Simultaneously and dependently invert Vs and Vp models for 3 runs at different frequency bands, starting at low frequency band 0-0.05Hz, then moving to 0-0.1Hz and finishing at 0-0.2Hz. A normalized error function is calculated based on forward simulation filtered at 0.2 Hz for all iterative inverted models.
Inversion at frequency band 0-0.05Hz for 5 iterations:
True model |
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Initial model |
Inverted model after 5 iterations |
Inversion at frequency band 0-0.1Hz:
Initial model for the second inversion |
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Inverted model after 1 iterations |
Inverted model after 6 iterations |
The normalized error and step length along the iterations
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Waveform comparison
vx |
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vy |
vz |
Inversion at frequency band 0-0.2Hz:The normalized error and step length along the iterations
Initial model for the third inversion |
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Inverted model after 2 iterations |
Resuming result for synthetic study of a homogeneous model with embedded low-velocity sphere:
The normalized error curve shows the actual errors between observed and simulated data filtered at a uniform frequency bandwidt from 0 - 0.2 Hz according to all iterative models in 3 inversion runs.
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Notice: since there are gaps at the turning points between the frequency bands and the error function does not always decrease along the iterations, connecting the error curves for each individual inversion run would be a better way to present the convergence of the method.
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Waveform comparison for observed data and simulated data from different inversion stages:
vx |
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vy |
vz |
