Summary Full waveform inversion (FWI) is a very important method for estimating the subsurface parameters. While it suffers from extensively computational cost, slow convergence rate, etc, which impede its practical application. In our implementation, to reduce the computational cost, a linear source encoding strategy is used for the gradient calculation. The gradient is a poorly scaled reverse time migration image based on cross-correlation imaging condition. The Hessian matrix can enhance the poorly scaled gradient considerably while it is extremely expensive to calculate the full Hessian directly. The Hessian matrix is thought to carry out source illumination compensation, which is actually equivalent to diagonal pseudo-Hessian. We can also construct the source illumination using phase encoding strategy. Thus, preconditioning the phase encoded gradient using phase encoded diagonal pseudo-Hessian forms phase encoded deconvolution imaging condition. These strategies can reduce the computational cost and improve the convergence rate of FWI. We carried out a numerical experiment with a portion of Marmousi model and analyzed the effectiveness of the proposed strategies.
We apply a sequential inversion scheme combining elastic FWI and Bayesian rock physics inversion to a VSP dataset acquired with accelerometers and collocated DAS fiber at the Carbon Management Canada's Newell County Facility. The goal is to build a baseline model of porosity and lithology parameters to support later monitoring of CO2 storage. The key strategies include an effective source approach to cope with near-surface complications, a modeling strategy to simulate DAS data directly comparable to the field data, and a Gaussian mixture approach to capture the bimodality of rock properties. We perform FWI tests on the accelerometer, DAS, and combined accelerometer-DAS data. While the results can accurately reproduce either type of data, the elastic models from the accelerator data outperform the other two in matching well logs and identifying the target reservoir. We attribute this result to the insignificant advantage of DAS data, in this case, over accelerometer data, which also suffers from single-component measurements and lower signal-to-noise ratios. The porosity and lithology models predicted from the accelerometer elastic models are reasonably accurate at the well location and are geologically meaningful in spatial distribution.
The nonlinearity of the seismic amplitude-variation-with-offset (AVO) response in the presence of large relative changes in acoustic and elastic medium properties is investigated with physical modelling data. A procedure for pre-processing reflection data, acquired using the CREWES-University of Calgary physical modelling facility, is enacted on a reflection from a water/plexiglas boundary. The resulting picked and processed amplitudes are compared with exact solutions of the plane-wave Zoeppritz equations, as well as first, second, and third order RPP approximations. We conclude that in the angle range 0–20°, the third order plane wave approximation is sufficient to capture the nonlinearity of the AVO response to within roughly 1% from a liquid-solid boundary with VP, VS and ρ contrasts of 1485–2745m/s, 0–1380m/s, and 1.00–1.19gm/cc respectively. This is in contrast to the linear Aki-Richards approximation, which is in error by as much as 25% in the same angle range.
Summary Characterizing the near-surface is an important part of solving seismic static problems. It is also a critical step as input for more general iterative inversion methods applied to land seismic data. In the case of converted waves this becomes even more true due to the large magnitudes of the shear-wave statics. In this study, a solution based on the difference in conversion traveltimes between receivers is proposed. This solution may be useful for inverting delay times retrieved by interferometric techniques. Due to the complexity of the partial derivatives of the forward modelling operator for this case we decided against local descent-based methods, adopting instead a simulated annealing inversion method. This is also justified by the complex topography of the objective function. Performing a representative number of iterations of the proposed algorithm successfully retrieves the true parameters of the model. Since traveltime differences were used, the inverted parameters only allowed us to compute changes in the depth of the base of the near-surface rather than its absolute value. This can be fixed through a calibration process given the depth of the low velocity zone for at least at one receiver location.
Forward modelling of any data event in a reflection seismic experiment with the Born series requires the calculation of a large number of terms, if the perturbation is large and spatially extended. Various partial series summations, the De Wolf approximation for instance, can be devised to separately model primary reflections. One such scheme has recently been used to derive direct inverse techniques for reflection seismic data. In this paper we extend this scheme to accommodate media with arbitrary 3-D heterogeneity, and point out that once any partial summation for primary reflections has been completed—however it is done—further arduous calculation for the similarly non-linear forward modelling of multiples can be avoided by using the de-multiple algorithms of inverse scattering. One by-product of these developments is a forward modelling expression for direct transmitted wave data, which may be of use for cross-well geophysical applications. Extension to absorptive media is straightforward.
Frequency-dependent seismic field data anomalies, appearing in association with low-[Formula: see text] targets, have, on occasion, been attributed to the presence of a strong absorptive reflection coefficient. This “absorptive reflectivity” represents a potent, and largely untapped, source of information for determining subsurface target properties. It would most likely be encountered where a predominantly elastic/nonattenuating overburden suddenly is interrupted by a highly attenuative target. Series expansions of absorptive reflection coefficients about small parameter contrasts and incidence angles can expose these anomalies to analysis, either frequency-by-frequency (amplitude variation with frequency [AVF]) or angle-by-angle (amplitude variation with angle of incidence [AVA]). Within this framework, variations in P-wave velocity and [Formula: see text] can be estimated separately through a range of direct formulas, both linear and with nonlinear corrections. The latter come to the fore when a contrast from an incidence medium [Formula: see text] (i.e., acoustic/elastic) to a target medium [Formula: see text] is encountered, in which case the linearized estimate can be in error by as much as 50%. Algorithmically, it is a differencing of the reflection coefficient across frequencies that separates [Formula: see text] variations from variations in other parameters. This holds for both two-parameter (P-wave velocity and [Formula: see text]) problems and five-parameter anelastic problems, and would appear to be a general feature of direct absorptive inversion.
Summary In early September of 2011, CREWES (Consortium for Research in Elastic-Wave Exploration Seismology) collaborated with Husky Energy, Geokinetics, and INOVA, to conduct a seismic experiment designed to study the initiation and recording of very low frequency seismic reflections. The motivation was to collect a dataset that will be useful to test inversion methods. The site chosen was a 4.5km line, near Hussar, Alberta, that passes through 3 wells owned by Husky and near two others, all with good logging suites. Both dynamite and Vibroseis sources were tested along with 5 different receiver types. A specially modified low-frequency vibrator, the INOVA AHV-IV (model 364), was brought to the experiment by INOVA and a more conventional Failing (Y2400) was rented. Both vibrators were programmed with specially designed low-dwell sweeps which spend extra time in the low -frequency range. The receiver used were Vectorseis 3C (MEMS) accelerometers, 10Hz SM-7 (ION-Sensor) 3C geophones, 4.5Hz Sunfull 1C geophones, 10 Hz SM-24 highsensitivity geophones, and Nanometrics Trillium seismometers. The first 3 types were planted densely along the entire line while the last two were only available in limited quantities. A total of 12 P-P and 8 P-S lines were recorded and are presently being processed. Spectral analysis of raw records shows that in large part the various instruments performed as expected. There was significant low frequency energy excited by all four sources with dynamite being the strongest, followed by the INOVA 364 low-dwell, the Failing low-dwell, and the INOVA 364 linear, in order of the strength of low frequency energy. The Vectorseis receivers seem to record strongly down below 1 Hz; however the response is higher than the corresponding geophones. The 10 Hz SM-7 and 4.5 Hz geophones performed well down to their resonant frequencies. After application of the inverse filters for their instrument response, it appears that signal was recovered down to perhaps 1.5 Hz. We qualify these remarks with a cautionary note as these measurements are based on raw data not final processed images.
The purpose of this paper is to present approximate expressions for the AVO and amplitude-variation-with-frequency (i.e., AVF) behaviour of reflections from an anelastic target. We extend previous work to allow for P, S, and converted wave data to be analysed. By altering the Zoeppritz equations to incorporate a nearly constant Q model in the target medium, and linearizing, approximate forms for PP, PS and SS reflection coefficients with corrections for anelasticity are derived. Inversion of these data is straightforward, with the PS and SS modes preferentially useful for computing QS, and the PP mode preferentially useful for computing QP. We find that reciprocal QP and QS are proportional to the reflection coefficients’ frequency rate of change.
Full-waveform inversion (FWI) methods can produce high-resolution images of the physical properties of the subsurface. FWI has become a powerful tool for time-lapse or 4D seismic inversion, with applications in the monitoring of reservoir changes with injection and production, and potentially long-term storage of carbon. Current time-lapse FWI strategies include the parallel strategy (PRS), the sequential strategy, the double-difference strategy (DDS), the common-model strategy (CMS), and the central-difference strategy (CDS). PRS time-lapse inversion is affected by convergence differences between the baseline and monitoring inversions, as well as nonrepeatable noise and nonrepeatable acquisition geometries between surveys. The other strategies are largely efforts to fix the sensitivities of PRS, but robust solutions are still sought. We hypothesize that several problems in time-lapse FWI arise from the independence of step lengths during updating. This is supported by synthetic data tests, which indicate that stepsize sharing reduces artifacts caused by the variability in PRS convergence. Two strategies, which we refer to as stepsize-sharing PRS (SSPRS) and stepsize-sharing CMS, are then designed to address these remaining issues. In this paper, we have tested our methods in five scenarios, including noise-free data, nonrepeated noises, nonrepeatable source positions, biased starting models, and a combination of the latter three. The comparisons between the SSPRS and other strategies indicate that the SSPRS can adapt to all tested scenarios well. Especially, except for the DDS which is extremely sensitive to the nonrepeatable source positions, only the SSPRS can provide meaningful results in the latter two scenarios when compared with others. Furthermore, given that SSPRS through its sharing incurs half of the time cost of seeking stepsizes compared with the PRS and DDS, the total computational cost of SSPRS is less than half of that of the CMS and CDS.
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