Wilson M. Figueiró

Modelagem acústica bidimensional usando diferentes parametrizações de campos de velocidades

The algorithm developed, in this work, is based on the finite difference method applied to the acoustic wave equation, assuming that the Earth has an acoustic behavior, that allow us to implement, in a numerical way, a seismic modeling employing regular grids in models representing two-dimensional geological media. Second derivatives with respect to space and time of wave equation are obtained by Taylor series expansion of fourth and second orders, respectively. The models are represented by two different kinds of parameterizations: blocks and trigonometric polynomials. Simulations of the wave propagation phenomenon are accomplished in several models represented by the two mentioned parameterizations, making possible to generate synthetic seismograms to be compared. Seismograms, obtained when the polynomial parameterization is used, show some undesired behaviors such as: production of artificial reflections, weakening of reflection events, suppression of diffractions, and a little alteration in calculated traveltimes and amplitudes. By the other hand, some advantages of the proposed polynomial parameterization are: economy of computer memory space (because a complicated velocity model can be represented by a few quantity of coefficients, it means: the model is not more stored in a file, but it is compressed, or contained, in a mathematical formula or an analytical representation); production of a smooth velocity model (useful to generate a time field to be used in seismic migration, for example, in reverse time migration); the polynomial coefficients are just the parameters of the model to be estimated by an inversion procedure (independently of the degree of geometrical complication of the model and how is varying the seismic velocity on it); realistic models are better represented by trigonometric polynomial than block parameterization; and the ambiguity commonly present in inversion techniques results, is reduced if sufficient data is available. Gibbs effects, present in polynomial representations, is avoided by the finite differences method by choosing conveniently the knots of the mesh or increasing the number of polynomial coefficients.

Time-lapse critical reflection: does it really work in seismic monitoring of low porosity and high effective stress conditions?

We present an evaluation of the time lapse critical reflection method from the point of view of sensitivity and uncertainty analysis. The purpose of this analysis is to establish the link between changes in the p-wave velocity in the reservoir, due to fluid substitution, and the critical distance (XC), a dynamic parameter. Two static parameters of the overburden are considered in the analysis: its thickness and its effective or equivalent P-wave velocity. Stochastic uncertainty analysis by means of Monte Carlo simulations was carried out to determine the sensitivity of XC to velocity contrast between that of the reservoir and the corresponding one to the overburden (incident medium). Results show that the effect of the velocity values in each medium, overburden and reservoir (reflecting medium), on estimates of XC depends on the velocity contrast between the two media. It turns out that the greater the velocity difference between the two media, the greater the effects associated with the reservoir P-wave velocity. On the other hand, the dependence of XC on overburden velocity (Vrms of the incident medium) is just the opposite. From the inversion viewpoint, predicting changes of the reservoir P-wave velocity from changes in critical distance is strongly dependent of the uncertainty in the initial estimate of the reservoir P-wave velocity, followed by degree of importance by the uncertainty in the overburden velocity. Other sources of uncertainty in this analysis turned out to be negligible. Geomechanical effects have not been accounted for in this analysis.

Seismic ray tomography using L1 integral norm

Seismic ray tomography methods are usually associated with substantial computer processing time. The reason for this is that at each step of the iterative inversion process defined by the tomographic method the two-point ray tracing problem must be solved for each source-receiver pair. In order to resolve this, an Euclidean norm (L2 vector norm), commonly used in error functions which are to be minimized in inversion procedures, is substituted by an L1 integral norm, which enables the estimation of model parameters by minimizing the area between observed and calculated traveltime curves that are interpolated (or adjusted) to the data points. Relatively simple mathematical developments and numerical experiments with two-dimensional compressional seismic wave velocity field models showthat L1 integral norm saves an enormous amount of processing time with no significant loss of accuracy. Occasionally, parameters of the model can be better estimated using L1 integral norm than the L2 vector norm that is traditionally utilized in seismic inversion tomography.

Time-lapse seismic modeling assisted by numerical reservoir simulation of water and gas flooding scenarios in oil reservoirs

In this project, we link fluid flow simulation results to time-lapse seismic through rock physics and modeling. Our goal is to examine the main effects of permeability barriers on seismic response using fluid flow simulations to generate pressure and saturation fields. To explore this problem, we have carried out water and gas injection numerical experiments in a simple reservoir model which has vertical and horizontal variations of porosity as well as permeability barriers. In each experiment, we change the barrier permeability values. By using fluid substitution theory, Gassmann and patchy models, and Batzle and Wangs empirical relationship we model the main seismic parameters, such as acoustic impedance and compressional velocity. After that, we generate synthetics seismograms and some contrast sections to compare the seismic images prior and after fluid injection events in subsequent time periods to analyze possible differences in the seismic parameters due to changes in barriers properties. The results show that barriers can increase fluid pore pressure changing the bulk modulus in the regions with barriers. The results also show that water flow does not have significant impact on seismic response when the barrier is present. On the other hand, gas flow and the degree of impermeability of the barrier can help us to understand how the barriers act on the seismic response and thus to reduce uncertainty. Finally, this paper presents a methodology to examine barriers effects on seismic response.

Seismic ray reflection tomography using integral function norm

Summary Seismic ray reflection tomography is usually related to the problem of the high processing time consumption. This occurs because the two-point ray-tracing problem must be solved, for each pair source-receiver, in each step of an iterative inversion process. In order to solve such kind of trouble, the vector norm, commonly used as error function to be minimized in inversion procedures, is substituted by an integral function norm, which allows us to estimate model parameters by means of area minimization between observed and calculated traveltime interpolated or adjusted curves. Relatively simple mathematical developments and a numerical experiment with a seismic velocity field model show that integral function norm permits to save a lot of processing time without an important loss of accuracy. Sometimes, parameters of the model can be better estimated using function norm than the vector norm traditionally used in seismic inversion tomography.

Time Lapse Critical Reflection: Sensitivity And Uncertainty Analysis

We present an evaluation of the time lapse critical reflection method from the point of view of sensitivity and uncertainty analysis. The purpose of this analysis is to establish the link between changes in the p-wave velocity in the reservoir, due to fluid substitution, and the critical offset xc (a dynamic parameter). Two static parameters of the overburden are considered in the analysis: its thickness and its velocity (vRMS). Stochastic uncertainty analysis by means of Monte Carlo simulations was carried out to determine the sensitivity of xc to velocity contrast. Results show that the effect of the velocity values in each medium, overburden and reservoir, on estimates of xc depends on the velocity contrast between the two media. It turns out that the greater the velocity difference between the two media, the greater the effects associated with the reservoir P-wave velocity. On the other hand, the dependence on overburden velocity is just the opposite. From the inversion viewpoint, that is, predicting changes of the reservoir P-wave velocity from changes in critical offset is a strongly dependent of the uncertainty in the initial estimate of the reservoir Pwaver velocity, followed by its degree importance by the uncertainty in the overburden velocity. Other sources of uncertainty in this analysis turned out to be negligible. Geomechanical effects have not been accounted for in this analysis.