Analysis of factors controlling the resolution of P-wave velocity and density in linearized least squares inversion.

摘要

In the conventional processing of band-limited seismic data, the acoustic impedance within the passband and the very low frequency velocities are well resolved. The velocity is poorly resolved between these two zones and a "gap" is recognized. A quantitative description of the resolution as a function of frequency has not been reported. Such a description is provided for P-wave velocity, density and impedance in the context of an acoustic, one-dimensional earth model. Emphasis is placed on the resolution of the low frequencies below the passband.; The data are plane-wave synthetic seismograms. Data are sensitive to either velocity or density perturbations within the passband due to a perturbation of the reflection coefficient. Data are sensitive to velocity perturbations below the passband due to a perturbation in the moveout. Data are insensitive to densities below the passband.; The issue is further addressed as a linearized inverse problem. In addition to the data sensitivity, the a priori model variance and data noise variance are incorporated into the problem by specifying the model and data covariance matrices.; With fixed density, the velocity resolution is improved with increasing aperture, input data quality, and data octave bandwidth. The resolution below the passband is improved with rougher earth model while the resolution within the passband is reduced.; The velocity resolution is reduced by the introduction of density variations. Generally, the amount of this reduction is less significant for low frequencies below the passband but is also depends on how well a particular low frequency velocity perturbation has been resolved. The resolution of the velocity in the passband is improved with increasing correlation between the velocity and density while the resolution below the passband is not affected.; For typical earth models with rms reflection coefficient of 0.02 and typical data with 8 db S/N and 2.4 octaves,the gap for the low frequency velocity can be filled to above 0 db output S/N at about 50{dollar}spcirc{dollar} aperture for white impedance data and the gap can be filled at 31{dollar}spcirc{dollar} for white reflectivity data. The real world situation is likely somewhere in between.