Seismic processing and imaging with diffractions

Abstract

Reflected and diffracted waves have different nature and role in the applied seismic. Moreover, diffractions itself can be classified in both real seismic diffractions and hypothetical seismic diffractions. The real seismic diffractions are seismic waves which are scattered on small heterogeneities in the subsurface or diffracted at the edges and tips, and recorded as the diffracted part of the whole wavefield. The hypothetical diffractions are mathematical constructions resulting from Huygens principle which helps to correctly image reflected events. These Huygens diffractions build a kernel of seismic reflection imaging, particularly, time migration applies to hyperbolas. The diffraction response in terms of a true Greens' function of the subsurface is good for depth imaging too. The time-migrated data represent pure reflected data with a higher resolution because real seismic diffracted events are collapsed, triplications unfolded and, thus, do not interfere with reflected events.

I present an approach to build the 'partly' time-migrated data. A partly time-migrated gather represents the energy of a hypothetical diffractor collected from several neighboring common-midpoint (CMP) gathers and spread in a considered output gather. The gather has a hyperbolic moveout and is known as the common scatterpoint (CSP) gather. A key concept of the method to generate CSP gathers is a new parametrization of the double square root (DSR) operator with the common-oset apex time. The stacking of the CMP data with the parametrized DSR operator represents a partial time migration by a direct mapping of summed amplitudes into the common-offset operator apex.

The traveltimes of time-migrated reflections can be expressed in terms of the ray propagation in the vicinity of the central image ray. This allows to establish a multiparameter stacking operator to produce time-migrated stacked sections. The multiparameter stacking operator depends on the model-based kinematic wavefield attributes. Since time-migrated reflections can be obtained by tracing of the image rays down in the subsurface, their kinematic attributes can be used to build smoothed velocity models. Moreover, estimation of kinematic attributes based on the coherence measure is preferable in the time domain due to absence of diffractions and triplications and regularity of the time-migrated gathers.

Although hypothetical diffraction gathers are very preferable to build seismic images, they are not suitable for high-resolution structural imaging. To image objects beyond the classical Rayleigh limit, it is indispensable to use real seismic diffractions. However, the imaging of seismic diffractions is a great challenge in seismic processing because they have weaker amplitudes compared to dominant reected events. Separation of diffracted from reected events is frequently used to enhance images of diffractions, and thus to achieve a super-resolution image. I present a method to effectively separate and image diffracted events in the time domain. The approach comprises two steps: attenuation of reected events by a simultaneous application of the common-reflection surface-based diffraction operator and a diffraction filter followed by a subsequent velocity analysis in both time and depth domain.