The California Community Earth Models for Seismic Hazard Assessments Workshop (this https URL, accessed December 16, 2024) was held online on March 4-5, 2024, with more than 200 participants over two days. In this report, we provide a summary of the key points from the presentations and discussions. We highlight three use cases that drive the development of community Earth models, present an inventory of existing community Earth models in California, summarize a few techniques for integrating and merging models, discuss potential connections with the Cascadia Region Earthquake Science Center (CRESCENT), and discuss what "community" means in community Earth models. Appendix B contains the workshop agenda and Appendix C contains a list of participants.

This paper reviews the most commonly used numerical methods for solving the differential equation governing the dynamic response of linear elastic Single-Degree-of-Freedom (SDOF) systems. For more than 80 years since its introduction, the response spectrum has remained the cornerstone of every seismic design code. The second-order differential equation that governs the dynamic response of a linear elastic SDOF system must be solved numerically to generate such response spectra. Although only one or two well-accepted time-discretization methods have been predominantly used by the earthquake engineering community over the past decades, these methods are directly or indirectly related to a broader family of methods for solving Linear Time-Invariant (LTI) systems, which have been extensively applied in other branches of engineering, particularly electrical engineering. It has recently come to my attention that a portion of our community, particularly students, may not be fully familiar with these methods. In this paper, I review these methods and describe their mathematical background, with a focus on the relative displacement of the SDOF system under ground acceleration-an essential quantity for various types of response spectra. I also briefly review some of the numerical methods traditionally used within our community, highlighting their similarities and differences. I evaluate the accuracy of all numerical methods introduced in this paper through several examples with available analytical solutions. This study focuses on time-domain solutions that can be employed for real- or near-real-time response prediction, which is particularly important for applications such as earthquake early warning and post-earthquake assessment. The paper is written to enable readers to implement these methods with minimal effort; however, MATLAB codes for all methods discussed are also provided.