors surrounding the rotating mass permits observer selection of the monitor sensor, hence controlling effective source orientation. DOV orientation can be guided by an on-board biaxial tiltmeter (for borehole tilt δ along an axis making angle φ with DOV sensor orientation, biaxial tilts T1 and T2 fix φ as T1=−cos φtan δ and T2= sin φtan δ). Numerical simulation of full-sensitivity time-lapse reservoir monitoring suggests it is feasible to resolve migrating oil/water substitution volumes of characteristic dimension 20 m with crosswell transmission data over ≈600-800 m offsets, or in backscatter data at offsets ≈100-200 m using a DOV and sensor array operating in a single well.