Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas‐sand deposit

Abstract

Prestack seismic reflection data contain amplitudes, traveltimes, and moveout information; waveform inversion of such data has the potential to estimate attenuation levels, reflector depths and geometry, and background velocities. However, when inverting reflection data, strong nonlinearities can cause reflectors to be incorrectly imaged and can prevent background velocities from being updated. To successfully recover background velocities, previous authors have resorted to nonlinear, global search inversion techniques.We propose a two-step inversion procedure using local descent methods in which we perform alternate inversions for the reflectors and the background velocities. For our reflector inversion we exploit the efficiency of the back-propagation method when inverting for a large parameter set. For our background velocity inversion we use Newton inverse methods. During the background velocity inversions it is crucial to adaptively depth-stretch the model to preserve the vertical traveltimes. This reduces nonlinearity by largely decoupling the effects of the background velocities and reflectors on the data. Nonlinearity is further reduced by choosing to invert for slownesses and by inverting for a sparse parameter set which is partially defined using geological reflector picks.Applying our approach to shallow seismic data from the North Sea collected over a gas-sand deposit, we demonstrate that the proposed method is able to estimate both the geometry and internal velocity of a significant velocity structure not present in the initial model. Over successive iterations, the use of adaptive depth stretching corrects the pull-down of the base of the gas sand. Vertical background velocity gradients are also resolved. For an insignificant extra cost the acoustic attenuation parameter Q is included in the inversion scheme. The final attenuation tomogram contains realistic values of Q for the expected lithologies and for the effect of partial fluid saturation associated with a shallow bright spot. The attenuation image may also indicate the presence of fracturing.

Effects of Surface Scattering in Waveform Inversion

“…Note that in order to match the relative amplitude of the various seismic phases generated by the strong velocity contrast and the free surface, the true Q model was supplied during the inversion. The importance of an accurate attenuation model in modeling multiples for waveform inversion was pointed out by Hicks and Pratt (2001). …”

“…In controlled source seismology the most popular forward solutions are finite difference frequency domain methods, mostly in a 2D viscoacoustic, isotropic implementation (e.g. Pratt, 1999;Hicks and Pratt, 2001;Operto et al, 2004;Ravaut et al, 2004;Operto et al, 2006;Bleibinhaus et al, 2007;Gao et al, 2007). The free surface is often ignored not only because modeling irregular topography is computationally extremely expensive, but also because modeling of free surface multiples requires extremely accurate background velocity and attenuation information, and also accurate correction factors for the geometric spreading of multiples, if the modeling is in 2D (Hicks and Pratt, 2001).…”

Using a Poroelastic Theory to Reconstruct Subsurface Properties: Numerical Investigation

“…Gauthier et al, 1986;Pratt et al, 1998) or 3D structures (for instance, Ben-Hadj- Ali et al, 2008;Sirgue et al, 2008). Applications to real data are even more recent (Hicks & Pratt, 2001;Operto et al, 2006;Pratt & Shipp, 1999). The elastic case is more challenging, as the coupling between P and S waves leads to ill-conditioned problems.…”

Simulation-enhanced fracture detection: research and demonstration in U.S. basins

“…Shin et al (2001) applied the reciprocity theorem to the virtual sources but they did not use a full matrix, keeping only diagonal elements of the approximate Hessian matrix; in contrast, we use all elements of the matrix and therefore obtain a higher quality result. Hicks and Pratt (2001) proposed a two-step inversion procedure which combined the gradient and Newton methods. For the gradient method they used 95,046 parameters, but only 15 parameters were used for the Newton method; in contrast, we can solve the problem with one step of the Gauss-Newton method with more than 10,000 parameters.…”