Airy Isostasy Research Articles

Io's Long‐Wavelength Topography as a Probe for a Subsurface Magma Ocean

AbstractWe investigated how spatial variations in tidal heating affect Io's isostatic topography at long wavelengths. The long‐wavelength relief is less than the 0.3 km uncertainty in Io's global shape. Assuming Airy isostasy, degree‐2 topography <0.3 km amplitude is only possible if surface heat flux varies spatially by <19% of the mean value. This is consistent with Io's volcano distribution and is possible if tidal heat is generated within and redistributed by a convecting layer underneath the lithosphere. However, that layer would require a viscosity <1010 Pa s. A magma ocean would have low enough viscosity but would not generate enough tidal heat internally. Conversely, assuming Pratt isostasy, we found ∼0.15 km degree‐2 topography is easily achievable. If a magma ocean was present, Airy isostasy would dominate; we therefore conclude that Io is unlikely to possess a magma ocean.

Effects of Transient Obliquity Tides Within Mimas' Warm, Icy Interior Preserved as a Frozen Fossil Figure

AbstractMimas has a high eccentricity and an anomalously high physical libration like its neighbor, Enceladus, but does not appear to have a geologically active surface. We investigate Mimas' interior with a technique that infers spatial variations in tidal heating from its global shape. To account for its hydrostatic shape, we find Mimas' normalized moment of inertia is 0.375 ± 0.0025, indicating a relatively undifferentiated world. Its remaining topography is consistent with a ∼30 km thick conductive ice shell in Airy isostasy atop a weakly convecting ∼30 km thick layer that itself mantles a ∼140 km radius ice‐rock interior. The convective shell's density must be closer to the interior density to satisfy our moment of inertia and provide a denser compensating layer for Airy isostasy. This ice‐rock interior is elongated along the Mimas‐Saturn axis, which can match Mimas' observed physical libration without appealing to an ocean. The inferred ice shell thickness variations indicate a high obliquity (≈1.7°). We suggest that the obliquity damped rapidly, after which topography froze in when internal heat was conducted out of Mimas quicker than isostatic ice shell thickness variations could relax. We speculate on several possible explanations for this transient high obliquity, including excitation by ring‐forming material following the recent tidal disruption of an eccentric satellite. We cannot rule out a young Mimantean ocean, but our inferred moment of inertia favors a Mimas that was solid when it experienced a period of high obliquity, did not significantly melt during a recent resonance with Enceladus, and is solid today.

On the More Complex Wavelength Dependency of Airy Isostasy in Icy Shells of Ocean Worlds

AbstractThe topography of ocean worlds is often used to infer ice shell thicknesses by assuming topography is compensated by a basal root. We systematically test the stability of isostatically compensated topography in ice shells. At short horizontal wavelengths, lithospheric strength can support surface topography, while at long wavelengths, buoyancy forces can support topography at the surface and base of the ice shell over geologic time scales. These behaviors are also seen for Airy isostasy in terrestrial worlds. Contrastingly at intermediate scales, the mechanically weak lower ice shell can inhibit the transfer of buoyancy forces to the surface. Factors such as surface temperature can alter the contribution of lithospheric strength, decreasing the stability of a compensating root. This nuanced understanding of icy shell lithospheres provides crucial insights for interpreting surface features and inferring underlying ice shell thickness, with substantial relevance for upcoming space missions to the Jovian system.

The Upper‐Mantle Structure Beneath Alaska Imaged by Teleseismic S‐Wave Reverberations

AbstractAlaska is a tectonically active region with a long history of subduction and terrane accretion, but knowledge of its deep seismic structure is limited by a relatively sparse station distribution. By combining data from the EarthScope Transportable Array and other regional seismic networks, we obtain a high‐resolution state‐wide map of the Moho and upper‐mantle discontinuities beneath Alaska using teleseismic SH‐wave reverberations. Crustal thickness is generally correlated with elevation and the deepest Moho is in the region with basal accretion of the subducted Yakutat plate, consistent with its higher density due to a more mafic composition. The crustal thickness in the Brooks Range agrees with the prediction based on Airy isostasy and the weak free‐air gravity anomaly, suggesting that this region probably does not have significant density anomalies. We also resolve the 410, 520, and 660 discontinuities in most regions, with a thickened mantle transition zone (MTZ) and a normal depth difference between the 520 and 660 discontinuities (d660‐d520) under central Alaska, indicating the presence of the subducted Pacific slab in the upper MTZ. A near‐normal MTZ and a significantly smaller d660‐d520 are resolved under southeastern Alaska, suggesting potential mantle upwelling in the lower MTZ. Beneath the Alaska Peninsula, the thinned MTZ implies that the Pacific slab may not have reached the MTZ in this region, which is also consistent with recent tomography models. Overall, the results demonstrate a bent or segmented Pacific slab with varying depths under central Alaska and the Alaska Peninsula.

Seismic Evidence for Metamorphic Densification of the Lower Continental Crust in Eastern North America

AbstractThe composition of the lower continental crust, as well as its formation, growth, and evolution, remains a fundamental subject to be understood. In this study, we carry out a comparative and integrative analysis of seismic tomographic models, teleseismic receiver function results, and Airy isostasy in order to investigate the properties of the lower continental crust in eastern North America. We extract the depths for Vs of 4.0 km/s, 4.2 km/s, and 4.5 km/s from three selected tomographic models and calculate the differences between the Vs depth contours and the Moho depth defined by receiver functions. We then calculate the Airy isostatic Moho depth and its misfit with the receiver‐function‐defined Moho. Our analysis reveals three key features: (a) the deepening of the Vs depth contours and the strong negative Airy misfit within the U.S. Grenville Province; (b) a seismically faster‐than‐average and compositionally denser‐than‐average lowermost crust in the eastern North American Craton and the Grenville Province; and (c) the thickest, seismically fastest, and densest lowermost crust beneath the southern Grenville Front, the southern Grenville‐Appalachian boundary, and the U.S.‐Canada national border. We suggest that the lower crust of the craton and the Grenville Province has densified through garnet‐forming metamorphic reactions during and after orogenesis, contributing to the widely distributed fast‐velocity layer. The lower crust beneath the tectonic boundaries could have experienced more extensive garnet growth during orogenesis and emplacement of mafic magma. This study provides new constraints on the seismic and compositional properties of the lower crust in eastern North America.

Topographic response to ocean heat flux anomaly on the icy moons of Jupiter and Saturn

Recent studies of ocean dynamics suggest that the long-wavelength topography of some icy moons may reflect the phase transitions (melting/freezing) at the interface between the ice shell and the water ocean. Despite the obvious importance of phase changes in the evolution of icy moons, very little is known about how these processes influence their shape, gravity and near-surface stress. Here we address this issue by performing a series of numerical experiments in which we explore the thermo-mechanical response of an ice layer to heat flux variations imposed at the bottom (phase) boundary. We assume that the heat flux from the ocean consists of two components: the heat flux originating in the deep ocean and associated with the global ocean circulation, and the heat flux due to the flow of water generated by variations in the melting temperature along the deformed ice–water interface. The effect of salinity on the heat flux from the ocean is neglected. We demonstrate that the mass exchange between the ocean and the ice layer is a natural consequence of the ice–water phase transition and it occurs in both convection and conduction modes, regardless of whether the system is in equilibrium or not. The magnitude of the heat-flux induced topography strongly depends on the viscosity of ice and the flow of water controlled by the melting temperature. When heat transfer in the ice shell occurs by convection, the surface topography is dominated by small-scale convective features varying in time and its large-scale component does not exceed 10 m. When the viscosity of the ice shell is high (≳1016 Pas) and the heat is transferred by conduction, the topography is negatively correlated with the heat flux from the ocean and its amplitude increases with increasing viscosity. Topographic amplitudes comparable to those observed on Titan, Enceladus and Dione are obtained only if the water flow associated with lateral variations in the melting temperature is neglected. This suggests that this flow may be too weak to reduce the variations in ice shell thickness and the motion of water along the phase boundary is more likely to be controlled by other factors, such as variations in salinity and the presence of non-ice material. In addition, we show that the standard formulation of Airy isostasy can lead to an error of 5%–15% in determining the variations in ice thickness and we propose a new formulation that takes into account the effect of thermal expansion.

Gravity‐Derived Antarctic Crustal Thickness Based on the Gauss‐FFT Method

AbstractThe information on crustal thickness in Antarctica can provide significant constraints on its crustal deformation and tectonic evolution. To generate reliable images of crustal features, we investigate the model of Moho depth and crustal thickness beneath Antarctica by applying the Bott‐Parker's formulas based on the Gauss‐fast Fourier transform method through a comprehensive analysis of gravity data, ice and sediment thicknesses and bedrock elevation, combined with seismic constraints. Tests with synthetic data indicate that the iterative inversion algorithm can yield a highly accurate Moho topography. Ultimately, inverted crustal thickness reveals a more detailed crustal image by clearly identifying more tectonic elements at different scales than previous results and correlates well with major tectonic provinces. Airy isostasy and flexural isostasy models are used to assess the crustal isostatic compensation. The distinctive negative isostatic anomalies are observed in the Transantarctic Mountains and the East Antarctic areas of the great escarpment in the Dronning Maud Land and Aurora and Wilkes Subglacial Basin, indicating that the low density of the uppermost mantle and lithospheric strength may play important roles in compensating for their elevations. Variations in crustal thickness in interior East Antarctica are analyzed; the thickened crust from Dronning Maud Land to the Gamburtsev Subglacial Mountains may be associated with the collision of continental blocks and is interpreted as the fossil sutures. We compare the relationship between the Moho and Curie interfaces and find that the uppermost mantle is magnetized in some areas of East Antarctica, which may indicate preserved Precambrian cratonic roots.

Lithospheric Structure of Venusian Crustal Plateaus

AbstractCrustal plateaus are Venusian highlands characterized by tectonized terrains. It is commonly interpreted that their topography is isostatically supported and that they represent fossils of an extinct tectonic regime. Using gravity and topography we perform a comprehensive investigation of the lithospheric structure of six crustal plateaus. We computed the admittance (gravity to topography wavelength‐dependent ratio) for each region and compared them to modeled admittances. Three compensation scenarios were tested: Airy isostasy, a surface‐loading flexural model, and a flexural model with surface and subsurface loads. Our results show that the topography of most plateaus is supported by crustal thickening and that the addition of a mantle support component is not necessary at the investigated wavelengths. The elastic thickness was constrained to be less than 35 km with a best‐fitting average of 15 km, confirming that these regions are consistent with an isostatic regime. The average crustal thickness of the plateaus ranges from 15 to 34 km, and if they are in Airy isostasy, this implies that the global average crustal thickness of Venus is about 20 km. Phoebe Regio is the sole exception of our analysis in that crustal thicknesses that are compatible with the other plateaus are obtained only when a buoyant layer is included. Heat flow estimations computed from the elastic thickness indicate that the plateaus formed under higher heat flow conditions compared to the current global average and could have caused localized melting. Present‐day heat flow predictions suggest that eclogitization could occur where the crust is thickest.

New Insights Into Crustal Properties of Anatolia and Its Surroundings Inferred From P‐Coda Autocorrelation Inversions

AbstractConstraints on crustal and uppermost mantle structure provide key information for understanding the geodynamic processes that have shaped the geological expressions and are currently causing deformation in Anatolia. We apply a novel method of Bayesian inversion of autocorrelated teleseismic P‐wave coda data to retrieve the crustal and uppermost mantle structures beneath Anatolia and southeast Europe. Our inversion provides estimates of Moho depth variations and crustal velocity structure (e.g., Vp, Vs, and Vp/Vs ratio). The Moho architecture in the study area can be summarized by (a) an overall west‐to‐east increase in the Moho depth from Greece to eastern Anatolia, (b) a homogeneously thin crustal structure beneath Greece, (c) complex, small‐scale crustal features and variations in western and central Anatolia, and (d) relatively long‐wavelength variations, but overall thick crust in eastern Anatolia. The apparent relation between the Moho depth variations and suture/fault zones implies a dominant control of structural inheritance on the past deformation in Anatolia. The overall Moho architecture appears to correlate well with the topography in Anatolia, although with some exceptions, in particular at smaller wavelength. These local inconsistencies in the topography‐Moho depth relation suggest a more complex, wavelength‐dependent isostatic state compared to what is expected from simple Airy isostasy. The observed deviations may originate from elastic effects, lithospheric density changes, or sub‐lithospheric dynamic effects. Obvious large lateral variations in Vp, Vs and Vp/Vs ratio estimates in our model can relate to such density variations within the crust especially between tectonic domains.

Estimating the lithospheric flexure of a plate with non-uniform flexural rigidity: a quantitative modelling approach

Lithospheric deformation is a fundamental process in plate tectonics. It is, therefore, critical to determine how the lithosphere responds to geological loads to better understand tectonic processes. The lithosphere can be modelled as the flexure of a thin, elastic plate over long-term (> 105 yr) geological timescales. The partial differential equation for the flexure of an orthotropic plate is used indirectly to calculate theoretical admittance and coherence, which are then compared against the observed admittance and coherence to invert for the non-uniform flexural rigidity (or effective elastic thickness, Te) of the plate. However, the process for accurately recovering variable lithospheric flexure remains unresolved, as the classical lithospheric model may overestimate the deflection of the plate. Here we adopt the classic lithospheric model with applied external and internal loads at the surface and Moho, respectively, and assume that the compensation material is denser than the mantle material beneath the Moho. The lithospheric flexure errors are derived mainly from the Te and Moho recovery errors in this lithospheric model. Synthetic modelling is then performed to analyse the influence of the Te and Moho errors. The analysis of synthetic modelling shows that: (1) the Te error-induced flexure errors exhibit a rippling pattern, and the rippling pattern is broader in high Te regions; (2) the Moho error-induced flexure errors mainly occur in the low Te regions, and applying Airy isostasy theory in low Te regions may still greatly overestimate the lithospheric deformation amplitude; and (3) the lithospheric flexure errors are dominated by the Te and Moho errors in the high and low Te regions, respectively.

Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

SUMMARY In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper I gave a general formulation of Airy isostasy as an elastic loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two examples of which are the constant load applied on the surface in the far past and the constant shape maintained by addition or removal of material at the compensation depth. The former model results in a shape decreasing exponentially with time and has no elastic analogue, whereas the latter (stationary) model is equivalent to a form of elastic isostasy. Viscoelastic and viscous approaches are completely equivalent. If both load and shape vary slowly with time, isostatic ratios look like those of the stationary model. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Mathematica and Fortran codes are available for computing the isostatic ratios of an incompressible body with three homogeneous layers.

Stretching in continental back-arc basins: Insights from subsidence analysis of the Neuquén Basin, Argentina

In the present contribution, we apply forward modelling and subsidence analysis to determine the initial lithospheric structure and the Neuquén Basin central area's stretching factor. The forward models determined that the initial thickness of the crust and the lithosphere would have been around 30 km and 100 km, respectively. Airy and regional isostasy models were considered for the calculation of the tectonic subsidence in outcrops and the subsurface. In both cases, results are very similar due to an elastic thickness of ~3 km for the beginning of the basin, which allows considering the Airy isostasy model as the representative for the analyzed period in the study area. Regarding the stretching factor, the results suggest that the extension varies between 1 and 1.32 for the analyzed area. Although these values seem to be higher than the previous estimations for the Neuquén Basin, they are consistent with those mentioned in the literature for the back-arc basins around the world with similar lithosphere structure and tectonic subsidence values. Furthermore, it should be mentioned that similar tectonic subsidence values could be obtained for the same area considering a lower stretching factor and a westward lithospheric thickening associated with the Neopaleozoic orogeny.

Isostasy with Love – I: elastic equilibrium

SUMMARY Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. On Earth, it is used to subtract from gravity anomalies the contribution of nearly compensated surface topography. On icy moons and dwarf planets, it constrains the compensation depth which is identified with the thickness of the rigid layer above a soft layer or a global subsurface ocean. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. Isostasy should instead be defined either by minimizing deviatoric elastic stresses within the silicate crust or icy shell, or by studying the dynamic response of the body in the long-time limit. In this paper, I implement the first option by formulating Airy isostatic equilibrium as the linear response of an elastic shell to a combination of surface and internal loads. Isostatic ratios are defined in terms of deviatoric Love numbers which quantify deviations with respect to a fluid state. The Love number approach separates the physics of isostasy from the technicalities of elastic-gravitational spherical deformations, and provides flexibility in the choice of the interior structure. Since elastic isostasy is invariant under a global rescaling of the shell shear modulus, it can be defined in the fluid shell limit, which is simpler and reveals the deep connection with the asymptotic state of dynamic isostasy. If the shell is homogeneous, minimum stress isostasy is dual to a variant of elastic isostasy called zero deflection isostasy, which is less physical but simpler to compute. Each isostatic model is combined with general boundary conditions applied at the surface and bottom of the shell, resulting in one-parameter isostatic families. At long wavelength, the thin shell limit is a good approximation, in which case the influence of boundary conditions disappears as all isostatic families members yield the same isostatic ratios. At short wavelength, topography is supported by shallow stresses so that Airy isostasy becomes similar to either pure top loading or pure bottom loading. The isostatic ratios of incompressible bodies with three homogeneous layers are given in analytical form in the text and in complementary software.

Quantification of Erosion and Uplift in a Rising Orogen—A Large-Scale Perspective (Late Tortonian to Present): The Case of the Gibraltar Arc, Betic Cordillera, Southern Spain

The present study deals with the morphometric quantification of erosion and illustrates the uplift component triggered by denudation (isostasy) in the growth and evolution of a rising orogeny by the application of Airy isostasy concepts. The Gibraltar Arc, located in the Western–Central sector of the Betic Cordillera, developed an exceptional geological scenario during the Messinian Salinity Crisis since the thin emerged fringe of the uprising Cordillera disconnected the Atlantic and Mediterranean basins, generating a relevant misbalance and asymmetry in the fluvial erosion between the two slopes of the emergent orogeny. Our analysis was applied to 50 individual drainage basins (spatial isostatic units) in the Western–Central Betic Cordillera, allowing us to obtain individual and bulk estimates for these isostatic parameters. GIS-based numerical estimations were obtained using LiDAR Digital Elevation Models (DEMs) provided by the Spanish Geographical Institute and reconstructed pre-incision surface models obtained from proxy paleo-elevation data, estimated from stratigraphic and geomorphological littoral to shallow marine markers. The obtained values for geophysical relief, denudation plates, erosion/uplift rates and computed accumulated uplift (245–407 ±20 m) are higher for the ancient Mediterranean slope of the orogen. On the contrary, the Atlantic slope presents an accumulated uplift of only 138–236 ±20 m, indicating the strong control of the ancient Messinian Atlantic–Mediterranean water divide. The temporal study of erosion indicates that most of the difference in uplift in the Mediterranean slope was achieved during or soon after the Messinian Salinity Crisis, resulting in mean uplift rates of 0.21 mm/y, but practically null (0.01 mm/y) for the Atlantic slope. The comparison of the geophysical relief models with proxy paleo-elevation data allowed us to assess the current state of the denudation process in the range. The results indicate that, towards the west of the range denudation compensated elevation, and is actively back-feeding isostatic rebound. Therefore, the contribution of external processes to mountain range elevation through isostasy is quantitatively estimated using elevation data. In this case, a relevant part of the surface uplift (50-55%) is undertaken by the orogen. Ultimately, the Messinian Salinity Crisis-related isostatic response to differential denudation may be behind the quaternary westward tilting of Iberia, causing more than 70% of the Peninsula to drain towards the Atlantic.

Is Airy Isostasy Applicable to Icy Moons?

AbstractAiry isostasy is commonly used in planetary science to explain the relationship between crustal thickness variations and topography. Recently, several researchers have questioned the validity of this concept and proposed alternative approaches. Here we examine the accuracy of these approaches by comparing their results with those obtained from the numerical solution of the equations governing the flow in the crust of a small icy moon with a subsurface ocean. We find that the traditional approach based on application of Archimedes' principle with elevations referred to the geoid, provides a satisfactory estimate of crustal thickness for low harmonic degrees. The alternative approach, based on the deviatoric stress minimization, gives correct results for isoviscous model, but its accuracy deteriorates as the viscosity contrast increases. The other alternative approach, in which the deviatoric stress is neglected, is significantly less accurate than other methods, leading to biased results for models with a thick crust.

Geochemical evidence for an orogenic plateau in the southern U.S. and northern Mexican Cordillera during the Laramide orogeny

AbstractPrevious studies of the central United States Cordillera have indicated that a high-elevation orogenic plateau, the Nevadaplano, was present in Late Cretaceous to early Paleogene time. The southern United States Cordillera and northern Mexican Cordillera share a similar geologic history and many of the same tectonic features (e.g., metamorphic core complexes) as the central United States Cordillera, raising the possibility that a similar plateau may have been present at lower latitudes. To test the hypothesis of an elevated plateau, we examined Laramide-age continental-arc geochemistry and employed an empirical relation between whole-rock La/Yb and Moho depth as a proxy for crustal thickness. Calculations of crustal thickness from individual data points range between 45 and 72 km, with an average of 57 ± 12 km (2σ) for the entire data set, which corresponds to 3 ± 1.8 km paleoelevation assuming simple Airy isostasy. These crustal thickness and paleoaltimetry estimates are similar to previous estimates for the Nevadaplano and are interpreted to suggest that an analogous high-elevation plateau may have been present in the southern United States Cordillera. This result raises questions about the mechanisms that thickened the crust, because shortening in the Sevier thrust belt is generally not thought to have extended into the southern United States Cordillera, south of ∼35°N latitude.

Crustal Structure in Alaska From Receiver Function Analysis

AbstractNew maps of crustal thickness and Vp/Vs in Alaska and western Canada were obtained using P receiver functions recorded at 198 stations from the USArray Transportable Array and the Alaska Regional Network. Our results indicate that topography and Moho depth are correlated as crustal thickness varies from 28 to 43 km across Alaska. A thick crust occurs under the mountains in the south and north with relatively thin crust in central Alaska. The deepest crustal root beneath the Brooks Range may have lost its buoyancy based on Airy isostasy. In addition, a buoyant upper mantle is required to support the high topography in east central Alaska. Vp/Vs is determined between 1.7 and 1.8 beneath most of Alaska except a high average of 1.9 in the south central region. We attribute this high Vp/Vs to the underplating of Yakutat and Pacific oceanic crust.

On the pitfalls of Airy isostasy and the isostatic gravity anomaly in general

On the pitfalls of Airy isostasy and the isostatic gravity anomaly in general

A thin, dense crust for Mercury

Crustal thickness is a crucial geophysical parameter in understanding the geology and geochemistry of terrestrial planets. Recent development of mathematical techniques suggests that previous studies based on assumptions of isostasy overestimated crustal thickness on some of the solid bodies of the solar system, leading to a need to revisit those analyses. Here, I apply these techniques to Mercury. Using MESSENGER-derived elemental abundances, I calculate a map of grain density (average 2974 ± 89 kg/m3) which shows that Pratt isostasy is unlikely to be a major compensation mechanism of Mercury's topography. Assuming Airy isostasy, I find the best fit value for Mercury's mean crustal thickness is 26 ± 11 km, 25% lower than the most recently reported and previously thinnest number. Several geological implications follow from this relatively low value for crustal thickness, including showing that the largest impacts very likely excavated mantle material onto Mercury's surface. The new results also show that Mercury and the Moon have a similar proportion of their rocky silicates composing their crusts, and thus Mercury is not uniquely efficient at crustal production amongst terrestrial bodies. Higher resolution topography and gravity data, especially for the southern hemisphere, will be necessary to refine Mercury's crustal parameters further.

Methods For Restoring and Describing Ancient Clinoform Surfaces

AbstractClinoform geometries demarcate a relative change from shallow to deeper waters and are therefore routinely used as paleogeography and paleobathymetry indicators. Distinct segments of the clinoform surface are defined based on their discrete breaks in slope, and these points define parameters which are used to describe and compare clinoform geometries from different basins and ages. In most cases, the breaks in slope are readily interpreted, but placement of the various breaks in slope remains mostly subjective and not strictly uniform. For clinoform geometries with gentle transitions and less accentuated breaks in slope, e.g., mud-prone systems, distinct breaks in slope can vary over many kilometers depending on selection criteria and detection method. The older and more complex history of the investigated strata, the harder it becomes to correctly place the different breaks in slope.This study proposes a common reference frame using an upper regional datum, in which the geometries of ancient clinoform surfaces can be restored. Restoration is performed with standard decompaction techniques, but we compare isostatic compensation using Airy isostasy with different scenarios of flexural support for the sediment load. Regression is used to fit a surface function to georeferenced points along the restored clinoform surface, and derivatives of this surface function are used to objectively and accurately describe and measure parameters such as relief, length, and gradient, in addition to numerically defining the bottomset, foreset, and topset segments of the clinoform surface. This enables comparison with modern counterparts unaltered by postdepositional subsidence and compaction, and the proposed procedure can be applied to 2D profiles from seismic, outcrop, or closely spaced well logs. It can also help in the analyses of 3D surfaces and the trajectory of discrete breaks in slope on successive clinoform surfaces. Accurate reconstructions and objective parameterization directly affect interpretation of shelf–slope sediment partitioning and depositional environment.