Taylor & Francis which is in publication of scholarly information of the highest quality and publishes books in Science, Built Environment, Humanities, Social Science, Education, Health, Behavioral Science, and other professional subjects, published “International Geology Review study” authored by Jefferson B. Williamsa, Markus J. Schwabb & A. Brauerb which confirms an early first-century earthquake in the Dead Sea.
Abstract
This article examines a report in the 27th chapter of the Gospel of Matthew in the New Testament that an earthquake was felt in Jerusalem on the day of the crucifixion of Jesus of Nazareth. We have tabulated a varved chronology from a core from Ein Gedi on the western shore of the Dead Sea between deformed sediments due to a widespread earthquake in 31 BC and deformed sediments due to an early first-century earthquake. The early first-century seismic event has been tentatively assigned a date of 31 AD with an accuracy of ±5 years. Plausible candidates include the earthquake reported in the Gospel of Matthew, an earthquake that occurred sometime before or after the crucifixion and was in effect ‘borrowed’ by the author of the Gospel of Matthew, and a local earthquake between 26 and 36 AD that was sufficiently energetic to deform the sediments at Ein Gedi but not energetic enough to produce a still extant and extra-biblical historical record. If the last possibility is true, this would mean that the report of an earthquake in the Gospel of Matthew is a type of allegory.
Other links are here: http://www.deadseaquake.info/
About the darkness:
There are two possibilities:
As reported by Discovery News, Jefferson B. Williamsa had intended to investigate if dust storm deposits coincided with the early this first century Jerusalem region earthquake leading to this darkness.
As per Wiki, Humphreys and Waddington of Oxford University reconstructed the Jewish calendar in the first century AD and arrived at the conclusion that Friday April 3 33AD was the date of the Crucifixion. Humphreys and Waddington went further and also reconstructed the scenario for a lunar eclipse on that day. They concluded that:
"This eclipse was visible from Jerusalem at moonrise. .... The start of the eclipse was invisible from Jerusalem, being below the horizon. The eclipse began at 3:40pm and reached a maximum at 5:15pm, with 60% of the moon eclipsed. This was also below the horizon from Jerusalem. The moon rose above the horizon, and was first visible from Jerusalem at about 6:20pm (the start of the Jewish Sabbath and also the start of Passover day in A.D. 33) with about 20% of its disc in the umbra of the earth's shadow and the remainder in the penumbra. The eclipse finished some thirty minutes later at 6:50pm."
The arguments against this:
But eclipses are too brief to account for the crucifixion darkness. The length of the crucifixion darkness described by biblical and extra-biblical sources was more than a full order of magnitude for the totality of eclipses.
Jesus' crucifixion took place around Passover, the middle of the lunar month and the time of a full moon. Solar eclipses naturally take place only at the time of the new moon.
Miracle
For these two reasons, medieval commentators viewed the darkness as a miraculous event rather than a natural one. Because it was known in medieval times that a solar eclipse could not take place during Passover, it was considered a miraculous sign rather than a naturally occurring event.
To some extent we have a flicker of evidence that these two events did take place in 33 AD. Even then they are difficult to fully explain in scientific terms as both these accounts suggest.
But, if we were to completely explain these two phenomenon of earthquake and darkness that occurred during this time of period as scientific events, then we cannot link it to something unusual that was happening on the cross and that is dying of Son of God to save sinners.