ESTIMATION OF THE QUALITY FACTOR (Q) WITH TOMOGRAPHY USING THE COMPLEX EIKONAL EQUATION.

Abstract:

The propagation of seismic wave through viscoelastic media is affected by the attenuation that is caused by the quality factor Q, resulting significant loss of signal strength and bandwidth. Gas trapped in sediment is a example of these media. Seismic images of geological structures underneath shallow gas often suffer from resolution degradation and effect of amplitude dimming, making their identification and interpretation difficult. This affects the ability to accurately predict reservoir properties. Thus, there is a need to compensate the attenuation due to Q, to be estimated using tomography seismic.

This work takes place in a viscoelastic medium in the frequency domain, where is incorporated the attenuation to replace the elastic real parameters by parameters visco-elastic complex frequency dependent, consequently the equations must work complex and thus solution should be sought in the complex space. Complex eikonal equation is obtained from the equation of motion in a viscoelastic medium in the frequency domain.

The objective is to apply a tomography method to estimate a model of complex velocity and Q model to achieve an improvement in seismic imaging in areas where there are strong attenuation factors or fractured media.

To achieve calculating Q, first complex eikonal equation is solved in a medium viscoelastic using ray tracing. The resulting travel time is complex; its real part describes the wave propagation and its imaginary part describes the effects of attenuation. A process of tomography is then performed, the initial models of complex velocity and Q are determined; the models are smoothly inhomogeneous, with a constant gradient of the square of slowness. For such models, an exact solution of the complex eikonal equation can be found analytically by using complex ray tracing. given the initial complex velocity models and Q, calculate theoretical travel times and and finally making the inversion using the Gauss-Newton method, fit the initial velocity model and Q to get the difference between the observed data and theoretical data is minimal.

The codes for the initial models of complex velocity and Q and codes of inversion develop in Python.

Keywords: Viscoelastic, complex eikonal equation, ray tracing, quality factor, tomography.