A simple analytical method to calculate the thermal parameter and temperature within subducted lithosphere

Temperature profoundly affects seismicity and rheology within subducted lithosphere; the thermal parameter Φ is often used to characterize the temperature structure of subduction zones. Φ is usually defined as tAgeV⊥, where tAge is the age of the plate as subduction begins and V⊥ is the lithosphere's vertical descent rate. But, interpretations of Φ can be confusing because its relationship with temperature is seldom expressed explicitly and because published estimates of Φ often vary by factors of two or more. This paper presents a particularly simple approximate model that leads to an analytical relationship between Φ/h and the minimum temperature within subducted lithosphere at a depth h. In spite of the model's simplicity, it gives reasonable approximate temperature estimates, e.g., for subduction zones where Φ is less than about 2500 km, the relationship between Φ and the observed maximum depth hmax of seismicty is consistent with the observation that seismicity ceases when interior slab temperature exceeds about 600-800 °C.