Q. 78: How did the earth ‘expand’ by replacement of cold lithosphere with warmer mantle rock?

CPT Q. #78 – 101 Q&A on Catastrophic Plate Tectonics

Question: 78. Please explain how, as you mention in one of your early papers, the earth “expanded’ due to replacement of cold lithosphere with mantle. It seems to me this explanation violates conservation of mass and energy. Lacking any net loss of mass or energy (temperature), it seems to also violate conservation of volume.

Response: I am not sure to which paper you are referring, but I am guessing it is the 1994 joint author paper on CPT. I am also guessing that your question is referring to the process that occurs at a mid-ocean ridge where cooling ocean lithosphere is migrating away from the ridge and hot mantle rock is being drawn up from below to fill the resulting void. There is certainly no net gain or loss of mass in this process, and the earth’s total mass is not affected.

However, what can easily be affected is ocean basin volume. Because of the principle of isostasy, which is closely related to Archimedes Principle, the height of the ocean bottom is dependent of the temperature distribution in the rock beneath it. When the average rock temperature is higher, the average rock density is lower, the resulting height of the rock column to satisfy isostasy is greater, and hence the depth of ocean water above that column is smaller. On the other hand, if the average temperature is lower, the average rock density is then higher, the resulting height of the rock column needed to satisfy isostasy is smaller, and the depth of ocean water above the rock column is greater. This implies that, averaged over an entire ocean basin, the average water depth is less if the average temperature of the rock beneath the ocean bottom is higher, and vice versa.

In the case of CPT, if prior to the onset of CPT the ocean lithosphere is relatively cold, then the average depth of the ocean basin will be deeper compared with the later state of affairs after much of the cold ocean lithosphere has subducted and has been replaced, in effect, with warmer rock that has risen from the mantle below beneath a spreading ridge. In other words, if the average temperature of the top 100 km of rock beneath an ocean basin increases, the volume of that ocean basin will decrease relative to some fixed reference condition. The physics involved is, first, the fact that rock density depends on temperature, with the volume coefficient of thermal expansion being about 3 x 10-5/°C and, second, the principle that, above some reference depth where rock can readily deform and flow, all columns of rock (plus any water that may reside on top) have equal weight.

Therefore, the ‘expansion’ to which you seem to be referring has to do with thermal expansion as rock temperature is increased. Also note that the expansion of the ocean floor rock, which likely occurred while CPT was occurring and caused sea level rise, also likely changed to contraction as CPT shut down and the ocean lithosphere cooled, with the result of sea level decline. Because rock volume so indisputably depends on temperature, there is no principle requiring “conservation of volume.”