## 1. Introduction

[2] Variations in the heat flow from the interior to the surface of a planet can have pronounced effects on tectonic, magmatic, and geological processes. In the absence of direct measurements, surface heat flow can be estimated from the elastic or mechanical thickness of the lithosphere, because the base of the lithosphere is defined approximately by a temperature at which crustal or mantle rocks undergo ductile flow on a geological timescale. Estimates of elastic lithosphere thickness (*T*_{e}) and loading styles for Mars have been derived from gravity, topography, and image data sets. In this paper, we present new estimates for *T*_{e} and heat flow on Mars from relationships between gravity and topography, making use of new measurements of both fields by the Mars Global Surveyor (MGS) mission.

[3] Many earlier studies exploited the distribution of tectonic features associated with large lithospheric loads to constrain lithospheric structure at the time of loading by means of comparisons with predictions of fault types and orientations derived from flexural models. In such analyses, topographic information is used to estimate the (surface) load and is usually the primary input to the models. For example, *Comer et al.* [1985] compared modeled surface stresses with the radial range of graben concentric to large volcanic loads, yielding best-fit *T*_{e} values in the range 20 to 50 km for the volcanoes of Tharsis Montes, Alba Patera, and Elysium Mons and *T*_{e} > 120 km for the Isidis basin mascon. *Hall et al.* [1986] confirmed the *Comer et al.* [1985] estimate of *T*_{e} (50 km) at Elysium Mons. The absence of prominent concentric graben around the Olympus Mons volcano led *Thurber and Toksöz* [1978] to derive a lower bound on *T*_{e} (>150 km). *Janle and Jannsen* [1986] combined this tectonic constraint at Olympus Mons with an analysis of gravity and topography to derive the limits 140 km ≤ *T*_{e} ≤ 230 km. *Schultz and Lin* [2001] estimated the lithospheric thermal gradient at Valles Marineris from boundary element models of rift flank uplift and obtained values consistent with *T*_{e} > 60 km. *Schultz and Watters* [2001] modeled the formation of thrust fault topography at Amenthes Rupes, determining the maximum depth of faulting to be 25–30 km.

[4] Other studies of lithospheric characteristics on Mars have relied primarily on relationships between gravity and topography, compared either directly as a function of position or in the harmonic domain. For example, *Turcotte et al.* [1981] used thin spherical-shell flexure models to demonstrate that long-wavelength topography on Mars is primarily supported by membrane stresses in the lithosphere. Under the thin-shell approximation, the ratio of spherical harmonic coefficients of gravitational potential to topography (for harmonic degrees 4 to 7) yielded a (global) *T*_{e} estimate of 175 km. *Banerdt et al.* [1982, 1992] and *Sleep and Phillips* [1985] combined gravity information with tectonic constraints to infer aspects of subsurface compensation and loading for assumed values of *T*_{e} on regional (Tharsis) to global scales. *Janle and Erkul* [1991] modeled gravity and topography data to evaluate end-member compensation models for and possible mantle density anomalies beneath the Tharsis Montes and Alba Patera. *Anderson and Grimm* [1998] analyzed harmonic expansions for gravity and topography in the vicinity of Valles Marineris, inferring *T*_{e} < 30 km and heat flux consistent with a wide-rift origin [*Buck*, 1991] and regularly spaced chasms.

[5] Several studies have taken advantage of the new MGS gravity and topography data. From an analysis of early MGS gravity and topography, *Anderson and Banerdt* [2000] interpreted a sharp dropoff in gravity/topopgraphy admittance at wavelengths shorter than 1000 km as evidence for a deep mantle load compensating the Valles Marineris troughs. *Arkani-Hamed* [2000], also from early MGS data, estimated *T*_{e} (80–100 km) for Olympus Mons and the Tharsis Montes and concluded that anomalously dense subsurface loads are present beneath these structures. *Turcotte et al.* [2002] used point correlations of gravity and topography to obtain values for mean crustal thickness (90 km) and density (2960 kg/m^{3}). From one-dimensional wavelet transforms they inferred a globally averaged elastic lithosphere thickness of 90 km. *McKenzie et al.* [2002] used Cartesian-domain admittance techniques to estimate *T*_{e} at Tharsis (70 km), Elysium (27 km), and the southern hemisphere (14.5 km). They inferred that crustal densities at Tharsis (3.0 kg/m^{3}) are similar to measured densities of Martian meteorites but that the crustal density at Valles Marineris is substantially lower (2.35 kg/m^{3}), suggestive of a large fraction of ice within the crust.

[6] In this paper, we exploit several recent advances in the harmonic analysis of gravity and topography. First, we localize the gravity and topography spectra with the spatio-spectral windowing method of *Simons et al.* [1997]. This formalism allows the inference of lithospheric properties for specific features rather than global averages (as, for example, by *Turcotte et al.* [1981]). Further, the large dynamic range of Martian topography renders inaccurate the first-order mass-sheet approximation for calculating gravity from relief of density interfaces, an essential step in modeling. We account for the effects of finite-amplitude relief with the higher-order gravity calculation of *Wieczorek and Phillips* [1998]. With the new gravity and topographic relief data from MGS as well as improved models, we explore the implications of localized admittances for the compensation of surface features and the thermal evolution of the planet.

[7] First, we compare observed admittance and correlation spectra with those predicted by spherical shell flexure models, in order to estimate the effective elastic lithosphere thickness *T*_{e} at the time of loading. The resulting *T*_{e} estimates can be used to constrain the thermal history of the lithosphere. We apply a standard procedure based on the properties of elastic/plastic flexed plates [*McNutt*, 1984] to convert *T*_{e} into estimates of thermal gradient and heat flux in the lithosphere. We compare these results with those obtained from earlier estimates of *T*_{e} for Mars [e.g., *Solomon and Head*, 1990], and we then evaluate the implications of our estimates for the thermal evolution of the planet.