Volkswagen AG and U.S. officials have reached a framework deal under which the automaker would offer to buy back almost 500,000 diesel cars that used sophisticated software to evade U.S. emission rules, two people briefed on the matter said on Wednesday. The German automaker is expected to tell a federal judge in San Francisco Thursday that it has agreed to offer to buy back up to 500,000 2.0-liter diesel vehicles sold in the United States that exceeded legally allowable emission levels, the people said. That would include versions of the Jetta sedan, the Golf compact and the Audi A3 sold since 2009. The buyback offer does not apply to the bigger, 80,000 3.0-liter diesel vehicles also found to have exceeded U.S. pollution limits, including Audi and Porsche SUV models, the people said. U.S.-listed shares of Volkswagen rose nearly 6 percent to $30.95 following the news. VW in September admitted cheating on emissions tests for 11 million vehicles worldwide since 2009, damaging the automaker's global image. As part of the settlement with U.S. authorities including the Environmental Protection Agency, Volkswagen has also agreed to a compensation fund for owners, a third person briefed on the terms said. The compensation fund is expected to represent more than $1 billion on top of the cost of buying back the vehicles, but it is not clear how much each owner might receive, the person said. Volkswagen may also offer to repair polluting diesel vehicles if U.S. regulators approve the proposed fix, the sources said.