SUMMARY

The correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green’s function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green’s function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2-D examples, our exact R/T approach can be extended to 3-D and various cases with different interface configurations in arbitrarily complex media, incorporating, for example, anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow and so on.

中文翻译：

---

使用界面条件对波动方程求解器进行基准测试：多孔介质的情况

概要

正确执行不同介质之间的连续性条件，对于从地震勘探到全球地震学的应用中使用的任何波动方程求解器的准确性都是至关重要的。理想情况下，我们希望根据解析格林函数对代码进行基准测试。但是，后者很少用于更复杂的媒体。在这里，我们提供了一个通用框架，通过比较平面波模拟与透射/反射（R / T）的系数来自具有精确边界条件（BCs）的平面波分析。我们表明，这对于大范围的入射角都适用，但是需要大量的计算资源来模拟平面波。我们进一步表明，由点源球面波仿真得到的数值格林函数的精度也可用于基准测试。在这种情况下，与平面波模拟相比，数据处理更为复杂，并且仅在临界角以下才显得足够准确。我们的方法适用于任何波动方程求解器，但我们选择了多孔弹性波动方程进行说明，这主要是由于很难对多孔弹性求解器进行基准测试，也由于人们对多孔弹性介质中的成像越来越感兴趣。尽管我们仅使用二维示例，但我们的确切R/ T方法可以扩展到3-D以及在任意复杂介质中具有不同界面配置的各种情况，例如，包括各向异性，粘弹性，双孔隙率，部分饱和度，两相流体，比奥/喷流等。