## 1. Introduction

[2] Interactions between surface and subsurface water influences not only hydrological, physical, chemical, and biological aspects at and under the surface but also conservation and management of water resources. Quantitative estimation of fluxes of recharging or discharging water provides fundamental information. To date, fluid fluxes were estimated in various environments, such as lakes [e.g., *Shaw et al.*, 1990; *Taniguchi and Fukuo*, 1996], coastal zones [e.g., *Cable et al.*, 1996; *Moore*, 1996; *Spinelli et al.*, 2002; *Taniguchi et al.*, 2002], submarine hydrothermal areas [e.g., *Schultz et al.*, 1992, 1996; *Cooper et al.*, 2000], and accretionary prisms in subduction zones [e.g., *Carson et al.*, 1990; *Tryon et al.*, 2001], with seepage meters, diffuse flowmeters, piezometers, and by chemical tracer methods.

[3] Measurement of subsurface temperature is one of the useful methods for estimating fluid flux through the earth material because moving fluid works as a “carrier” of heat. This method is based on solving a partial equation describing flows of heat and fluid. Under thermally stable boundary conditions, *Bredehoeft and Papadopulos* [1965] obtained an analytical solution describing vertical temperature distribution in the layer where fluid moves vertically at a constant velocity. On the basis of this analytical solution, they presented a type curve method for estimating vertical fluid flow velocity from a vertical temperature profile. This method was used to many studies investigating vertical groundwater movement [e.g., *Sorey*, 1971; *Cartwright*, 1979; *Boyle and Saleem*, 1979]. *Sleep and Wolery* [1978] discussed an analytical solution expressing vertical temperature distribution in sediment in which total heat transported by both advection and conduction is conserved at any depth. Using this analytical solution, *Williams et al.* [1979] and *Becker and Von Herzen* [1983] estimated both heat and fluid fluxes from vertical temperature profiles measured at the Galapagos Rift, eastern Pacific Ocean. These two analytical solutions presented by *Bredehoeft and Papadopulos* [1965] and *Sleep and Wolery* [1978] are simple mathematically but apply only to steady state problems under stable boundary conditions.

[4] There are several theoretical and practical studies that estimated fluid flow velocity from temperatures of sediment with a time-dependent thermal boundary condition. *Taniguchi et al.* [1999a] presented a series of type curves for estimating vertical groundwater flux in sediment in which water flows vertically at a constant rate and temperature at the surface increases linearly. They used these type curves to evaluate not only the groundwater flux but also surface warming in the Tokyo metropolitan area, Japan. *Taniguchi et al.* [1999b] presented another set of type curves for estimating vertical groundwater flux in sediment in which water flows vertically at a constant rate and temperature at the surface is expressed as a step function. They estimated vertical groundwater fluxes in the Collie River Basin in Western Australia where the ground surface temperature increased by the land cover change from forest vegetation to pasture or crops. *Suzuki* [1960] obtained an algebraic equation describing thermal response of soil in which fluid flows vertically at a constant rate and temperature at the surface changes periodically. *Stallman* [1965] developed Suzuki's work and obtained the analytical solution by the method of undetermined coefficients. On the basis of this analytical solution, he suggested that a fluid flow velocity of 0.3 cm d^{−1} can be estimated by analyzing thermal response of soil to diurnal temperature variation at the surface. Using the Stallman's analytical solution, *Taniguchi* [1993] presented a type curve method for estimating vertical steady fluid flow velocity from seasonal change in a vertical temperature profile in a relatively shallow depth borehole. He used this method to estimate vertical fluid flux from borehole temperatures measured at Nagoya Plane, Japan.

[5] The thermal response of sediment with vertical water flow to surface temperature variation depends on the direction and velocity of the fluid flow, the physical properties of the sediment and water, and the period of the surface temperature variation. However, the quantitative dependences of the thermal response to these parameters have not been discussed in a systematic way until now. In this paper, we examine them on the basis of Stallman's analytical solution. Finally, we adapt the analytical solution to estimate the fluid flux and thermal diffusivity of seawater-saturated sediment from temperatures measured at the TAG hydrothermal mound, 26°N on the Mid-Atlantic Ridge.