An attempt to correct strain data measured with vault-housed extensometers under variations in temperature

• Vault-housed extensometer strain data are distorted by variations in temperature.
• We derive formulae to synthesize variations in temperature inside the vaults.
• We assess the validity of the formulae by using real datasets.
• Temperatures can be synthesized only when suitable reference data exist.
• Correction of strain data is more difficult than expected.

Strain data obtained by vault-housed extensometers have precisions on the order of nanostrains, but they are distorted by variations in temperature, which cause two types of noise: “actual variations” due to the thermo-elastic effect of the Earth's crust, and “false variations” due to the thermal expansion of extensometer, which occurs when the extensometers themselves are subjected to variations in temperature. Here, I explore a method of removing false variations, which are severe when the vault is located at shallow depths. If variations in temperature at arbitrary points inside a vault are estimated, false variations can be removed from the recorded variations in strain. I derive formulae that enable variations in temperature to be estimated at various points in a vault, based on measured variations at reference points. The formulation is valid if some simplification is allowed. I examined whether variations in temperature inside a vault can be estimated in terms of the derived formulae, and obtained the following results. When the reference temperature data are obtained from adequate points in the vault, variations in temperature at another point can be estimated with an accuracy of 0.1 °C. However, when the reference temperature data are obtained from outside the vault, estimated variations in temperature are rather inaccurate, which means that the false variations in strain cannot be removed accurately. Moreover, the data indicate that the thermal diffusivity of the ground is temporally variable, and this introduces another difficulty in correcting false variations in strain data. These results indicate that correcting the distortions in strain data due to variations in temperature is much more difficult than anticipated.