Houston Flooding Pushed the Earth's Crust Down 2 Centimeters

Hopefully, the deformation is an elastic response to the loading, not additional compaction of the sands and and gravels of the depleted near-surface aquifers in the Houston area.

Hmmm.... Is it crustal deformation or compression of the clay beds under Houston/subsidence?

'But because some stations located on bedrock also experienced the depression, he believed that the key mechanism was crust deformation.'

I had no idea we had bedrock.

Ah, my miss. I skimmed the article.

If it is crustal deformation, which is implied by the article Lee linked, then isostatic rebound will occur. It does take time for water to recharge near surface aquifers, so clay beds between the sand and gravel deposits may have been compressed by the additional overburden pressure. Clay bed compression normally occurs when the adjacent aquifers have been pumped dry. The overburden pressure then "squeezes" the water out of the clay and into the adjacent sand and gravel deposits, thereby reducing the volume occupied by the clay.

The other subsidence mechanism is when an aquifer composed of sand and gravel has been dewatered. Without hydrostatic pressure, the loose grains of sand and gravel in the bed can rearrange themselves into a closer packing structure. This collapse irreversably reduces the porosity of the aquifer matrix. In the past, I worked with computer modelling software authored by the USGS. The software had a module that would compute the subsidence caused by dewatering of clay beds from over pumping of the adjacent aquifer(s).

Also see: https://en.wikipedia.org/wiki/Earth_tide for information on solid earth tides.