Seismic Facies Characterization by Scale Analysis

Over the years, there has been an ongoing struggle to relate well-log and seismic data due to the inherent bandwidth limitation of seismic data, the problem of seismic amplitudes, and the apparent inability to delineate and characterize the transitions that can be linked to and held responsible for major reflection events and their signatures. By shifting focus to a scale invariant sharpness characterization for the reflectors, we develop a method that can capture, categorize, and reconstruct the main features of the reflectors, without being sensitive to the amplitudes. In this approach, sharpness is defined as the fractional degree of differentiability, which refers to the order of the singularity of the transitions. This sharpness determines mainly the signature/waveform of the reflection and can be estimated with the proposed monoscale analysis technique. Contrary to multiscale wavelet analysis the monoscale method is able to find the location and sharpness of the transitions at the fixed scale of the seismic wavelet. The method also captures the local orders of magnitude of the amplitude variations by scale exponents. These scale exponents express the local scale-invariance and texture. Consequently, the exponents contain local information on the type of depositional environment to which the reflector pertains. By applying the monoscale method to both migrated seismic sections and welllog data, we create an image of the earth's local singularity structure. This singularity map facilitates interpretation, facies characterization, and integration of well and seismic data on the level of local texture.