Lower crustal reflectivity from waveform inversion

Deep seismic reflection profiles show that the lower part of the continental crust often contains many strong subhorizontal reflections. Based on forward modelling, these reflections are interpreted as a sequence of alternating high- and low-velocity layers. A waveform inversion provides an optimum model by minimizing the misfit between observed data and synthetic seismograms. However, it is very difficult to invert for the whole data set, partly because of the large computation time needed in modelling and partly because the high amplitude reflected energy in the upper crust dominates the misfit function.

To overcome these difficulties we propose a three-step strategy for inverting the deeper part of seismic reflection data over a narrow aperture in which the velocity structure can be assumed to be 1-D. First, both source wavelet and recorded wavefield are propagated in the plane-wave domain downwards to a particular depth for a given 1-D medium. Because the source-receiver distances are short for deep reflections it is assumed that these reflections are at normal incidence. It is also assumed that the near-surface velocity is known or has been estimated using other inversion schemes. The downward propagation algorithm takes account of nearsurface effects, such as multiple reflections and attenuation. Second, starting from a known background-velocity model, a non-linear iterative waveform inversion is applied to the propagated data set. The method is based on minimizing the difference, sample by sample, between observed and calculated wavefields in a least-squares sense. The forward modelling, which consists of calculating the data from the model, uses a reflectivity method to compute the synthetic seismogram in the plane-wave domain. The model perturbation is calculated with the help of the conjugate gradients method. The non-linear inversion gives the short wavelengths of impedance contrast, which is a function of density and velocity, in the lower crust. Third, an interpretational step is tried in order to recover the medium wavelengths of velocity.

The algorithm is tested on synthetic data and then applied to a part of the WAM data set, south-west of England. A good fit to the real data with the optimum model predicts that the velocity contrast of the layers in the lower crust varies from 0.2 km s⁻¹ to 0.5 km s⁻¹ and the thickness from at least 0.075 km to 1 km.