The rapture is mentioned here,
in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed. (1 Corinthians 15:52 [NIV])
This rapture happens at the second coming of Jesus Christ, after he descends, hence,Two men will be in the field; one will be taken and the other left. (Matthew 24:40 [NIV])
In which case, the trumpet that is sounded in this passage in 1 Thessalonians, is the same trumpet that is sounded in the passage in 1 Corinthians, which is also the same trumpet that is sounded in Matthew in reference to the second coming,For the Lord himself will descend from heaven with a cry of command, with the voice of an archangel, and with the sound of the trumpet of God. And the dead in Christ will rise first. Then we who are alive, who are left, will be caught up together with them in the clouds to meet the Lord in the air, and so we will always be with the Lord. (1 Thessalonians 4:16 [ESV])
And so, the gathering of all the elect from the entire earth by angels, at the second coming, is the "rapture" of the elect, hence,"Then will appear the sign of the Son of Man in heaven. And then all the peoples of the earth will mourn when they see the Son of Man coming on the clouds of heaven, with power and great glory. And he will send his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of the heavens to the other. (Matthew 24:30 [NIV])
And angels will not only gather the elect who are alive at the second coming, but also the elect who have died previously, hence why in 1 Corinthians and in 1 Thessalonians the dead are raised first at the second coming of Jesus Christ,And he will send his angels and gather his elect from the four winds, from the ends of the earth to the ends of the heavens. (Mark 13:27 [NIV])
...the dead will be raised imperishable... (1 Corinthians 15:52 [NIV])
And so, all the elect will be gathered and taken by angels to meet the Lord in the air at his second coming,...the dead in Christ will rise first... (1 Thessalonians 4:16 [ESV])
...will be caught up together with them in the clouds to meet the Lord in the air, and so we will always be with the Lord. (1 Thessalonians 4:16 [ESV])