Simulation of Wave Propagation Using Finite Differences in Oil Exploration

Abstract

This paper presents a numerical solution for the 2D acoustic wave equation, considering heterogeneous media. It has been developed through a software in Fortran 90 that uses a second-order finite difference approximation. This program generates a set of patterns to detect the presence of oil in the subsurface. The algorithm is based on a geological domain where the sources (shots) and receivers are located. Each process takes care of a subset of sources and returns to the primary method patterns and seismograms corresponding to its group of sources. In the end, an image of the resulting seismogram is shown along the analyzed geologic profile. Stability and convergence tests were performed to ensure the reliability of the results. These tests were performed using a geological profile 100,000 m long and 17,400 m deep, divided into strata. For the execution of the software, a cluster of 16 processors was used as a computational platform.

Review: Fractal Geometry in Precipitation

“…where f C is the Coriolis parameter and f x := f x , f y ≡ 1 ρ ∂P ∂x , ∂P ∂y is the acceleration caused by the gradient of the pressure P at the position (x, y) ∈ R 2 for a fluid with density ρ. Under a computational perspective, differential equations can be expressed in terms of finite differences according to a discretization of the time t ≈ nδ for some small-time lapse δ > 0 and n ∈ N [58]. For example, as the u-component of wind is now u(t) ≡ u(nδ) ≡ u n , then…”