Ignoring density in waveform inversion |

Though the method is conceptually appealing, several barriers have prevented waveform inversion from becoming viable for real data: it is only able to recover anomalies that are either very small in magnitude or that have similar spatial wavelengths as the seismic data; it is computationally expensive, especially if based on time-domain modeling; and when the physics of wave-propagation is simplified to reduce cost and complexity, the inversion may not converge to a useful solution. In this report we investigate the last issue.

Early formulations (Tarantola, 1984; Lailly, 1984) describe the method as simultaneous inversions for the source function, the density field, and the bulk modulus field. Woodward (1990) and Luo and Schuster (1991) choose to invert only for a velocity field. Due to the limited geometries of seismic reflection surveys, there is an ambiguity between velocity and density: a velocity anomaly, a density anomaly, or a combination of the two can all create reflections, and near-vertical-incidence waves do not contain much information to distinguish between these cases.

Here we first present a simplified formulation of waveform inversion, based on Tarantola (1984), and show the results of inverting a small synthetic dataset modeled with the same physics--the constant-density acoustic wave equation--as used in the inversion. Then we show results from a velocity-only inversion of a dataset modeled with both velocity and density contrasts.

Ignoring density in waveform inversion |

2007-09-18