In the beginning God created the world (Gen 1:1) and He created it good (Gen 1:31). He created it as a home for men (Gen 1:28, 2:15) where He could interact with them (Gen 3:9). He called this place where men could interact with God Heaven (Gen 1:8).
God created men in order to establish relationship with them .. a relationship based on trust and love.
A relationship based on faith and love cannot exist without both parties being capable of rejecting that relationship.
God, willing to show mercy (Gen 2:17, Gen 3:21), then began on His plan to reconcile the world to Him (Rev 13:8). The only way men's lives can be fulfilled as designed is in relationship with God (1 Cor 15:20-23). In order to teach men this fact, He withdrew from a complete relationship based on faith and love to a position of authority. But He did not disown His loving nature (2 Tim 2:13) nor did He suddenly discover authority.
This means not only has man been increasingly left to fend for himself and suffer the consequences of his mistakes, but also the earth has been left to its own devices (Rom 8:19-21).
When the history of mankind in rebellion against God has run its course God will create a new earth and a new heaven (probably on that new earth) and those who choose to be on the ark, be in the covenant, come under His commandments, be in the body, be in the kingdom, or simply show faith will join Him (John 14:1-4). Those who reject Him will be left on this earth to fend for themselves as they so chose.
When God created our current earth He had some features that He maintained. Those features provided a source of water that is not functioning today (Gen 2:10). When he left man to his own devices He also quit maintaining the earth. The source of water failed, pressure built up and the earth blew its top (Gen 7:11). This event flooded the earth, sent parts of it into orbit and destroyed all the land animals and all of humanity except for Noah (2 Pet 3:6).
After this massive eruption the earth was significantly non-spherical. Physics dictates that the greater this non-sphericity the more energy is available to reform the earth into a sphere. That energy dissipated rapidly at first until now there is little remaining. What is remaining can (along with other factors) cause earthquakes.
If we were curious and faithful enough we would be able to investigate to establish these events and what the original features were (Rom 1:18-23). But given that the world has rejected God it comes as no surprise that the world would generally reject His account of its history (2 Pet 2-3). Nobody likes to be reminded of their failure.
That's how man's rejection of God causes earthquakes.