Waveform inversion of seismic refraction data and applications to young Pacific crust

• Published in: Geophysical Journal of the Royal Astronomical Society Vol. 82; no. 3; pp. 375 - 414
• Main Authors: Shaw, Peter R., Orcutt, John A.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.09.1985
• ISSN: 0956-540X; 0016-8009; 1365-246X
• DOI: 10.1111/j.1365-246X.1985.tb05143.x

We present a method for constraining the velocity—depth structure in the Earth using seismic refraction waveform data. We test the method with synthetic ‘data’ from known models, and apply it to a set of data collected in 1982 June from the East Pacific Rise at 13°N, from the MAGMA expedition. In this iterative process WKBJ seismograms are computed for a starting model; the difference between these and the observed seismograms is used to update the model subject to physical constraints. An important first step in the inverse scheme is the linearization of the WKBJ seismogram equation, allowing us to compute ‘differential seismograms’, partial derivatives of the synthetic seismogram with respect to specific model parameters. This linearization provides the means for estimating required model perturbations, based on the misfit in the seismograms. The choice of a suitable numerical strategy for computing an updated model is a crucial second step in formulating a working algorithm. Because the data contain noise, synthetic seismograms can only fit the data to this noise level. In this case, infinitely many models fit the data to this tolerance, and some of these estimates are non-physical, involving negative layer thicknesses. A successful strategy must choose from among these possibilities a well-defined, physically reasonable new model. In a commonly-used approach to solving non-linear problems the perturbation to the starting model is minimized while improving the fit to the data. After several iterations the final model, which possesses no special properties, still tends to resemble the starting model. When used with the MAGMA data this technique essentially does not perturb the model at all. A method we find much more satisfactory involves solving for the new model directly while applying physically important constraints. As constraints we require the velocity gradient remain below a fixed value and penalize the ‘roughness’ of the new model. We thus solve for the smoothest model fitting the data to the specified misfit. This method offers substantial advantages when applied to the MAGMA data and enables us to constrain such geologically interesting model features as transition zones. We find a steep velocity gradient in the upper crust with velocities of 6 km s−1 occurring less than 1 km into the crust. Below about 1 km the gradient abruptly decreases, and the crustal material is much more uniform.