Brief discussion on the artificial boundary conditions in numerical simulation of seismic wave motion

Researchers in the field of numerical simulation of seismic wave motion have been suffering from the challenge in understanding and studying artificial boundary conditions (ABC), which is mainly attributed to the lack of systematic discussion and effective integration of ABCs which are originated from various wave problems. In order to establish a systematic overall understanding on the essence of ABC and the basic performance of various specific ABCs, we conduct a simple, intuitive and logically clear discussion on those important issues of ABC, including the essence of ABC and its primary methods, the theory of accuracy control, numerical stability. ABC is essentially a collective name of all the computation methods that are used to calculate the motion on an artificial boundary caused by out-going waves. The computational mode of ABC can be intuitively classified into three fundamental branches, i.e., time-space extrapolation, stress equilibrium on an artificial boundary, and regional attenuation. On this basis, we discuss the similarity on the implementation pattern, the theory of accuracy control, and numerical stability for the ABCs in the same branch, as well as those discrepancies among different ABC branches. Consequently, a number of important issues on ABC can be clarified, such as the following viewpoints. Liao’s time-space extrapolation rule is actually the most fundamental principle for the accuracy evaluation of all the extrapolation-type ABCs and stress-type ABCs. The stability problem for Liao’s ABC applied in finite element wave motion simulation is mainly caused by the difficulty embedded in the combination of the boundary’s finite-difference-type formula and the inner-domain finite-element formula. Attenuation-type ABCs provide an observation view angle that is totally different from extrapolation-type ABCs and stress-type ABCs, thus they play an irreplaceable and unique role in artificial boundary problems.