
the answer
On a daily basis, the depth is between 50 and 100 cm. It depends on the soil materials and water content. The depth is greater in soils of high conductivity and low heat capacity. So dry sand would have a thick layer in which the soil temperature changes daily, and wet organic soils have a thin layer. On an annual basis, the depth at which temperatures do not vary is between 15 and 25 m. The ground with a larger value is bedrock or frozen sand. Clay has a lower value. One of the difficulties with this question at long timescales is that, with climate warming, temperatures even at significant depths are changing slowly.
The constant temperature recorded at depth is similar to the mean annual air temperature, but in places where there is a snow cover it is commonly higher. The nearer the surface, the depth on a daily basis is related the the ground temperature in the previous two weeks or so, unless the ground is freezing or thawing, when much energy is used to melt or freeze ice and water, and not to change the soil's temperature.
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