Numerical Solution of the Poroviscoelastic Wave Equation on a Staggered Mesh

✍ Scribed by José M Carcione; Hans B Helle

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 136 KB
• Volume: 154
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6321

✦ Synopsis

Computation of the spatial derivatives with non-local differential operators, such as the Fourier pseudospectral method, may cause strong numerical artifacts in the form of noncausal ringing. This situation occurs when regular grids are used. The problem is attacked by using a staggered pseudospectral technique. The nature and the causes of acausal ringing in regular grid methods and the reasons why staggered grid methods eliminate this problem are explained in the papers by Fornberg [7] andÖzdenvar andMcMechan [8]. Thus, the objective here is not to propose a new method, but to develop the algorithm for the poroviscoelastic wave equation [3]. Özdenvar and McMechan [9] developed a pseudospectral staggered-grid algorithm for the poroelastic differential equations expressed in the displacement formulation. Here, the equations are expressed in the velocity-stress formulation, including attenuation mechanisms due to fluid/matrix interactions. As is well known, one of the advantages of using the velocity-stress differential equations is the avoidance of the differentiation of the material properties, which eliminates numerical artifacts and makes the algorithm more stable [11].

The algorithm is illustrated for a physical situation that requires very high accuracy, such as the gas-water contact in a natural gas reservoir, where large contrasts in material properties occur. The staggered-grid solution is noise-free in the dynamic range where regular grids generate artifacts that may have amplitudes similar to those of physical arrivals. 520