请大家帮忙分析一下句子成分～～多谢！！

As the first same-sex couples began registering for marriage in Australia,one woman.........就逗号前面这个as引导的状语从句，began
是谓语动词，registering是宾语，那么for marriage是什么语？？是修饰宾语的定语？还是和registering一起作句子的宾语？？

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