Roustam Seif

3D Elastic Wave Modeling Using Modified High-Order Time Stepping Schemes with Improved Stability Conditions

Summary We present two Lax-Wendroff type high-order time stepping schemes and apply them to solving the 3D elastic wave equation. The proposed schemes have the same format as the Taylor series expansion based schemes, only with modified temporal extrapolation coefficients. We demonstrate by both theoretical analysis and numerical examples that the modified schemes significantly improve the stability conditions.

High-Order Rotated Staggered Finite Difference Modeling of 3D Elastic Wave Propagation In General Anisotropic Media

Summary We analyze the dispersion properties and stability conditions of the high-order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high-order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost-effectively.

Joint inversion of time-lapse seismic and production data using VFSA with Local Thermal Regulation and pilot point parameterization

Summary Estimation of reservoir parameters is im portant for prediction and optimization of oil production. Time-lapse seismic data, commonly acquired in mature oil fields to identify profitable bypassed zones, can be used to estimate reservoir parameters by posing the history matching process as a joint inversion problem. Due to the size of the problem and existence of multiple minima (of the error function), only global optimization techniques, such as Very Fast Simulated Annealing (VFSA) have an opportunity to find the global minimum. However, even for the VFSA technique, the computational cost of the forward modeling (particularly, the reservoir simulation) can make the inversion process impractical in real applications if we consider that many inversions are required to estimate the solution uncertainty. To improve the convergence characteristics of the VFSA technique, we have developed a modification of this technique where a regulation of the local temperature associated with the model variables is driven by the local changes of the error function. We call this modification Local Thermal Regulation (LTR) and show that the time (or number of iterations) spent for convergence can be reduced by 25 to 50%, while maintaining the same degree of ergodicity of the conventional VFSA technique.

Partitioned least-squares operator for large-scale geophysical inversion

Least-squares (LS) problems are encountered in many geophysical estimation and data analysis problems where a large number of observations (data) are combined to determine a model (some aspect of the earth structure). Examples of least squares in seismic exploration include several data processing algorithms, theoretically accurate LS migration, inversion for reservoir parameters, and background velocity estimation. A frequently encountered problem is that the volume of data in 3D is so large that the matrices required for the LS solution cannot be stored within the memory of a single computer. A new technique is described for parallel computation of the LS operator that is based on a partitioned-matrix algorithm. The classical LS method for solution of block-Toeplitz systems of normal equation (NE) to the general case of block-Hermitian and non-Toeplitz systems of NE. is generalized. Specifically, a solution of a block-Hermitian system of NE is shown that may be obtained recursively by linearly combining the solutions of lesser order that are related to the forward and backward subsystems of equations. This results in an efficient parallel algorithm in which each partitioned system can be evaluated independently. The application of the algorithm to the problem of 3D plane wave transformation is demonstrated.

Stochastic Inversion for Reservoir Properties Using Time-lapse Seismic and Well Production Data

We present a new method to create stochastic models which honor both time-lapse seismic and well production data. A two-stage inversion workflow is used. The stochastic modeling allows us to estimate the uncertainty in the reservoir model and predict the realizations and production data. We firstly design three experiments which show the advantage of using time-lapse seismic data in the reservoir modeling and prediction. From these experiments, the inversion result using time-lapse data gives a better match to the actual saturation distribution. Finally, we describe and then present possible ways to address the uncertainty of in the required functions (variogram model, the relationship between porosity and permeability) used in our inversion approach.