Alfred Edersheim, on Page 1135 of his book, The Life and Times of Jesus the Messiah, writes:
It could not have been an eclipse, since it was the time of full moon; nor can we place reliance on the later reports on this subject of ecclesiastical writers. It seems only in accordance with the Evangelic narrative to regard the occurrence of the event as supernatural, while the event itself might have been brought about by natural causes; and among these we must call special attention to the earthquake in which this darkness terminated.
Personally I do not see how this event can be explained by natural phenomena at all. Possibly God miraculously did 'something' to the earth, in and around the region where Christ died, that started with darkness and ended with an earthquake.
I could not shake this question, after mulling it over I have an alternate option that came to mind. Although God is free to reverse the laws of nature when He performs a miracle, He often uses natural causes directed by His hand. Like with the plague of locusts, He sent a wind to blow existing locusts into Egypt (Exodus 10:13). It seems possible (not probable) that God caused an volcanoe in an unpopulated region to blow an ash cloud at a high elevation over the cross. There is volcanic activity around Israel, but even much further away God may have blown in a black ash cloud. Earthquakes are directly related to Volcanoes, so this also supports the rest of the narrative. If this was the case, it would have been a very ominous site, for the sky could have been filled all around with a dense gray-black plume-like covering.
Under this scenario the miracle would be in God causing it to fill the sky and then be whisked away, just at the right time, without any noticeable wind blowing on the surface of the ground. There is no mention of wind during the crucifixion so the still silence under a black covering would have been all the more eerie, creating a deafening silence, so that all would hear when the centurion said, “Surely this man was the Son of God!” (Mark 15:39)