Early-arrival waveform inversion for near-surface velocity and anisotropic parameters: inversion of synthetic data |

modelbw2
True model. a): velocity model; b):
model.
Figure 5. |
---|

initmodbw
Starting model. a): velocity model; b):
model.
Figure 6. |
---|

invmodvvbw
Inversion results using velocity parametrization, expressed in vertical velocity and
. a): velocity model; b):
model.
Figure 7. |
---|

invmodsebw
Inversion results using logarithmic slowness parametrization, expressed in vertical velocity and
. a): velocity model; b):
model.
Figure 8. |
---|

For velocity parametrization, the gradient for vertical velocity has more terms than the gradient for horizontal velocity. This leads to more updates for vertical velocity than for horizontal velocity and tends to result in the epsilon update having a sign opposite to that of the vertical velocity update. Since this is not always geologically true, such inversion model parametrization is not ideal, at least for gradient-based inversion methods. Inversion using logarithmic slowness parametrization results in reasonable data matching; however, relatively smooth updates in the inversion result do suggest data misfit from ambiguity between changes and vertical velocity changes. This ambiguity can potentially be mitigated by proper model styling.

resdbw
Data residual as a function of iteration number during inversion using different inversion model parametrizations. Continuous: velocity parametrization; dashed: logarithmic slowness parametrization.
Figure 9. |
---|

For comparison, isotropic inversion is also performed on this model. Two types of starting velocity are used: one is the same vertical velocity model as the starting model in joint inversion, and the other is the horizontal velocity model calculated from the vertical velocity and of the starting model used in joint inversion. The inversion results and data misfit are shown in Figures 11 and 12. It is obvious that inversion results are more geologically reasonable starting from the smooth vertical velocity model. This is also supported by data misfit. Comparing results with the true vertical velocity model and the true horizontal velocity model (Figure 10), it is interesting to see that in the better inversion result, the shallow parts mostly agree with the true vertical velocity model, and the deeper parts mostly agree with the true horizontal velocity model.

isomodbw
True velocity model. a): vertical velocity; b): horizontal velocity.
Figure 10. |
---|

isoinvbw
Velocity model from isotropic inversion starting from, a): smooth vertical velocity; b): smooth horizontal velocity.
Figure 11. |
---|

isoresdbw
Data residual as a function of iteration during isotropic inversion using different starting models. Continuous: starting from smooth vertical velocity; dashed: starting from smooth horizontal velocity.
Figure 12. |
---|

Early-arrival waveform inversion for near-surface velocity and anisotropic parameters: inversion of synthetic data |

2012-05-10