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This research was supported in part by Saudi Aramco. The second author's work was also partially supported by the NSF grant DMS-1016150. We thank Anton Duchkov, Mauricio Sacchi, Jörg Schleicher, Aldo Vesnaver, and four anonymous reviewers for valuable comments and suggestions. We thank Tariq Alkhalifah and Tim Keho for useful discussions. This publication is authorized by the Director, Bureau of Economic Geology, The University of Texas at Austin.