Oil giant BP has announced a big rise in third-quarter profits and says it has reached a "turning point" for its oil and gas operations and production.BP reported third-quarter profits of $5.14bn (£3.2bn), a near tripling of the $1.85bn replacement cost profit it made in the same period a year ago.Chief executive Bob Dudley said operations were "regaining momentum" and the firm had "greater confidence".BP's profits and reputation were hit by last year's Gulf of Mexico oil spill.The firm is also increasing its asset selling programme from $30bn to $45bn.It had decided to sell non-core assets in order to pay for the clean-up operation in the Gulf of Mexico and to compensate victims.'Firm foundations'BP's profits were helped by higher oil prices, with Brent crude currently trading at $110 a barrel, compared with $84 a barrel in October 2010.This helped to offset lower production levels.Oil production in the July to September period fell by 12% on the same quarter last year to 3.3m barrels per day, due to the suspension of production in the Gulf.It was only last week that BP won approval to resume drilling in the Gulf of Mexico, 18 months after the Deepwater Horizon disaster.Even allowing for the businesses BP is selling, production fell by 8%, but the company said it expected output to pick up in the fourth quarter."The past year has been unprecedented in its challenges, and BP has responded well," said Mr Dudley."We have laid firm foundations for the future - in safety, in our organisation and in developing new growth opportunities."As our extended turnaround programme moves towards completion we are seeing production return, particularly from Angola, the UK North Sea and the US Gulf of Mexico, where we produce our higher-value barrels."Shares in BP rose 4.5% in morning trading.