The first time Brother Branham mentioned earthquakes was around 1935, when he said the time would come when the ocean/sea would weep its way into the desert. In 1958 (and other times), he speaks about the ocean weeping its way into the desert.
“Oh, the blessed eternal God, love of God, had no beginning; and it'll never have an end. When the oceans has wept themselves into deserts, and the world has got so full of sin, till the heavens has turned its back on it, and it staggers out through space, like a drunk man coming home, the love of God shall still endure, saints' and angels' song.”
"When the earth is staggering like a man coming home drunk by atomic power shaking her, when the oceans has wept theirself into deserts, and seeing that it reached the ears of God, and the stars refuse to shine, the love of God will still be the same. It can never fail."

Brother Branham referred back to this after the prophecy was given on April 29, 1965, concerning Los Angeles sinking to the bottom of the sea.
“But it said, ‘The time will come---’ I didn't know it till Mrs. Simpson brought me the sermon the other day. And I got it wrote in a little book, that the desert, that the ocean shall weep its way into the desert. That was 30 years ago.

"And, of course, the Salton Sea is about 200 feet below sea level, and if that big churning, that earth swallowing in like that, with hundreds of square miles, hundreds and hundreds of square miles sinking into the earth, that'll throw a tidal wave plumb to Arizona. Sure, it would.

"Oh, we're at the end time, glorious hour, the appearing of the Lord Jesus. He said, ‘There shall be earthquakes in divers places, perplexed of time, distress between nations, men's hearts failing in fear.’ Said, ‘When these things begin to happen, raise up your head, your redemption's drawing nigh.’” [Luke 21]
“Mrs. Simpson…went and got a prophecy that I made about 1935 or something like that, and said: 'The time would come…that the sea would weep its way into the desert.'

"Look what’ll take place. If that thousands of square miles falls down into the lava of the earth and slides in, there’ll be millions die at one time. And that’ll cause such a tidal wave---

"Remember, plumb up into the Salton Sea is a hundred or two hundred feet lower than the sea level. That water will probably come almost to Tucson with that tidal wave coming across there. And the sea shall weep its way into the desert---"