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 as possible in both frequency and time domains.
The synthetic data set used in this paper provides a benchmark for future testing of modelling, inversion, and imaging algorithms for wide-angle lithospheric imaging.