Doctrine and Covenants section 88: 100,101 – Third Resurrection
100 And again, another trump shall sound, which is the third trump; and then come the spirits of men who are to be judged, and are found under condemnation;
101 And these are the rest of the dead; and they live not again until the thousand years are ended, neither again, until the end of the earth.
Revelation 8: 10,11
10 And the third angel sounded, and there fell a great star from heaven, burning as it were a lamp, and it fell upon the third part of the rivers, and upon the fountains of waters;
11 And the name of the star is called Wormwood: and the third part of the waters became wormwood, and many men died of the waters because they were made bitter.
As you can see from studying there is a rapture for the first three trumpets that sound. I believe the reason is that Jesus is giving souls a chance to repent and are caught up according to their faith. The ones who are left are evil in heart, and the Jews are left when Jesus returns later to save them from destruction, armageddon which happens during the 6th Trumpet.