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Viscoelastic dislocation theory is important to understanding fundamental geodynamics and validating numerical models in the study of earthquake deformation. Available mathematical solutions differ in assumed Earth geometry and formulation of gravity terms, but the main challenge they commonly face is Inverse Laplace Transform (ILT). Limitations in previously used ILT methods tend to degrade the performance and/or accuracy of the solutions. To overcome these limitations, we have derived new Green's functions for a layered spherical Earth based on the Fixed‐Talbot ILT method. The new solution uses a precise density‐gravity relation, includes pre‐stress advection, buoyancy, and self‐gravitation, invokes the bi‐viscous Burgers rheology, and yields deformational and gravitational changes both at the surface and in the interior of the Earth. The Fixed‐Talbot ILT method, which involves a left‐open parabolic integration path in the complex plane, greatly improves computing efficiency and allows convenient use of a large number of Earth layers. Comparison with other existing solutions demonstrates the excellent performance of the new solution. Taking the postseismic deformation of the 2004 Sumatra Mw 9.2 earthquake as an example, we illustrate how to integrate numerically our Green's functions to represent realistic slip distribution over a three‐dimensionally curved fault. The combination of computational efficiency, mathematical completeness in modeling gravitational effects, adaptability to any radial structure of the Earth, and ability to provide results at any depth including the surface enables a powerful tool for forward and inverse modeling of viscoelastic earthquake cycles in a self‐gravitating spherical Earth. Plain Language Summary: Because of Earth's viscoelastic behavior, earthquake‐induced deformational and gravitational changes evolve with time, providing important geodetic signals for the study of earthquake processes. Precise mathematical solutions to describe these changes can be obtained for laterally uniform Earth models, but the efficiency, adaptability, and/or accuracy of the solutions are often hindered by limitations in a key step of deriving these solutions: the Inverse Laplace Transform (ILT). In this work, we derive a new solution by using an advanced method, termed the Fixed‐Talbot method, for the ILT. Our solutions differ from most other available solutions also in the precise formulation of the density‐gravity relation and full inclusion of all the gravity effects. By numerically comparing with other existing solutions, we demonstrate the excellent performance and advantages of the new solution. Using the postseismic deformation of the 2004 Sumatra Mw 9.2 earthquake as an example, we illustrate how to handle arbitrary slip distributions on a three‐dimensionally curved subduction megathrust by numerically integrating the point‐source solution. The new solution provides a powerful and convenient tool for modeling earthquake cycles. Key Points: New solution for deformation and gravitation response of self‐gravitating, viscoelastic, and layered spherical Earth to shear dislocationFixed‐Talbot method for inverse Laplace transform improves efficiency, adaptability, and accuracy of earthquake deformation modelingExamples provided to demonstrate solution performance for complex Earth stratification and distributed slip on 3D‐curved megathrust fault [ABSTRACT FROM AUTHOR]

Following great subduction earthquakes, postseismic deformation of coastal areas shows consistent seaward motion but complex vertical deformation. Understanding both the horizontal and vertical components in the same geodynamic framework presents challenges. Here, by modeling short‐term (a few years) postseismic viscoelastic relaxation (VER) and afterslip following synthetic and real subduction earthquakes, we demonstrate that the complexity of the vertical deformation can be explained in simple terms. Along a margin‐normal profile, VER results in an up‐down‐up trisegment, long‐wavelength pattern common to most megathrust earthquakes, including near‐trench uplift, midway subsidence, and near‐arc uplift, with locations controlled by coseismic fault slip. The magnitude of the first two segments is controlled mainly by oceanic mantle viscosity, and the third by mantle wedge viscosity. In contrast with VER, afterslip results in an up‐down bimodal pattern of variable wavelengths specific to individual earthquakes. Its site‐specific and heterogeneous nature is primarily responsible for the complexity in vertical deformation, but its effect can be adequately modeled using a simple elastic model. If the coast is near the megathrust rupture zone, variable combinations of the VER and afterslip effects lead to either uplift or subsidence. If the coast is in the near‐arc segment of VER deformation, uplift usually occurs. Modeling the common VER process enables the identification of site‐specific afterslip, which helps to understand the mechanism of afterslip in the context of the broad spectrum of fault slip behavior. Our results also have important implications to deciphering coastal paleoseismic records to constrain coseismic versus postseismic deformation of ancient earthquakes. Plain Language Summary: How the Earth surface deforms after great subduction earthquakes yields important information on the physical properties of the mantle and the megathrust fault. A few years after these earthquakes, postseismic deformation of coastal areas shows consistent seaward motion but complex vertical deformation. Our work is focused on understanding this complexity. The postseismic deformation consists of two components. One is due to the gradual response of the mantle, called viscoelastic relaxation, and the other is due to the continuing slip of the megathrust around the rupture zone, called afterslip. We show that the two components have different spatiotemporal characteristics governed by different parameters of the subduction zone system. The combined effects of the two components at different distances from the earthquake rupture zone explain the observed complexity. Understanding the mechanisms of postseismic deformation helps us to understand mantle and fault properties and to properly interpret geological data that constrain deformation due to ancient earthquakes. Key Points: Viscoelastic relaxation (VER) after great subduction earthquakes generates a common up‐down‐up postseismic deformation pattern from trench to arcSite‐specific, heterogenous afterslip causes complexity of coastal vertical postseismic deformation, depending on coast‐rupture distanceSeparately modeling VER and afterslip helps to understand rheology, fault slip behavior, and paleoseismic records [ABSTRACT FROM AUTHOR]

Subduction megathrust ruptures that breach the trench, such as in the 2011 M = 9 Tohoku‐oki earthquake, can be very tsunamigenic. However, whether buried ruptures are intrinsically less tsunamigenic has not been fully investigated. Here, we conduct this investigation by studying the mechanics of seafloor deformation and the resultant tsunami runup. With a trench‐breaching rupture, deformation is dominated by the rigid‐body translation of the frontal upper plate, and seafloor uplift is enhanced by the horizontal motion of the sloping seafloor. With a buried rupture, the rigid‐body motion is reduced, but the shortening of the upper plate due to seaward slip termination causes elastic thickening to enhance tsunamigenic seafloor uplift. By combining a finite‐element deformation model and a shallow‐water equation tsunami model, we systematically test various subduction zone geometrical and slip parameters to study the trade‐off between rigid‐body translation and elastic thickening in causing seafloor uplift and tsunami runup. To isolate the effect of slip depth, we compare scenarios with the same peak slip and rupture width. We find that very shallow ruptures, including those breaching the trench, are generally less tsunamigenic than deeper ruptures. Given peak slip, tsunamigenic potential is maximized if the rupture is not too shallow or too deep but is buried to moderate depths. Our model tests using variable hypothetical rupture depths suggest that, with a slip magnitude as large as in the 2011 Tohoku‐oki earthquake, tsunami runups as high as the observed would occur even if the rupture were fully buried. Plain Language Summary: During subduction earthquakes, sudden seafloor deformation due to megathrust slip raises seawater to generate tsunamis. If the slip breaches the trench, seawater is raised by the seaward motion of the sloping seafloor. If the near‐trench part of fault refuses to slip, in a scenario called buried rupture, the seafloor will bulge to raise seawater. Here we combine computer models of seafloor deformation and tsunami propagation to study how the two types of rupture control tsunami runup. We find that, given slip size and location, their tsunamigenic potential is similar owing to a trade‐off mechanism. With buried rupture, tsunami generation is weakened by lessened motion of the sloping seafloor but strengthened by increased seafloor bulging. The effect is the opposite for a trench‐breaching rupture. We also find that if a rupture is buried to an optimal moderate depth, the bulging effect and tsunami size are maximized. These findings clarify that the key reason for a large tsunami is how large, not just how shallow, the megathrust slip is. This knowledge helps to understand why some recent megathrust earthquakes, including the 2011 M = 9 Tohoku‐oki earthquake, were so tsunamigenic. For tsunami hazard assessment, the tsunamigenic potential of buried ruptures should not be underrated. Key Points: Tsunamigenic seafloor uplift due to megathrust slip reflects a trade‐off between rigid‐body translation and elastic thickeningModerately buried slip is usually more tsunamigenic than trench‐breaching slip of the same size, because of enhanced elastic thickeningWhat determines tsunami size, such as in the 2011 Tohoku‐oki tsunami, is mainly how large, not just how shallow, the offshore slip is [ABSTRACT FROM AUTHOR]

Dense Global Navigation Satellite System (GNSS) observations enable the development of megathrust interseismic locking models for the southern Kurile subduction zone where many great earthquakes have occurred. Inversion of these data assuming uniform elastic Earth has yielded slip deficit rates that are unreasonably high and/or full locking depth that is unreasonably large. Using the finite element method, here we construct a new Kurile locking model that includes interseismic viscoelastic stress relaxation and non‐uniform compliance of the elastic upper plate. Inverting the same geodetic data using the new subduction zone model alleviates the previously seen unreasonable features in inferred megathrust locking state. In the new model, full locking extends to shallower depths than the downdip limit of some large megathrust earthquakes including the 2003 Mw 8.0 Tokachi‐oki earthquake, supporting the notion of the shrinking of the locked area before the earthquakes and/or propagation of seismic rupture into creeping areas as previously predicted by friction or dynamic rupture models. By modeling the effects of a few recent M 8 earthquakes, we show that postseismic transients of recent earthquakes, although second‐order, should be addressed in deriving megathrust locking models. The locking state near the trench cannot be resolved by the land‐based GNSS data regardless of the improved model rheology and structure, although independent observations, such as slow earthquakes, may be used to speculate on the near‐trench locking state in various part of the margin in the absence of seafloor geodetic observations. Key Points: Viscoelastic mantle relaxation and non‐uniform compliance of upper plate are of first order importance to interseismic deformationInvoking relaxation and non‐uniform compliance in geodetic inversion leads to shallower megathrust locking than in previous modelsImproved model structure and rheology do not improve resolution of near‐trench locking state, demonstrating need for seafloor geodesy [ABSTRACT FROM AUTHOR]

Localized geodetic deformation of arctan shape around locked strike‐slip faults is widely reported, but there are also important exceptions showing distributed deformation. Understanding the controlling mechanism is important to hazard assessment and geodynamic analysis. Here we use simple finite element viscoelastic earthquake cycle models to investigate the basic mechanics of this process. Our models feature a vertical strike‐slip fault in an elastic layer overlying a viscoelastic substrate of Maxwell or Burgers rheology, with or without a low‐viscosity shear zone representing deeper extension of the fault. We demonstrate that the primary control on the localization of interseismic deformation is the recurrence interval of past earthquakes. Given viscosity, shorter recurrence leads to greater localization, regardless of the rheological model used. The presence of a low‐viscosity deep fault does not change this conclusion, although it tends to lessen localization by promoting faster postseismic stress relaxation. Distributed deformation, although less reported, is a natural consequence of very long recurrence and in theory should be as common as localized deformation. We think that the apparent propensity of the latter is likely associated with the much greater quantity and better quality of geodetic observations from higher‐rate and shorter‐recurrence faults. Our results also show the important role of nearby earthquakes along the same fault. For faults of relatively short recurrence, frequent ruptures of nearby segments, modeled using a migrating rupture sequence, further enhance localization. For faults of very long recurrence, faster near‐fault deformation induced by a recent earthquake may give a false impression of localized interseismic deformation. Key Points: Shorter earthquake recurrence intervals lead to more localized interseismic deformation; long recurrence leads to distributed deformationRecent rupture of currently locked segment, or of other nearby segments of the same fault, enhances localized deformationApparent universality of localized deformation may owe to abundance of data from shorter‐recurrence faults with recent earthquakes [ABSTRACT FROM AUTHOR]

We determine late Holocene (past 4 kyr) vertical land motion (VLM) rates from relative sea level observations along the coastline of western North America and compare these to contemporary (decadal‐scale) rates inferred from Global Positioning System data. The residual rates (contemporary minus late Holocene) indicate uplift at most locations, which likely reflects short‐term signals associated with the Cascadia subduction earthquake cycle and processes that were recently activated. Regarding the latter, we model and remove the signals associated with ground water extraction and twentieth‐century glacier retreat, which have a significant influence in, respectively, California and southern British Columbia. We interpret the remaining signal as being dominated by interseismic deformation associated with the locking of the Cascadia megathrust. A preliminary comparison of this signal with output from a model of interseismic deformation indicates good agreement at most locations within a range of key model parameter values. This agreement is particularly encouraging as the locking model is based on the inversion of only horizontal land motion observations. Considering the data‐model fit at all locations, preference was found for models featuring nearly full locking to a relatively shallow depth (<30 km), although the locking state preference is variable along the coast and not strong. The best fitting parameter set varies considerably from site to site, and no set of parameter values was able to capture the residual VLM rates in northwestern Vancouver Island. Our study indicates that the residual VLM data provide useful constraints for megathrust locking models of Cascadia subduction. Key Points: Contemporary and late Holocene rates of vertical land motion are quantified along the western coast of North AmericaContemporary minus Holocene rates are interpreted in terms of recent surface loading and interseismic deformationVertical land motion observations provide useful constraints on locking models of the Cascadia subduction zone [ABSTRACT FROM AUTHOR]

Rupture‐zone averaged static stress drop in the 2011 M=9 Tohoku‐Oki earthquake was less than 5 MPa, but it caused a stress reversal in most of the offshore forearc, although the reversal is less well constrained far offshore by earthquake mechanisms because of 20‐ to 30‐km errors in event depths. Using a finite element model of force balance, we demonstrate that the stress reversal unambiguously indicates (1) a very weak subduction megathrust and (2) very low differential stresses in the forearc. Prior to the reversal, the upper limit of megathrust strength could not be determined from forearc stresses. In the forearc, effects of megathrust friction and gravity are in a fragile balance, and stresses fluctuate around a neutral state in earthquake cycles. If most of the offshore forearc is to be compressive before but extensional after the earthquake, the effective friction coefficient of the megathrust must be ~0.032. Under low differential stresses associated with megathrust weakness, the forearc is generally well below yielding. Applying the concepts of dynamic Coulomb wedge, we show that the inner wedge, and by inference farther landward, stays stable throughout earthquake cycles. The outer wedge is stable most of the time but may occasionally enter a critical state during great earthquakes; its geometry suggests that complete stress drop of the underlying shallow megathrust is unlikely to have happened. We reason that the occurrence of earthquakes and active faulting under low stress in the stable forearc is due to heterogeneities in structure, stress, and/or pore fluid pressure. Key Points: Stress reversal in offshore forearc due to the Tohoku‐Oki earthquake indicates weak subduction megathrust with effective friction ~0.032Most of the forearc is under very low differential stress and is stable throughout subduction earthquake cycles except the outer wedgeEarthquakes and active faulting in a strong and stable forearc reflect heterogeneities in structure, stress, and/or pore fluid pressure [ABSTRACT FROM AUTHOR]

In a viscoelastic Earth, stresses slowly built up due to fault locking are relaxed concurrently during the entire interseismic period. This interseismic stress relaxation causes crustal deformation much farther away from the locked fault than can be explained using elastic models that neglect the relaxation. Here we develop a viscoelastic geodetic inversion model to address this problem at Cascadia. We invert ~500 horizontal velocity vectors based on continuous and campaign geodetic measurements over the past two decades. Ambiguities arising from long‐term rotation of upper‐plate crustal blocks are addressed by test‐correcting the geodetic velocities with two different block‐motion models. Fault back slip (i.e., slip deficit) Green's functions are derived using a Maxwell viscoelastic finite element model with realistic subduction zone structure and megathrust geometry. The preferred model features a narrow and shallow megathrust locked zone, consistent with earlier thermorheological reasoning. For an elastic model to fit the data to the same fidelity, megathrust locking has to extend to much greater depths. However, even with the viscoelastic model, the land‐based geodetic data still cannot resolve whether there is some creep (incomplete locking) in the shallowest part of the megathrust far offshore. Neither can the land data fully resolve along‐strike variations of the locking state. These ambiguities can be resolved only when adequate seafloor geodetic data are obtained. Key Points: Widespread interseismic deformation reflects viscoelastic relaxation but may be interpreted as deep locking by elastic modelsViscoelastic geodetic inversion models indicate megathrust locking at shallow depths at CascadiaRegardless of Earth rheology, near‐trench ambiguity of locking state can be resolved only by future seafloor observations [ABSTRACT FROM AUTHOR]

Abstract: After a great subduction earthquake, viscoelastic stress relaxation causes opposing motion of Earth's surface in the strike‐normal direction, with the dividing boundary located roughly above the downdip termination of the rupture. As the effect of the viscoelastic relaxation decays with time, the effect of the relocking of the megathrust becomes increasingly dominant to cause the dividing boundary to migrate away from the rupture zone, eventually leading to wholesale landward motion. The evolution of the postseismic deformation is controlled not only by mantle viscosity but also by the size of the earthquake. Large coseismic fault slip induces greater stress perturbation that takes a longer time to relax, and a greater rupture length along‐strike results in a pattern of postseismic viscous mantle flow less efficient for stress relaxation. Here we employ spherical‐Earth finite element models of Burgers rheology to quantify postseismic deformation processes for ten 8.0 ≤ Mw ≤ 9.5 subduction earthquakes. Using geodetic data as constraints, we reconstruct spatiotemporally continuous evolution of the postseismic deformation following each earthquake. We comparatively examine the “reference time” when the dividing boundary of the opposing motion passes through the map view location of the 50‐km depth contour of the subduction interface. Our results suggest a positive dependence of the reference time on earthquake size, although site‐ and/or event‐specific factors such as subduction rate, afterslip, and postseismic locking state of the megathrust also affect the evolution. Upper mantle viscosities constrained by available geodetic observations show somewhat different values between subduction zones located far from one another. [ABSTRACT FROM AUTHOR]