From Twitter to Whirlpool, Lockheed Martin and Coca-Cola, companies in all sorts of industries have been beating earnings estimates and soothing concerns of an earnings recession.

The first quarter reporting season is well underway, with about 20 percent of the S&P 500 having reported. From banks like J.P. Morgan Chase to motorcycle maker Harley-Davidson, companies have beat estimates at a pace of slightly more than three-to-one, about in line with a normal quarter. But this quarter was expected to be anything but normal, with companies seeing the first decline in profits in three years.

"I think the tone from earnings this season has been pretty strong across the board. I think there was a lot of pessimism coming into the earnings season, just because investors saw a negative number. They were very concerned about whether we were going to have an earnings recession. What we're experiencing were strong beats and wide spread beats," said Patrick Palfrey, senior equities strategist at Credit Suisse.

As of April 1, earnings for the first quarter were expected to be down about 2% for the S&P 500, according to Refinitiv. But as of Tuesday morning, the surge of earnings beats has narrowed the expected decline to just 1.3% , and some strategists say earnings could even turn out to be positive by the time the last S&P companies report.

"What I do know is the earnings season is corroborating a lot of the success we're seeing, and it's really eliminated concerns around profit recession, concerns about economic slowdown and concerns about trade and China. That all has been removed from the table," said Palfrey.

Stocks traded higher Tuesday, driven by optimism from a slew of solid earnings reports, and the S&P 500 closed at a new all-time high of 2,933. The previous closing high was 2,930, from Sept. 20. The Dow is still about 1% below its closing high.

The stock market has gained heading into the earnings season, and the S&P 500 is up 3.5% for the month of April so far, giving it a 17% gain year-to-date.

"The market maybe knew the recession fears were not as strong as some were making them out to be," said Paul Hickey, co-founder of Bespoke. He said while there has been mixed economic data, weekly jobless claims have held at low levels and last month's retail sales finally showed a solid gain, after mixed reports since December and after the government shutdown in January.

RBC chief U.S. equities strategist told CNBC that the bar was too low for earnings this quarter, with analysts dramatically reducing forecasts.

"What struck me among the very early reports was the earnings beats were pretty strong, but the sales beats pretty weak. I think its tough to gauge the trend," said Lori Calvasina, who appeared on "Squawk on the Street."

"One, companies are defending their margins…. And second, the underlying macro backdrop, the revenue trends. You're not seeing a lot of surprises, but we're also not seeing a lot of reasons we should be concerned we're going off the edge of a cliff. So I agree the bar has been set too low. I don't see the earnings recession coming," she said.

Companies have reported better profits despite the headwinds of tariffs and currency fluctuations. Some are holding down costs or even raising prices, like Whirlpool said it did to counter higher freight and raw material costs.

The pace of earnings beats has also been solid, with profits topping estimates by 5.5%, up from the recent average of 5.4% in the past year, or the longer term 3.4%, according to Refinitiv data.

"I thought people had marked down the year-on-year change too much," said Sam Stovall, CFRA chief investment strategist. "I think the market was cautious heading into the earnings season, and now that earnings are coming out, I'm not surprised they're beating expectations."

Stovall said fears of an earnings recession were clearly overblown, based on the results so far. "It implies we will not have an earnings recession, which is two consecutive quarters of EPS [earnings per share] declines," he said, adding earnings recessions often morph into real recessions. "This may be like 2015 and 2016, where it was a false alarm."

Stovall said he believes the first quarter may be the worst in terms of earnings growth, with second quarter S&P earnings now expected to grow by a flattish, but positive 0.3 percent.

One reason for better earnings is companies are also reviving their brands, like Coca-Cola which sold more water and soft drinks. Coke on Tuesday said it had organic sales growth of 6%, excluding the impact of currency swings and acquisitions.

Social media company Twitter also surprised with better earnings. but it also grew monthly active users by 9 million, bringing its total to 330 million in the first quarter. Analysts had expected a decline in users.

Defense contractor Lockheed Martin saw a 47 percent jump in profits, and it raised its 2019 profit forecast. The world's largest defense contractor, Lockheed also updated its forecast for 2019 financial results, with earnings anticipated between $20.05 a share and $20.35 a share—up from a range of $19.15 a share to $19.45 share.

Harley-Davidson earnings per share topped expectations, but its earnings were lower than a year ago. Harley said falling demand, higher costs from U.S. tariffs on raw materials and European taxes on imports of its motorcycles hurt its earnings. It reported net income of $127.9 million on consolidated revenue of $1.38 billion, compared to $174.8 million on consolidated revenue of $1.54 billion in 2018, a decline of 26.8%.

Palfrey said the earnings expectations for the quarter were distorted by the poor earnings forecast for the energy sector and some big tech names, but the median company could still be up 6 to 7%.

"The typical company has done very well, and that is being reflected in the results we're seeing every single day," said Palfrey. "That's one of the reasons why investors' concerns about the earnings recession they worried about are melting away."

Hickey said it may be too soon to call the all clear on profits, but he did note Tuesday was the busiest day of reporting season so far.

He noted of 50 names that reported Tuesday morning, two-thirds have exceeded EPS forecasts, and more impressive was the fact that two-thirds of those companies reporting have beast revenue estimates.