The loss of a family member is an event, and an event cannot be overcome, only accepted. But I am assuming you meant to ask "how to overcome
the grief of loosing your family in an earthquake?", which I will simplify to "how to overcome the grief of losing a loved one?"
Since one cannot change past events, the only rational mental end state is
acceptance, which coincidentally is also commonly seen as the last stage of grief. The faster we can accept past events, the faster the grief they inflict can be overcome. However, in situations like these our emotional responses often interfere with the process of acceptance. The loss of a loved one can come as a great mental shock. Why?
Because of one's attachment and one's perception of loss.
Attachment to material things, including people and indeed one's own life, is the source of most if not all of man's suffering. Since all that is material is fleeting, loss of these things is unavoidable, and attachment to these things is irrational. By attaching ourselves to things which one will unavoidably lose, one is setting themselves up to suffer. Sadly, we live in a world in which a deeply materialistic worldview is almost universally perpetuated.
Furthermore, when one loses a loved one many will, consciously or unconsciously, make the assumption that they will never see them again. This assumption, whatever the basis may be, is irrational, since no one knows what happens after a person dies. Making the assumption that death is the end, regardless of how well-informed one thinks it is, is a choice, and once again one has created their own suffering.
Take a child's toy and it may cry, for it was attached to the toy. It therefore suffers.
Skip forward one hour and look at the child. It is no longer crying. Why? The past hasn't changed and its toy was still taken. The child has moved on and is thinking about something else. It no longer suffers.