INVERSION OF REFLECTION SEISMIC AMPLITUDE DATA FOR INTERFACE GEOMETRY

Reflection seismic tomography using only traveltime data may be unable to resolve the ambiguity caused by trade-off between reflector position and velocity anomaly. The inclusion of amplitude data in the inversion may help to resolve this problem because the amplitudes and traveltimes are sensitive to different features of the model, therefore providing us with more accurate information about underground structures and velocity distribution. The amplitude of a reflected seismic wave is determined partly by the reflection coefficients and partly by the curvature of the reflector. The latter causes the spherical divergence of the seismic rays to be modified at the reflection point (focused or defocused) and can be represented using a simplified analytical expression. We show, using geologically relevant synthetic models, that the information contained in amplitude versus offset data (here excluding traveltime data) suffices to constrain accurately the geometry of an arbitrary 2-D reflector separating constant velocity layers. The most effective inversion method is a subspace gradient algorithm using a model parametrization in which the interface is described as a discrete Fourier series with fixed upper and lower bounds on the wavenumber. Model parameters are allocated to separate subspaces first on the basis of different physical dimensionality. We also found that declaring separate subspaces for those parameters defining short, intermediate and long wavelength components of the interface geometry, based on the magnitude of singular values of the Frechet derivative matrix, is very effective in accelerating convergence and obtaining a more accurate solution. The inversion is robust with respect to data errors and poor initial estimates.