Kurt Marfurt's paper compares the accuracy of finite-difference and finite-element methods for solving the scalar and elastic wave equations. It highlights that for homogeneous media, explicit finite-element and finite-difference schemes are comparable for the scalar wave equation and elastic equations with Poisson's ratio less than 0.3. However, finite-elements are superior for Poisson's ratio between 0.3 and 0.45. Implicit time integration schemes like the Newmark method are less accurate than explicit central-difference schemes, especially when time steps exceed the Courant condition. Frequency-domain finite-element solutions using a weighted average of consistent and lumped masses yield the most accurate results and are the most cost-effective for CDP, well log, and interactive modeling. The paper discusses the importance of minimizing numerical errors such as attenuation, polarization errors, anisotropy, phase and group velocity errors, parasitic modes, diffraction, scattering, and reflection/transmission coefficient errors. It also explores the accuracy of numerical solutions for scalar and elastic wave equations, noting that finite-element solutions generally perform better than finite-difference solutions for higher Poisson's ratios. The paper concludes that the frequency-domain finite-element method with a weighted average of consistent and lumped mass matrices provides the most accurate and stable results for a given cost. It also emphasizes the importance of considering computational costs and the need for accurate modeling in heterogeneous media. The paper recommends the use of frequency-domain finite-element methods for their accuracy and efficiency in seismic modeling.Kurt Marfurt's paper compares the accuracy of finite-difference and finite-element methods for solving the scalar and elastic wave equations. It highlights that for homogeneous media, explicit finite-element and finite-difference schemes are comparable for the scalar wave equation and elastic equations with Poisson's ratio less than 0.3. However, finite-elements are superior for Poisson's ratio between 0.3 and 0.45. Implicit time integration schemes like the Newmark method are less accurate than explicit central-difference schemes, especially when time steps exceed the Courant condition. Frequency-domain finite-element solutions using a weighted average of consistent and lumped masses yield the most accurate results and are the most cost-effective for CDP, well log, and interactive modeling. The paper discusses the importance of minimizing numerical errors such as attenuation, polarization errors, anisotropy, phase and group velocity errors, parasitic modes, diffraction, scattering, and reflection/transmission coefficient errors. It also explores the accuracy of numerical solutions for scalar and elastic wave equations, noting that finite-element solutions generally perform better than finite-difference solutions for higher Poisson's ratios. The paper concludes that the frequency-domain finite-element method with a weighted average of consistent and lumped mass matrices provides the most accurate and stable results for a given cost. It also emphasizes the importance of considering computational costs and the need for accurate modeling in heterogeneous media. The paper recommends the use of frequency-domain finite-element methods for their accuracy and efficiency in seismic modeling.