1-D seismic inversion of dual wavefield data: Part I, Nonuniqueness and stability

Abstract

The inversion problem for determining seismic impedance is nonunique and nonstable because of limited recording aperture, data bandwidth, and data noise. For large reflection angles, small errors in the reflection coefficients give rise to arbitrarily large errors in the seismic impedance estimates. Spatial resolution of the seismic impedance response is controlled by the dominant wavelength corresponding to the source time wavelet; aperture limitations control the resolution of material impedance and interval velocity. Analysis of a linearization‐approximation approach shows that this method degenerates into a single‐parameter estimator for material impedance when using only small‐offset data and for velocity when using only far‐offset data. A nonlocal inversion method is introduced to estimate the material impedance and interval velocity by exploring interval velocity space and computing an associated variance estimate surface. Using this method, the resolution of the material impedance and compressional and shear interval velocities is shown to be poor in the elastic case because of a “valley” feature in the variance estimate surface; in the acoustic problem, resolution of the material impedance and interval velocity is excellent.