There is no earthquake mentioned here, so please don't call it "Paul's sudden destruction earthquake".  Also, it should be noted that this sudden destruction occurs when the day of the Lord arrives "like a thief in the night".  I can see no reason at all to not directly relate that to this:
2 Peter 3
10 But the day of the Lord will come like a thief. The heavens will disappear with a roar; the elements will be destroyed by fire, and the earth and everything done in it will be laid bare.
They both are talking about what will happen when the day of the Lord (which they both relate to the second coming of Christ) arrives like a thief (unexpectedly).  Paul did not specify what causes the destruction, but Peter did.  It said it will be by fire.  We should accept what Peter taught and not act as if he was talking about something different than Paul when it's very obvious that they spoke about the same exact thing (destruction occurring on the day of the Lord).
		
		
	 
I can see no reason at all to not directly relate that to this: I agree. Both Paul and Peter speak of the very same Day of the Lord. Are you forgetting something here? Many people forget TIME. Do you imagine the Day of the Lord comes and ends in a flash - a second or less? Maybe you imagine it is a 24 hour day like all other "days." The truth is, the Day of the Lord is a long, extended period of time when God bring judgment first, then eternity. 
Let's examine Peter's statement: Yes, He agrees with Paul, 
the DAY of the Lord will come as a thief. Peter probably read Paul's letter. Comparing scripture with scripture, this will happen at the 6th seal where John tells us the Day begins. 
Next, Peter tells us 
"the heaven's will disappear with a roar." Where else do we read this? At the 6th seal John wrote, " the heaven departed as a scroll when it is rolled together..." So this event would be in the first second or seconds of the Day of the Lord.
Next, Peter tells us, 
"the elements will be destroyed by fire..." Would this have to come in the first seconds, or could it come later in the Day? The way Peter wrote it, it could come later. It could be at the end of the Day. All we can prove from what Peter said is that sometime during this Day of the Lord, the elements will burn. Where else do we read about this?
1 Corinthians 3:13 Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is.
Notice the time here:
 "THE DAY shall declare it." It is Day of the Lord timing. Where do we find "fire" that might give us timing information? 
2 Thes. 1:  7 And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels, 8 In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ:
So it seems the fire that tries the works of man, the fire that comes from elements burning may well come when Jesus comes. It is a coming for vengeance. 
Do we see any hint of vengeance in His coming in 1 Thes. 4 - a coming FOR His saints? No, we see vengeance in His coming as shown in Rev. 19, His coming to Armageddon. It is at this coming that the armies of heaven are mentioned. 
Therefore, I conclude that this phrase from Peter is not at the START of the Day of the Lord, but after some TIME has passed. You may not believe it, but from the 6th seal to the coming in Rev. 19 is going to be over 7 years of time. The 6th seal is opened just before the 70th week, and Jesus coming to Armageddon is some unknown time after the week. This is still in agreement with Peter. The DAY is still ongoing at Armegeddon. 
They both are talking about what will happen when the day of the Lord (which they both relate to the second coming of Christ) arrives like a thief (unexpectedly).  As explained above, this is the arrival or START of the Day. 
Paul did not specify what causes the destruction, but Peter did.  It said it will be by fire.  Now you are trying to align two scriptures that will not fit together. Paul's destruction is RIGHT THEN, at the same moment that those alive and in Christ are caught up, those left behind suffer the sudden destruction - at the START of the DAY. Again I find you just not understanding TIME. The truth is, the entire 70th week of events, 7 trumpet judgments, 7 vial judgments and many events between, will take place just after the DAY starts, but before the fire destroys and tries men's works. It may not fit your theory, but it is scripture. 
In summary, the DAY starts with the 6th seal, then,
the 7th seal officially starts the 70th week. Then,
The 70th week and Day of the Lord open with the first trumpet judgments. 
Then the first half of the week passes with these trumpets. Then,
The 7th trumpet marks the midpoint of the week and the abomination. Then,
Those in Judea begin to flee. Then, 
War in heaven breaks out: the 7th trumpet is Michael's signal to begin. Then,
John sees the Beast arise. Then, some unknown time after,
The second Beast arrives on the scene. Then,
They erect an image and create a mark. Then,
God sends angels to warn the people, the days of GT are about to begin. Then,
Days of great tribulation begin.
The beheaded begin to show up in heaven. Time passes, Then,
When the beheading reaches a peak, God sends the vials to shorten those days
Then, DARK days of dread and pain and waiting for the end of the 42 months.
Then, the 7th vial hits that ENDS the 70th week. 7 years have passed
Then, armies of the world are sent to Israel, to wipe Israel off the map. Then, 
Some of Jerusalem is taken, many carried away as slaves
Those who fled are almost to be captured near Bozrah
Just when it seems all hope is lost for Israel, JESUS SHOWS UP!
This is scripture rightly divided and understood. Anything else is myth.