We study the problem of Cross-lingual Event Argument Extraction (CEAE). The task aims to predict argument roles of entity mentions for events in text, whose language is different from the language that a predictive model has been trained on. Previous work on CEAE has shown the cross-lingual benefits of universal dependency trees in capturing shared syntactic structures of sentences across languages. In particular, this work exploits the existence of the syntactic connections between the words in the dependency trees as the anchor knowledge to transfer the representation learning across languages for CEAE models (i.e., via graph convolutional neural networks -- GCNs). In this paper, we introduce two novel sources of language-independent information for CEAE models based on the semantic similarity and the universal dependency relations of the word pairs in different languages. We propose to use the two sources of information to produce shared sentence structures to bridge the gap between languages and improve the cross-lingual performance of the CEAE models. Extensive experiments are conducted with Arabic, Chinese, and English to demonstrate the effectiveness of the proposed method for CEAE.