Numerical simulations of wave propagation produce different errors and the most well known is numerical dispersion, which is only valid for homogeneous media. However, there is a lack of error studies for heterogeneous media or even for the canonical case of media that have two constant velocity layers. The error associated with media that have two layers is called an interface error, and it typically converges to zero with a lower order of convergence compared to the theoretical convergence rate of the finite-difference schemes (FDS) for homogeneous media. We evaluated a detailed numerical study of the interface error for three staggered-grid FDS that are commonly used in the simulation of seismic-wave propagation. We determined that a standard staggered-grid scheme (SSGS) (also known as the Virieux scheme), a rotated staggered-grid scheme (RSGS), and a Lebedev scheme (LS) preserve the second order of convergence at horizontal/vertical solid-solid interfaces when the medium parameters have been properly modified, such as by harmonic averaging of finely layered media for the stiffness tensor and arithmetic mean for the density. However, for a fluid-solid interface aligned with the grid line, a second-order convergence can only be achieved by an SSGS. In addition, the presence of a fluid-solid interface reduces the order of convergence for the LS and the RSGS to a first order of convergence. The presence of inclined interfaces makes high-order (second and more) convergence impossible.

Interpretation of seismic responses from subsurface fault zones is hampered by the fact that the geologic structure and property distributions of fault zones can generally not be directly observed. This shortcoming curtails the use of seismic data for characterizing internal structure and properties of fault zones, and it has instead promoted the use of interpretation techniques that tend to simplify actual structural complexity by rendering faults as lines and planes rather than volumes of deformed rock. Facilitating the correlation of rock properties and seismic images of fault zones would enable active use of these images for interpreting fault zones, which in turn would improve our ability to assess the impact of fault zones on subsurface fluid flow. We use a combination of 3D fault zone models, based on empirical data and 2D forward seismic modeling to investigate the link between fault zone properties and seismic response. A comparison of spatial statistics from the geologic models and the seismic images was carried out to study how well seismic images render the modeled geologic features. Our results indicate the feasibility of extracting information about fault zone structure from seismic data by the methods used.