NEW YORK — Consumer and media research firm Scarborough Research is reporting that broadband penetration has increased more than 300 percent since 2002. Broadband is defined as U.S. adults who have a DSL or cable modem Internet connection in their household. In 2002, 12 percent of U.S. adults had a broadband connection in their household. Now, almost half (49 percent) have broadband ­ an increase of more than 300 percent, bringing broadband penetration to a mainstream level. San Francisco is the top local U.S. market for broadband penetration, according to Scarborough. Other top broadband markets include Boston and San Diego. In these cities, 61 percent of adults have a broadband connection in their household. Broadband subscribers are more likely than other Internet users to be engaged with Internet content. They are 30 percent more likely than total Internet users to have downloaded podcasts during the past month, 29 percent more likely to have downloaded/watched TV programs and 27 percent more likely to have downloaded/listened to other audio clips during this timeframe.