SUMMARY A comprehensive validation of 2‐D, frequency‐domain, acoustic wave‐equation tomography was undertaken in a ‘blind test’, using third‐party, realistic, elastic wave‐equation data. The synthetic 2‐D, wide‐angle seismic data were provided prior to a recent workshop on the methods of controlled source seismology; the true model was not revealed to the authors until after the presentation of our waveform tomography results. The original model was specified on a detailed grid with variable P‐wave velocity, S‐wave velocity, density and viscoelastic Q‐factor structure, designed to simulate a section of continental crust 250 km long and 40 km deep. Synthetic vertical and horizontal component data were available for 51 shot locations (spaced every 5 km), recorded at 2779 receivers (spaced every 90 m), evenly spread along the surface of the model. The data contained energy from 0.2 to 15 Hz. Waveform tomography, a combination of traveltime tomography and 2‐D waveform inversion of the early arrivals of the seismic waveforms, was used to recover crustal P‐velocity structure from the vertical component data, using data from 51 sources, 1390 receivers and frequencies between 0.8 and 7.0 Hz. The waveform tomography result contained apparent structure at wavelength‐scale resolution that was not evident on the traveltime tomography result. The predicted (acoustic) waveforms in the final result matched the original elastic data to a high degree of accuracy. During the workshop, the exact model was revealed; over much of the model the waveform tomography results provided a good correspondence with the true model, from large‐ to intermediate‐(wavelength) scales, with a resolution limit on the order of 1 km. A significant, near‐surface low‐velocity zone, invisible to traveltime methods, was correctly recovered; the results also provided a high‐resolution image of the complex structure of the entire crust, and the depth and nature of the crust–mantle transition. Some inaccuracies were observed near the edges of the images due to the limited ray coverage inherent to the footprint of the survey geometry. Several aspects of the waveform tomography strategy were critical to the success of the acoustic method with realistic, synthetic, viscoelastic data: (i) the accuracy of the starting model from traveltime tomography, (ii) implementation in the frequency domain, (iii) the use of complex‐valued frequencies to effect time damping of the data residuals, (iv) the selection of a suitable subset of data and data frequencies, (v) progressive inversion of low‐ to high‐frequency components of the data, (vi) initial, pre‐inversion matching of the amplitudes between observed and modelled data, and (vii) sufficient preconditioning of both the data and the update images. Combined, these strategies were effectively equivalent to a multiscale approach that mitigated the non‐linearity of the seismic inverse problem. During the inversion we carried out repeated forward modelling to ensure our modelled waveforms matched the observed data as closely...
S U M M A R YWe provide a series of numerical experiments designed to test waveform tomography under (i) a reduction in the number of input data frequency components ('efficient' waveform tomography), (ii) sparse spatial subsampling of the input data and (iii) an increase in the minimum data frequency used. These results extend the waveform tomography results of a companion paper, using the same third-party, 2-D, wide-angle, synthetic viscoelastic seismic data, computed in a crustal geology model 250 km long and 40 km deep, with heterogeneous P-velocity, S-velocity, density and Q-factor structure.Accurate velocity models were obtained using efficient waveform tomography and only four carefully selected frequency components of the input data: 0.8, 1.7, 3.6 and 7.0 Hz. This strategy avoids the spectral redundancy present in 'full' waveform tomography, and yields results that are comparable with those in the companion paper for an 88 per cent decrease in total computational cost. Because we use acoustic waveform tomography, the results further justify the use of the acoustic wave equation in calculating P-wave velocity models from viscoelastic data.The effect of using sparse survey geometries with efficient waveform tomography were investigated for both increased receiver spacing, and increased source spacing. Sampling theory formally requires spatial sampling at maximum interval of one half-wavelength (2.5 km at 0.8 Hz): For data with receivers every 0.9 km (conforming to this criterion), artefacts in the tomographic images were still minimal when the source spacing was as large as 7.6 km (three times the theoretical maximum). Larger source spacings led to an unacceptable degradation of the results.When increasing the starting frequency, image quality was progressively degraded. Acceptable image quality within the central portion of the model was nevertheless achieved using starting frequencies up to 3.0 Hz. At 3.0 Hz the maximum theoretical sample interval is reduced to 0.67 km due to the decreased wavelengths; the available sources were spaced every 5.0 km (more than seven times the theoretical maximum), and receivers were spaced every 0.9 km (1.3 times the theoretical maximum). Higher starting frequencies than 3.0 Hz again led to unacceptable degradation of the results.
Subsalt imaging has been a long-term challenge for the oil and gas industry. The substantial progress made in data acquisition and imaging since the late 1990s has made some subsalt imaging problems tractable, but building earth models that enable imaging under complex salt remains a challenge. Labor-intensive workflows remain industry standard practice. Not only are these costly and time consuming, they have also performed poorly in many areas of economic interest. Various automatic model-building tools have been proposed to overcome these disadvantages. One such tool, full-waveform inversion (FWI), has already revolutionized velocity-model building in areas with shallow gas. Prior to 2006, imaging in these areas had been considered challenging and labor intensive, just as imaging under complex salt remains today. Modeling indicates that low frequencies and wide offsets may be the key to success when building velocity models using FWI. Just how low and how wide that may be required for FWI success depends on the particular problem. At the Atlantis Field in the deepwater Gulf of Mexico we recently acquired wide-offset ocean-bottom-node data with conventional airguns. By taking care during the acquisition, we recorded usable signal down to a lower frequency than previously achieved. We then applied FWI to the resulting data set and used the resulting velocity model, unmodified, to reverse time migrate the seismic data. It produced some of the best subsalt images of the Atlantis reservoir structure ever seen. Furthermore, the FWI velocity model revealed several major interpretation errors in the legacy salt model; thus the FWI result also offered an excellent basis for updating the salt model with the conventional workflow. These results demonstrate that with appropriate seismic data to support it, and with due care taken during processing and inversion, FWI truly offers a paradigm shift in model building and imaging in areas of complex salt.
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