Classical heat-flow measurements near the San Andreas Fault (SAF) show no fault-centered thermal anomaly despite 28–34 mm/yr of relative plate motion, which has been interpreted since the 1970s to require a depth-averaged shear stress below about 20 MPa — an apparent friction far below laboratory values for rocks (the "heat flow paradox"). Fulton and Saffer (2009) showed at Parkfield, California, that thermal refraction by sediment–basement conductivity contrasts plausibly generates the large observed scatter in heat-flow data but cannot conceal the anomaly expected from a strongly loaded fault. This task asks whether any quantitatively plausible combination of masking mechanisms — thermal refraction with realistically undersampled conductivity structure, steady and earthquake-triggered groundwater advection, partitioning of earthquake slip energy away from heat, and along-strike variation of the regional thermal field — can reconcile the missing anomaly with a strong fault, or whether the data robustly require a weak fault. Transient and topographically driven advection have been tested and both fail to mask a fault-centered anomaly under realistic parameters, and a 2023 energy-budget reanalysis extended the paradox by showing that the low-friction reading of the heat-flow data conflicts with the elastic power accumulating in southern California. The problem remains open and is now centered on the joint energy budget and on direct thermal constraints.

Background

Surface heat flow — the outward conductive flux of heat through the Earth's surface, measured in boreholes as the product of thermal conductivity and the vertical temperature gradient (typically tens of mW/m²) — is the most direct observable of frictional heating on faults. A fault slipping at a long-term rate v under an average shear stress τ deposits heat at the rate τ·v per unit fault area, and this heat diffuses conductively to the surface over ~10⁴–10⁵ yr, producing a fault-centered heat-flow high. Because laboratory friction experiments (Byerlee's law) give friction coefficients of roughly 0.6–0.85 for most rocks at seismogenic conditions, a fast-slipping fault loaded by regional tectonic stresses should generate a readily detectable anomaly. Yet heat-flow measurements along the San Andreas Fault (SAF) in the California Coast Ranges have never shown one. Lachenbruch and Sass (1992), synthesizing decades of measurements including the Cajon Pass scientific well, formalized this "heat flow paradox": the absence of an anomaly bounds the depth-averaged shear stress on the SAF to roughly 10–20 MPa, corresponding to an apparent coefficient of friction (the ratio of shear to effective normal stress resolved on the fault, μ_app) below about 0.2. Independent evidence points the same way: the maximum horizontal compressive stress is oriented at a high angle to the SAF (Zoback et al., 1987; Hickman and Zoback, 2004, from the pilot hole of the San Andreas Fault Observatory at Depth — SAFOD, a scientific borehole northwest of Parkfield that crosses the actively creeping fault at ~2.5–3 km depth), implying very low resolved shear stress on a weak fault embedded in strong crust. However, two complications have always qualified the thermal inference. First, Coast Ranges heat-flow data show large, short-wavelength scatter (tens of mW/m² over kilometer scales) whose origin must be understood before any anomaly can be detected or excluded. Second, several processes could in principle redistribute or dissipate fault-generated heat so that it never appears as a fault-centered anomaly: thermal refraction (the defocusing and focusing of vertical heat flux by lateral contrasts in thermal conductivity, e.g. between low-conductivity Tertiary sediments and crystalline basement); advective redistribution by topographically driven groundwater flow or by transient, earthquake-triggered fluid pulses; and partitioning of the earthquake slip-energy budget — the work done during faulting is divided among frictional heat, radiated seismic waves, creation of new fracture surface, and endothermic alteration reactions, with the heat fraction (the complement of the seismic efficiency, defined as the ratio of radiated energy to total mechanical work) only poorly constrained. Fulton and Saffer (2009) addressed the first complication with two-dimensional conductive models of the Parkfield region incorporating realistic conductivity contrasts (basement-to-sediment conductivity ratio up to 3) and a geophysically constrained basement-sediment contact, with frictional heating parameterized at 85% of the total slip work. They concluded that refraction plausibly explains the observed scatter in amplitude and wavelength, but that even with large refraction effects, low background heat flow, a regional NW–SE heat-flow decrease, or 5 Myr of nonsteady-state conduction, the data are most consistent with a fault producing little to no frictional heat: models with depth-averaged shear stresses of 48 or 100 MPa are inconsistent with observations. Their discussion nevertheless identified the unresolved uncertainties that limit complete closure of the fault-strength inference: the spatial statistics of in-situ thermal conductivity λ within geologic units at sub-km to tens-of-km scales (some mapped units are represented by zero to a handful of samples); the earthquake energy partition; unquantified transient or coseismic advective processes; and along-strike variations in background thermal state and radiogenic heat production (heat generated by the decay of uranium, thorium, and potassium in crustal rocks). The problem thus stands at the intersection of conductive and hydrothermal heat transport, borehole geophysics, and the earthquake energy budget, and its answer determines whether the oldest quantitative argument for a weak San Andreas Fault is sound.

Problem Statement

Given the terrain-corrected surface heat-flow data around the San Andreas Fault near Parkfield, California (Fulton and Saffer, 2009; Popek and Saffer, 2011), and the classical bound they imply (no fault-centered anomaly, hence depth-averaged shear stress below roughly 20 MPa and apparent friction below ~0.2), determine whether this absence of a frictional heat-flow anomaly can be quantitatively reconciled with a fault that sustains high, Byerlee-type shear stress (tens of MPa) during slip, once all physically plausible masking and redistribution mechanisms are included with field-constrained parameters. The mechanisms to be treated jointly are: (i) thermal refraction by lateral thermal-conductivity contrasts between Tertiary sediments and basement, including the poorly sampled in-situ conductivity distribution at sub-km to tens-of-km scales; (ii) redistribution of fault-generated heat by steady topographically driven groundwater advection and by transient, earthquake-triggered fluid flow through the heterogeneous permeability structure of the upper ~2–3 km; (iii) the partitioning of earthquake slip energy among frictional heat, radiated seismic waves, new surface creation, and endothermic alteration reactions (the thermal efficiency of earthquakes); and (iv) along-strike variations in regional background heat flow and radiogenic heat production at scales larger than a single transect. Alternatively, demonstrate that no realistic combination of these mechanisms can hide the thermal signature of a strong fault, so that the data require low shear stress, and reconcile that low-stress inference with the elastic power accumulating in the region (the rate at which elastic strain energy is stored in the surrounding crust, as defined by Ziebarth et al., 2023) and the radiated energy of its earthquakes. The overarching objective is complete closure of the fault-strength inference from thermal and energy-budget data: every requested result (per-mechanism quantification, joint masking analysis, and energy-budget consistency) serves this single objective and must be answered for the inference to count as closed.

References

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