| Summary: | Reflection seismologists illuminate the subsurface by introducing energy into the ground. These propagating waves encounter heterogeneities in the subsurface material and are partly reflected back up to the surface where they are recorded as seismograms. The seismic energy source in most cases cannot be reliably measured in a laboratory but must be accurately estimated to allow one to extract the physical parameters which characterize the subsurface (such as velocity and density). The source and multiple earth parameters may be simultaneously successfully estimated by inversion.
When the seismogram model is the plane-wave convolutional model derived from the constant density, variable sound velocity acoustic wave equation, perturbations in the seismic data stably determine perturbations in the source and reflectivity (the high-frequency relative fluctuation in the velocity). The stability of this determination improves as the angular range over which the data is defined increases.
A more realistic model for wave propagation in the earth is the plane-wave convolutional model derived from the viscoelastic wave equation. Waveform inversion applied to field data from the Gulf of Mexico successfully estimates the long-wavelength compressional velocity, three elastic parameter reflectivities, and the anisotropic seismic source. The resulting reflectivities match measured well log data and agree with commonly-accepted lithological relationships. These inversion results predict 70% of the total seismic data and 90% of the data in an interval around the gas sand target.
The resolution matrix measures how close inversion-estimated reflectivities are to the true parameters which generated the data and is useful when independent information such as well logs is unavailable. However, computing the resolution matrix from the singular value decomposition of the forward map (the usual technique) is prohibitive for real seismic inverse problems. Instead we approximate the resolution matrix from Lanczos estimates of the eigenvectors of the normal matrix. The resolution matrix indicates that our inversion-estimated source provides well resolved reflectivities in the depth interval of interest.
|
|---|
