The "1970s oil crisis" was nothing to do with the perception of declining oil reserves.
The first crisis was a result of the Yom Kippur War. A coalition of states led by Egypt and Syria, and supported by the USSR, attacked Israel. Israel fought back, supported mostly by the USA, but with other Western nations too. After the fighting was over, OPEC (the cartel of middle-Eastern oil producing states) decided to fuck with the West for supporting Israel by massively reducing the supply of oil.
The second crisis was in 1979 when revolution in Iran replaced the pro-West Shah with decidedly anti-West religious fundamentalists who, again, reduced the oil supply to fuck with the West.
This is not to say that oil reserves are doing anything by declining - they are a fundamentally finite resource - but your recollection of history is slightly flawed.
Santayana said "Those who cannot remember the past are condemned to repeat it." Well, here we are again...