Variations In Elastic Thickness Research Articles

Evolution of Impact Basin Gravity Signatures on the Lunar Farside: A Long‐Term Alteration Process

AbstractLunar impact basins are critical markers to understand the early bombardment history. This study focuses on isostatic compensation processes at 16 lunar farside basins, exploring how long‐term alteration processes affect estimates of impactor sizes and timing. Using a lithospheric flexure model, we analyze the isostatically compensated gravity signature of these basins. Our approach is based on previously published basin formation models using the iSALE‐2D shock physics code. Here we investigate how isostatic compensation processes alter the gravity signature using models of basin formation as initial conditions. We compare our results with the present day observed gravity data. We assume that isostatic compensation is the result of flexural deformation of the crust‐mantle boundary with varying lithospheric elastic thicknesses. Our results indicate that the effect of isostatic compensation on the gravity signature varies depending on the thermal conditions at the time of impact. We find that despite this variability, the overall influence of isostatic compensation on the gravity signature is generally moderate to minor. Additionally, our analysis is consistent with previous studies that have shown that the elastic thickness varies across the Moon. Our findings contribute to our understanding of the relationship between basin formation and the thermal evolution of the Moon. The variations in elastic thickness found provide nuanced insights into lunar geological processes and improve our understanding of the early history of the Moon.

A corrected finite-difference scheme for the flexure equation with abrupt changes in coefficient

Abstract. The fourth-order differential equation describing elastic flexure of the lithosphere is one of the cornerstones of geodynamics that is key to understanding topography, gravity, glacial isostatic rebound, foreland basin evolution, and a host of other phenomena. Despite being fully formulated in the 1940s, a number of significant issues concerning the basic equation have remained overlooked to this day. We first explain the different fundamental forms the equation can take and their difference in meaning and solution procedures. We then show how numerical solutions to flexure problems as they are currently formulated are in general potentially unreliable in an unpredictable manner for cases in which the coefficient of rigidity varies in space due to variations of the elastic thickness parameter. This is due to fundamental issues related to the numerical discretisation scheme employed. We demonstrate an alternative discretisation that is stable and accurate across the broadest conceivable range of conditions and variations of elastic thickness, and we show how such a scheme can simulate conditions up to and including a completely broken lithosphere more usually modelled as an end-loaded, single, continuous plate. Importantly, our scheme will allow breaks in plate interiors, allowing, for instance, the creation of separate blocks of lithosphere which can also share the support of loads. The scheme we use has been known for many years but remains rarely applied or discussed. We show that it is generally the most suitable finite-difference discretisation of fourth-order, elliptic equations of the kind describing many phenomena in elasticity, including the problem of bending of elastic beams. We compare the earlier discretisation scheme to the new one in one-dimensional form and also give the two-dimensional discretisation based on the new scheme. We also describe a general issue concerning the numerical stability of any second-order finite-difference discretisation of a fourth-order differential equation like that describing flexure wherein contrasting magnitudes of coefficients of different summed terms lead to round-off problems, which in turn destroy matrix positivity. We explain the use of 128 bit floating-point storage for variables to mitigate this issue.

Lateral Variations in Foreland Flexure of a Rifted Continental Margin: The Aquitaine Basin (SW France)

AbstractRift inheritance can play a key role in foreland basin geometry and behavior. If the foreland basin initiates soon after rifting, thermal cooling can also contribute significantly to subsidence. We investigate the effects of crustal inheritance (Aptian‐Cenomanian rifting) on the evolution of the Campanian to middle Miocene flexural Aquitaine foreland basin, northern Pyrenees, France. Surface and subsurface data define rifted crustal geometry and postrift thermal subsidence. Analysis of Bouguer gravity anomalies coupled with flexural modeling constrains the lateral variations of elastic thickness, plate flexure, and controlling loads. The Aquitaine foreland is divided along‐strike into three sectors. The relative role of surface and subsurface (i.e., buried) loading varies along‐strike, and the elastic thickness values decrease from the northeast (25 km) to the southwest (7 km) where the plate is the most stretched. The eastern foreland crust was not rifted and underwent a simple flexural subsidence in response to orogenesis. The central sector was affected by crustal stretching. Here the basin is modeled by combining topographic and buried loads, with postrift thermal subsidence. In the western sector, the foreland basin was created mainly by postrift thermal subsidence. The eastern and central sectors are separated by the Eastern Crustal Lineament, which is one of a series of inherited transverse faults that segment the orogen.

Strength and elastic thickness variations in the Arabian Plate: A combination of temperature, composition and strain rates of the lithosphere

The Arabian Plate shows a strong asymmetry between its Shield and Platform, in terms of topography, seismic velocity and density structure of the upper mantle. This asymmetry also results in significant rheological differences between these blocks, as revealed by the effective elastic thickness (EET) estimates, obtained using a spectral gravity method. However, these estimates may be biased due to various factors. Therefore, other approaches based on a direct rheological modeling of the lithospheric structure should be employed to verify these results. In this study, we use a recent model of the lithosphere, based on an integrative interpretation of the gravity field and seismic tomography, to correct an initial thermal model obtained from the inversion of seismic velocity, assuming a uniform composition. The results are used together with the most recent crustal model of the Arabian Plate to construct two alternative models of strength and EET of the lithosphere. The first model (Model I) assumes a constant value of 10−15s−1 for the strain rates. In the second model (Model II), we used the strain rates obtained from a global mantle flow model. Model I confirms the asymmetry in the rigidity of the Shield and Platform. In contrast, Model II shows that the influence of the variable strain rates causes a significant increase in the strength and EET of the central and eastern part of the Shield and in contrast to previous studies, reveals that most of the Arabian Plate is a long-term stable tectonic feature, predominantly characterized by large EET values (≥70km).

Variations in elastic thickness and flexure of the Maracaibo block

We estimate the lateral variations of the elastic thickness of the Maracaibo block with a 3D numerical approach by using centered finite differences. The calculation is based on solving the fourth-order partial differential equation that governs the bending of a thin plate fixed on its boundaries (zero displacement) with variable thickness (or elastic thickness for this particular case). An initial plate-load model is built and is iteratively modified to fit the general basement configuration and gravity data. The final result is an elastic thickness map that covers the Maracaibo block and the surrounding sections of the South American plate. It shows that the elastic thickness ranges from 30 km to 18 km with a mean value of 23.6 km and a mode of 26 km. The largest elastic thickness values are associated with the location of the Santa Marta Mountains and the Barinas Apure Basin, while the smallest ones with the Mérida Andes-Maracaibo Basin flexural system. The current basement configuration within the Maracaibo basin, formed as a result of its geodynamic evolution, has affected the mechanical properties of the Maracaibo block near the current Mérida Andes position. The load of the Perijá Range is compensated by a complex stress tensor, and that of the Santa Marta Mountains does not have an isostatic root as it is held by a relatively strong lithosphere.

India–Madagascar paleo-fit based on flexural isostasy of their rifted margins

The present study contributes new constraints on, and definitions of, the reconstructed plate margins of India and Madagascar based on flexural isostasy along the Western Continental Margin of India (WCMI) and the Eastern Continental Margin of Madagascar (ECMM). We have estimated the nature of isostasy and crustal geometry along the two margins, and have examined their possible conjugate structure. Here we utilize elastic thickness (Te) and Moho depth data as the primary basis for the correlation of these passive margins. We employ the flexure inversion technique that operates in spatial domain in order to estimate the spatial variation of effective elastic thickness. Gravity inversion and flexure inversion techniques are used to estimate the configuration of the Moho/Crust–Mantle Interface that reveals regional correlations with the elastic thickness variations. These results correlate well with the continental and oceanic segments of the Indian and African plates. The present study has found a linear zone of anomalously low-Te (1–5km) along the WCMI (~1680km), which correlates well with the low-Te patterns obtained all along the ECMM. We suggest that the low-Te zones along the WCMI and ECMM represent paleo-rift inception points of lithosphere thermally and mechanically weakened by the combined effects of the Marion hotspot and lithospheric extension due to rifting. We have produced an India–Madagascar paleo-fit representing the initial phase of separation based on the Te estimates of the rifted conjugate margins, which is confirmed by a close-fit correlation of Moho geometry and bathymetry of the shelf margins. The matching of tectonic lineaments, lithologies and geochronological belts between India and Madagascar provide an additional support for the present plate reconstruction.

Deformation of an elastic shell with variable thickness: a comparison of different methods

SUMMARY Deformation of the outermost parts of single-plate planetary bodies is often modelled in terms of the response of a spherical elastic shell to surface or basal loading. As the thickness of such elastic lithosphere is usually much smaller than the radius of the body, the deformation is commonly approximated by that obtained for a thin elastic shell of uniform thickness. The main advantage of the thin shell approximation is its simplicity—the solution can be expressed analytically if the thickness of the shell is uniform, but even in the case of a thin shell of variable thickness, when the problem must be solved numerically, the computational costs are much lower than in a fully 3-D case. Here we analyse the error of the thin shell approximation by comparing it with the solution obtained for a shell of finite thickness using finite element methods. Special attention is paid to a shell of variable thickness and, in general, to the effect of elastic thickness variations on local deformation. For a shell of uniform thickness with the outer radius corresponding to Mars, we find that the error in radial displacement at low harmonic degrees (l≤ 20) does not exceed 5 per cent for small shell thicknesses (d≤ 50 km) and 10 per cent for thick shells (d∼ 250 km). Similar accuracy is also found for a shell of variable thickness if the thin shell approximation is used. Our numerical tests indicate that local deformation of a shell is mostly sensitive to the average thickness of the shell in the near zone while the effect of thickness variations in the far zone can be neglected in the first approximation. Consequently, the extremely simple thin shell method, designed for shells of uniform thickness, can be effectively used to obtain a reasonably accurate estimate of deflection even in the case of a shell with varying thickness. Finally, we investigate the deformation of an elastic lithosphere due to viscous flow beneath the shell, and we propose an extension of the concept, recently developed to correct dynamic topography for the effect of an elastic lithosphere, to the case of a shell of variable thickness.

Gravity analysis of Parga and Hecate chasmata: Implications for rift and corona formation

The two largest rift systems on Venus, Parga, and Hecate chasmata contain one third of all coronae. We map variations in elastic thickness and apparent depth of compensation (ADC) in these two regions using the admittance function for gravity and topography. We examine the relationship between rifting and coronae by comparing lithospheric structure with corona characteristics including volcanism, topographic shape, fracture pattern, diameter, and stratigraphic age. At Hecate chasmata, both ADC and elastic thickness correlate with two main rift branches, the fracture style and corona characteristics. Hecate chasma thus appears to be dominated by extensional processes. Parga chasma shows little correlation between lithospheric properties and the location of coronae or rift segments. The ADC at Hecate and Parga chasmata is mostly less than 75–100 km, implying that there is not large‐scale upwelling underlying the rift systems. The variations in the corona population sizes between Parga chasma, which has 131 coronae, and Hecate chasma, with 50 coronae, suggest differences in the evolution of the two rift systems. The much larger population of coronae at Parga contains more small coronae, many of which have relatively low volcanism and post date the rift. Further, many of the small coronae occur in chains and have similar diameters, as predicted by Rayleigh‐Taylor type instabilities. These characteristics suggest that the smaller coronae may form via a later, secondary decompression melting phase. Thus, Hecate chasma may be younger than Parga chasma and could experience a secondary stage of corona formation in the future.

Effective elastic thickness variations along the Andean margin and their relationship to subduction geometry

We present a new map of the spatial variations in effective elastic thickness, Te, along the Andes estimated using Bouguer coherence. The Te variations reflect interactions between subducting slab and preexisting terrane structure. In the forearc, conductive cooling of the continent by the subducting slab exerts primary control on rigidity, resulting in Te that is highest (∼40 km) where the oceanic lithosphere is oldest and coldest (∼20°S). In the central Andes, Te is relatively low (∼20 km) along the volcanic chain and the Altiplano and Puna plateaus. We interpret this weakening to reflect a high geothermal gradient maintained by advective magmatic processes, a shallow and hot asthenosphere, and a very weak lower crust throughout this region. East of the plateaus, high Te delineates underthrusting of the Brazilian shield. Finally, north and south of the plateaus, flat subduction areas are characterized by high Te, high shear wave velocity, thick thermal lithosphere, and low heat flow, indicating that continental lithosphere there is thicker, colder, and stronger. On the basis of these relationships we suggest that variations in slab dip along the margin relate to variations in structure of the continental lithosphere. In particular, we propose that upper plate structure influences the width and viscosity of the asthenospheric wedge, which control the suction moment responsible for the subduction angle at depths ≥70–100 km. For example, when oceanic lithosphere subducts beneath thin continental lithosphere, the low‐viscosity asthenosphere allows the slab to detach from the continent and sink into the mantle at normal angles. However, when oceanic lithosphere subducts close or beneath thick and strong continental lithosphere, the asthenospheric wedge narrows and corner flow drags high‐viscosity mantle from the base of the thick (>150 km), cold continent into the wedge. Suction forces increase with both narrowing of the wedge and its increasing viscosity. We estimate the asthenospheric viscosity underneath thick, cold continents to be ≥1020 Pa s, sufficient to induce flat subduction. Later, after prolonged hydration and weakening of the continent's base, asthenospheric flow into the wedge may resume, allowing the slab to sink again into the mantle at normal angles.

Reappraising elastic thickness variation at oceanic trenches

We reassess the variation of elastic thickness as a function of lithospheric plate age using a global database of bathymetric and free‐air gravity profiles which are perpendicular to oceanic trenches. As in many previous studies, our starting point is the well‐known floating elastic plate model. In order to remove the influence of short‐wavelength features not associated with lithospheric bending, adjacent profiles from 10‐Myr bins have been stacked together to construct average profiles with standard deviations. Each average profile was then inverted in a two‐stage procedure. First, singular value decomposition was used to determine two unknown flexural parameters, together with a regional slope and offset, for any given elastic thickness. This procedure was repeated for a range of elastic thicknesses. Second, residual misfit was plotted as a function of elastic thickness, and the global minimum was identified. This two‐stage procedure makes no prior assumptions about magnitude of the load, size of the bending moment, or whether the elastic plate is broken/continuous. We obtained excellent fits between theory and observation for both bathymetric and gravity profiles from lithosphere with an age range of 0–150 Ma. The shape of the residual misfit function indicates the degree of confidence we have in our elastic thickness estimates. The lower limit of elastic thickness is usually well determined but upper limits are often poorly constrained. Inverse modeling was carried out using a range of profile lengths (250–300, 500, and 700 km). In general, our estimates show no consistent increase of elastic thickness as a function of plate age. This surprising result is consistent with recent reassessments of elastic thickness beneath seamounts and implies either that elastic thickness is independent of plate age or that elastic thickness cannot be measured with sufficient accuracy to reveal such a relationship. Modeling of short free‐air gravity profiles (250–300 km) does tentatively suggest that elastic thickness increases linearly from 5 to 10 km between 0 and 20 Ma and from 10 to 15 km between 20 and 150 Ma. This variation roughly matches the depth to the 200°C isotherm which corresponds to an homologous temperature of 0.4 for wet peridotite. Unfortunately, for longer profile lengths, there is no temporal dependence, and elastic thicknesses vary considerably for all plate ages. Bathymetric profile modeling yields similar results although uncertainties are larger.

Global mapping of crustal and lithospheric thickness on Venus

We have produced a high‐resolution global admittance map of Venus using a spatiospectral localization technique, calculating 64,800 admittance spectra evenly spaced in latitude and longitude. We grouped the admittance spectra into 35 classes that we inverted for elastic, crustal, and lithospheric thickness using bottom‐loading, top‐loading, and short‐wavelength top‐loading models with long‐wavelength bottom‐loading (“hot spot”) models. Our best fit models identify 17 classes consistent with top loading (40% of the surface), 7 with bottom loading (39%), and 4 with a long‐wavelength bottom‐loading model (15%). The remaining seven classes (6% of the surface) generally had large‐amplitude top‐loading signatures that could not be fit with our models. For the classes that were successfully modeled the estimated range of crustal (0–90 km) and elastic thickness (0–100 km) is larger than results for most previous studies, primarily because of the incorporation of bottom loading. Nearly half of the planet has elastic thickness <20 km, which we cannot distinguish from isostasy, suggesting that these regions are tectonically inactive. A key finding is that the lithospheric properties typically vary over scales of 1000 km or less except in some plains and crustal plateau regions. Both the scale and range of crustal and elastic thickness variations indicate that Venus remains an active planet and that geologic processes may be more complex than previously recognized. In many regions the correlation with surface geology is not obvious, and this suggests that deformation of the lower lithosphere and crust may occur with little surface manifestation.

Variations in elastic thickness in the Canadian Shield

We have compared different spectral methods (the standard windowed Fourier transform, the multitaper method (MTM), and the maximum entropy method (MEM)) to determine the coherence between Bouguer gravity and topography and estimate the variations of the effective elastic thickness (Te) of the lithosphere. These methods differ significantly in spatial resolution (1000 to 2000 km) determined by the width of the windows required to resolve the wavelength of transition from low to high coherence. The tests with synthetic data show that the standard deviation on elastic thickness estimates is high with the three methods but that the mean value obtained by the maximum entropy is close to the input value, while the other methods underestimate the elastic thickness.In the Canadian Shield, the effective elastic thickness values vary from ≈40 km to >100 km over distances less than the width of the moving window. There is no clear geographical or geological pattern in these variations as high and low elastic thickness values are found near the edge as well as in the center of the continent, and in all provinces regardless of their age. Correlation between Te and the heat flow field is weak. The values of Te being much higher beneath Hudson Bay than the Williston Basin are consistent with models of basin evolution and seismic estimates of mantle temperatures.

Effects of lithospheric properties on the formation of Type 2 coronae on Venus

Over 500 coronae occur on Venus. A recent survey defined Type 2 coronae as those with <50% complete fracture annuli. This paper synthesizes the results from a statistical study of the size, topographic morphology and geologic setting of the entire corona population and a study of the gravity and topography of the 32 Type 2 coronae resolved in the gravity data. Using the estimated lithospheric properties, loading signature, and geologic characteristics, we examine the factors controlling corona morphology, size and fracture completeness (Type 1 versus Type 2). We find no difference between lithospheric properties in the plains and fractures belts. Nearly half of the Type 2 coronae studied are isostatically compensated, and probably inactive. This implies that the final stage of a corona may have a wide range of topographic morphologies. Elastic thickness has no correlation with diameter and therefore does not limit corona size. The ratio of crustal thickness to plume diameter does not control morphology as a function of size, as predicted by a spreading drop model. However, rim‐only coronae, which are predicted to form via isostatic rebound of crust thickened by delamination, are supported by a density interface. Isostasy and delamination of the lower lithosphere are likely to have a greater effect on corona formation, and possibly in understanding the evolution of the Venusian lithosphere, than variations in elastic thickness. The role of isostasy in the formation of Type 2 coronae suggests that surface fractures may be reduced due to low strain rates.

Spatial variations of flexure parameters over the Tibet–Quinghai plateau

We investigate the Tibet–Quinghai plateau and the Tarim basin in terms of spatial variations of the elastic thickness ( T e) in the frame of the thin plate flexure model. The method of investigation makes use of a convolutive method, which allows high spatial resolution of the flexure properties and overcomes some of the problems tied to the spectral admittance/coherence methodologies. We study the relation between the topographic and subsurface loads and the observed crust–mantle interface (CMI) undulations, the latter having been obtained from gravity inversion. The gravity data used for the inversion are a unique set of high quality data available over the Chinese part of the plateau, and constitute the highest resolution grid today available in this impervious area. The gravity inversion is constrained by results from the study of the propagation of seismic waves. The two extensive sedimentary basins, the Tarim and the Qaidam basins, are modeled by forward gravity modeling. The oscillations of the CMI obtained from the gravity inversion agree well with those expected by loading the thin plate model of spatially variably elastic thickness with the surface and subsurface loads. It is found that the modeling of the sedimentary basins is essential in the flexure analysis. The spatial variations of elastic thickness correlate with the extensions of the different terrains that constitute the plateau. Most of the Tibet plateau has low T e, varying in the bounds 10–30 km, with lower values in the Qiangtang terrain, where the T e reaches 8 km. The Tarim and the Qaidam basins, Precambrian platforms overlain by sediments, are rigid and have a T e of up to 110 km and 70 km, respectively. The flexural analysis distinctly discerns the Tibet plateau, with thick crust, part of which is molten, from the cratonic areas, the Tarim and Qaidam basins, which though of thinner crust, act as undeformable rigid blocks.

Conditions for flow in the continental crust

Earthquake focal depth distributions and effective elastic thickness variations on the continents suggest that in old cold regions such as shields, the lower continental crust can be stronger than the upper mantle, and imply that the upper mantle can flow even when the lower crust does not. However, in other places substantial flow in the lower crust does occur, particularly near extensional metamorphic core complexes. We suggest that the lower crust only flows when its viscosity is significantly reduced, either by heating from igneous intrusions or by the addition of water. In both cases, the important characteristics of the flow are a consequence of the limited time over which the viscosity reduction occurs. The timescale is controlled either by conductive cooling of intrusions, or by the separation of melt from its matrix, which removes the water.

Elastic Thickness Estimates for Venus Using Line of Sight Accelerations from Magellan Cycle 5

The elastic thickness, T e, for various regions of Venus is estimated by comparing the observed line of sight (LOS) acceleration of the Magellan spacecraft with that predicted using a spherical harmonic representation of the topography, to degree and order 360. At long wavelengths (typically longer than about 500 km) the transfer function between the topography and gravity, or admittance, usually has a flat spectrum with a magnitude of between 20 and 50 mGal Km −1, which is most likely due to convective support. In particular, the topographic highs associated with Beta, Phoebe, Bell, and Eistla are thought to be dynamically supported. At shorter wavelengths, the admittance increases, suggesting a component of flexural support. The elastic thicknesses are constrained by fitting theoretical admittance curves to the observed short wavelength values for the admittance. Results from Magellan cycle 5 show evidence of regional variations in elastic thickness between about 19 and 29 km, with a mean value of around 21–23 km, assuming a crustal thickness of 16 km and a density of 2670 kg m −3. The observed variations in admittance between different regions are unlikely to be due to differences in crustal thickness or density, and probably represent real variations in T e. The values obtained are similar to those from an identical analysis using cycle 4 data. Estimates of the elastic thickness of the Ovda and Alpha regions are unreliable, probably because the topography is not well determined. No reliable estimates of elastic thickness could be made from cycle 6 data where the altitude of the spacecraft was higher than about 300 km, due to the reduction in short wavelength signal amplitude with altitude.

Elastic thickness of the lithosphere in the Central Canadian Shield

We have used the coherence between Bouguer gravity and topography to determine the elastic thickness (Te) of the lithosphere in central Canada. In order to improve the resolution, we have estimated the spectra with the maximum entropy method. The variations in elastic thickness delineate three main regions: (1) The Interior Platform where Te varies between 25 and 50 km; (2) The Shield includes several high rigidity cores, in particular in the Trans‐Hudson orogen and in the Hearne Province where Te >80 km; (3) The Hudson Bay basin has an elastic thickness between 50 and 70 km with higher values in the eastern part.The results suggest that Te is controlled by the thermal regime in the platform. There is no difference in Te between the Proterozoic and Archean Provinces of the Shield. In the platform, the elastic thickness is lowest where sediments are thickest, indicating that low rigidity has amplified the subsidence of the basin.

High heat flow in the trans‐Hudson Orogen, Central Canadian Shield

Nine new heat flow and heat production measurements are presented for the Trans‐Hudson Orogen, an Early Proterozoic Province between the Archean Superior and Hearne Provinces of the Canadian Shield. Seventeen heat flow values now available in this region range between 23 and 81 mW.m−2. The highest value is anomalous and is due to heat refraction effects in and around highly conducting quartzite formations. When refraction effects are accounted for, the Flin Flon and Thompson belts appear as distinct crustal blocks with different mean heat flow values of 42±3(s.d.) mW.m−2 and 54±8(s.d.) mW.m−2. Such differences can be accounted for by variations in the amount of felsic rocks in the uppermost 15 km of the crust. Comparison between heat flow and elastic thickness studies show that variations in elastic thickness of the lithosphere are not thermally induced.

Thermomechanical evolution of oceanic fracture zones

A fracture zone (FZ) model is constructed from existing models of the thermal and mechanical evolution of the oceanic lithosphere. As the lithosphere cools by conduction, thermal and mechanical boundary layers develop and increase in thickness as (age)1/2. Surface expressions of this development, such as topography and deflection of the vertical (i.e., gravity field), are most apparent along major FZ's because of the sharp age contrast. A simple model, including the effects of lateral heat transport but with no elastic layer, predicts that variations in seafloor depth and deflection of the vertical will become increasingly smooth and ultimately disappear as the FZ ages. Observations, however, show that both the FZ topography and the deflection of the vertical remain sharp as the FZ evolves. These two observations, as well as the observed asymmetry in deflection of the vertical profiles across the Udintsev, Romanche, and Mendocino FZ's, are explained by including a continuous elastic layer in the model. The asymmetry in deflection of the vertical is a consequence of elastic thickness variations across the FZ. Modeling also shows that the evolution of the FZ topography is extremely sensitive to the initial thermal structure near the ridge‐transform intersection. Model geoid steps and their development with age are used to access techniques for measuring geoid offsets across FZ's. Reasonable step estimation techniques will underestimate the overall step amplitude by up to 50%. This implies that abnormally thin thermal boundary layers, derived from studies of geoid height versus age, are not required by the data.