Spectral-Element and Adjoint Methods in Seismology

We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem

COMMUNICATIONS IN COMPUTATIONAL PHYSICS Vol. 3, No. 4, pp. 935-949 Language Change and Social Networks

Abstract. Social networks play an important role in determining the dynamics and outcome of language change. Early empirical studies only examine small-scale local social networks, and focus on the relationship between the individual speakers’ linguistic behaviors and their characteristics in the network. In contrast, computer models can provide an efficient tool to consider large-scale networks with different structures and discuss the long-term effect of individuals ’ learning and interaction on language change. This paper presents an agent-based computer model which simulates language change as a process of innovation diffusion, to address the threshold problem of language change. In the model, the population is implemented as a network of agents with age differences and different learning abilities, and the population is changing, with new agents born periodically to replace old ones. Four typical types of networks and their effect on the diffusion dynamics are examined. When the functional bias is sufficiently high, innovations always diffuse to the whole population in a linear manner in regular and small-world networks, but diffuse quickly in a sharp S-curve in random and scale-free networks. The success rate of diffusion is higher i