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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Evaluating the Feasibility of Using Strain Measured During Sinusoidal Rate Pumping Tests to Characterize an Aquifer

Pumping tests with sinusoidal variation in pumping rate have been proposed as a method for improving aquifer characterization. These tests can interrogate a larger aquifer volume than slug tests and they can be more sensitive to small variations in drawdown. Current methods of using sinusoidal variations of rate are based on measuring pressure signals from the reservoir or aquifer, which requires access to monitoring wells. An alternative approach has been developed that measures the strain in the vadose zone instead of pressure in the reservoir. An instrument has been developed at Clemson University that can measure small strains using optical fiber sensors, and we propose that it can be used to measure strain during sinusoidal pumping tests. The objective of this project is to evaluate the feasibility of measuring and interpreting the vertical strain in the vadose zone generated during a sinusoidal rate pumping tests to estimate aquifer and/or overburden properties. Pumping tests were performed at a site with a water table at 9 m and saturated saprolite from 9 to 30m depth. Sinusoidal pumping tests in the saprolite used different pumping amplitudes and periods while pressure was measured at three piezometers and vertical strain was measured in the vadose zone from 1 to 7 m depth. The delay time of the pressure increased linearly with distance, and it increased with the square root of the period, while the amplitude of the pressure decreased with distance and increased with amplitude. Vertical strain in the vadose zone varied with the same period as the pumping rate and the delay times were similar to those for pressures measured at similar radial distances. Delay times for the strain increased with an increasing propagation of the strain field. The hydraulic diffusivity was estimated using delay times for pressure and strain, and the results were compared with the values estimated from a constant-rate pumping test. The hydraulic diffusivity from the constant rate test was 0.039 m2/sec, whereas it was 0.053 (±0.05) m2/sec and 0.035 (±0.03) m2/sec from the pressure data and 0.08 (±0.022) m2/sec and 0.035 (±0.001) m2/sec from the strain data from sinusoidal tests of various periods and amplitudes. There is no statistical difference among these values. This study indicates that strain measurements in the vadose zone can be used to estimate aquifer properties during sinusoidal pumping tests.

Blais, Riley↗
DOE OSTI2021

In Situ Synchrotron X-ray Micro-Diffraction Investigation of Elastic Strains in Laminated Ti-Al Composites

Spatially resolved elastic strains in the bulk interior of a laminated Ti-Al metal composite were studied during in situ tensile loading at strains up to 1.66% by a synchrotron-based micro-diffraction technique, namely differential aperture X-ray microscopy (DAXM). For both Al and Ti grains, deviatoric elastic strains were estimated based on polychromatic X-ray microbeam diffraction, while lattice strains along the normal direction of the tensile sample were directly measured using monochromatic X-ray microbeam diffraction. The estimated deviatoric strains show large spatial variations, and the mean values are consistent with the external loading conditions, i.e., increasing tensile strain along the tensile direction and increasing compressive strain along the sample normal with increasing loading. The directly measured lattice strains also show large spatial variations, although the magnitude of this variation is smaller than that for the estimated deviatoric strain. The directly measured lattice strains in Ti grains are largely consistent with the external loading, whereas those in Al grains are in contradiction with the external loading. The causes of the experimental results are discussed and related to both the laminated microstructure of the composite material and the limitations of the techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Residual strain and microstructure evolution in 316L stainless steel fabricated by hybrid additive/subtractive manufacturing

The extreme thermal gradients in additive manufacturing (AM) result in residual strains. Subsequent machining operations can relieve the AM strains but can introduce additional strains. AM and machining on the same platform, also called interleaving, during hybrid manufacturing has been shown to improve productivity. However, the impacts of these operations on the resulting residual strains are not well understood. In this investigation, neutron diffraction was used to measure residual strains in hybrid manufactured 316L stainless steel where blown-powder laser directed energy deposition (DED), and machining operations were interleaved in 1-inch intervals. We observe that the dominant texture developed during AM, resulting from different spot sizes and deposition parameters, significantly affects residual strain evolution. A dominant <011> texture along the build direction does not show any strain localization during interleaved deposition and machining whereas a dominant <001> texture shows strong tensile strain localization consistent with the pauses for machining at the end of AM step. Using coolant during machining can further alter the residual strain evolution. Our work shows that a combination of AM parameters and machining strategy can be used to influence the nature and magnitude of residual strains in components fabricated using convergent manufacturing technologies.

Hybrid manufacturing↗
DOE OSTI2026

Strain-Modified Raman Responses in Monolayer MoS 2 Nanobubbles Resolved at 5 nm

The formation of nanoscale bubbles is an unavoidable consequence during the transfer of two-dimensional materials onto target substrates, driven by van der Waals interactions at the interface. While often viewed as imperfections, these nanoscale bubbles have garnered considerable scientific interest due to the substantial in-plane strain gradients they induce, which in turn give rise to a variety of intriguing optoelectronic effects, particularly in semiconducting transition metal dichalcogenides. Determining and analyzing the strain distribution within nanobubbles at the nanoscale is crucial for advancing our understanding of these underlying strain-induced effects. Here, we present a high-resolution scanning tunneling microscopy-based tip-enhanced Raman spectroscopic investigation of localized nanoscale strain distribution within the nanobubbles formed between monolayer MoS 2 and Au interface. By employing cryogenic temperature (78 K), we successfully differentiate the nanoscale Raman signatures between nanobubble edge and pristine MoS 2 . We verify a maximum tensile strain of ∽1.15–1.34% at the nanobubble edge, which gradually diminishes toward the center, yielding a cross-sectional strain profile consistent with a doughnut-shaped distribution. Furthermore, we report to achieve ∽5 nm spatial resolution in probing such edge-localized strain within the nanobubble. In addition, comparative average strain analysis of such MoS 2 nanobubbles is conducted via geometric mechanistic analysis such as membrane and nonlinear plate theories, providing key insight into the geometric nature near the bubble edge. Our work provide fundamental information about strain-induced nanoscale chemical understanding of 2D materials on the nanometer scale, paving the way for practical applications of nanobubbles in strain-engineered optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗
DOE OSTI2023

Adaptive sampling for accelerating neutron diffraction-based strain mapping *

Abstract Neutron diffraction is a useful technique for mapping residual strains in dense metal objects. The technique works by placing an object in the path of a neutron beam, measuring the diffracted signals and inferring the local lattice strain values from the measurement. In order to map the strains across the entire object, the object is stepped one position at a time in the path of the neutron beam, typically in raster order, and at each position a strain value is estimated. Typical dwell times at neutron diffraction instruments result in an overall measurement that can take several hours to map an object that is several tens of centimeters in each dimension at a resolution of a few millimeters, during which the end users do not have an estimate of the global strain features and are at risk of incomplete information in case of instruments outages. In this paper, we propose an object adaptive sampling strategy to measure the significant points first. We start with a small initial uniform set of measurement points across the object to be mapped, compute the strain in those positions and use a machine learning technique to predict the next position to measure in the object. Specifically, we use a Bayesian optimization based on a Gaussian process regression method to infer the underlying strain field from a sparse set of measurements and predict the next most informative positions to measure based on estimates of the mean and variance in the strain fields estimated from the previously measured points. We demonstrate our real-time measure-infer-predict workflow on additively manufactured steel parts—demonstrating that we can get an accurate strain estimate even with 30%–40% of the typical number of measurements—leading the path to faster strain mapping with useful real-time feedback. We emphasize that the proposed method is general and can be used for fast mapping of other material properties such as phase fractions from time-consuming point-wise neutron measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Influence of chemical strains on the electrocaloric response, polarization morphology, tetragonality, and negative-capacitance effect of ferroelectric core-shell nanorods and nanowires

Using Landau-Ginzburg-Devonshire (LGD) approach, we proposed the analytical description of the influence of chemical strains on spontaneous polarization and the electrocaloric response in ferroelectric core-shell nanorods. We postulate that the nanorod core presents a defect-free single-crystalline ferroelectric material, and elastic defects are accumulated in the ultrathin shell, where they can induce tensile or compressive chemical strains. Finite-element modeling (FEM) based on the LGD approach reveals transitions of domain-structure morphology induced by chemical strains in the Ba Ti O 3 nanorods. Namely, tensile chemical strains induce and support the single-domain state in the central part of the nanorod, while the curled domain structures appear near the unscreened or partially screened ends of the rod. The vortexlike domains propagate toward the central part of the rod and fill it entirely, when the rod is covered by a shell with compressive chemical strains above some critical value. The critical value depends on the nanorod sizes, aspect ratio, and screening conditions at its ends. Both analytical theory and FEM predict that the tensile chemical strains in the shell increase the nanorod polarization, lattice tetragonality, and electrocaloric response well above the values corresponding to the bulk material. The physical reason for the increase is strong electrostriction coupling between the mismatch-type elastic strains induced in the core by chemical strains in the shell. Comparison with earlier XRD data confirmed an increase of the tetragonality ratio in tensile Ba Ti O 3 nanorods compared to the bulk material. Obtained analytical expressions, which are suitable for the description of strain-induced changes in a wide range of multiaxial ferroelectric core-shell nanorods and nanowires, can be useful for strain engineering of advanced ferroelectric nanomaterials for energy storage, harvesting, electrocaloric applications, and negative capacitance elements. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
DOE OSTI2025

Geometric transport signatures of strained multi-Weyl semimetals

The minimal coupling of strain to Dirac and Weyl semimetals, and its modeling as a pseudogauge field has been extensively studied, resulting in several proposed topological transport signatures. In this work, we study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudogauge field for any winding number larger than one. Here we focus on the double-Weyl semimetal as an illustrative example to show that the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Specifically, the Fermi surface of the double-Weyl semimetal acquires nematic order. By extending chiral kinetic theory for such nematic fields, we determine the effective gauge fields acting on the system and show how strain induces anisotropy and affects the geometry of the semiclassical phase space of the double-Weyl semimetal. Further, the strain-induced deformation of the Weyl nodes results in transport signatures related to the covariant coupling of the strain tensor to the geometric tensor associated with the Weyl nodes giving rise to strain-dependent dissipative corrections to the longitudinal as well as the Hall conductance. Thus, by extension, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures. Further, we highlight that the most general way to view strain is as a symmetry-breaking field rather than a pseudogauge field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Uncovering hidden bias in neutron diffraction residual strain measurements

When calculating residual strain via neutron or X-ray diffraction, uncertainties propagated from the peak fit are often inadequate to describe the true scatter of measurements about a singular strain state, such as one that should describe a macroscopic continuum. Because diffraction is inherently a selective process, orientation-dependent scatter arises from the sub-sampling of strong microstructure and strain gradients. This paper investigates the appropriateness of propagated uncertainties with reference to their original intention, i.e. noise about a mean value. Thirty-six unique orientations of strain measurements are taken at multiple locations within an additive friction-stir deposition component with fine-scale gradients (∼200 µm) of plastic strain, texture and residual elastic strain. Multiple strain and stress calculation pathways are compared: direct substitution of three measurements into Hooke's law, direct inversion of any six unique orientations into the strain state tensor and thirty-six measurement least-squares estimation. For the last two cases, the appropriateness of the uncertainty interval is statistically evaluated on the basis of a physical constraint: common agreement under the strain transformation law. For this sample, the direct inversion of six measurements retains a conservative estimate of the uncertainty. However, propagated uncertainties in the least-squares solution greatly underestimate the true experimental scatter. A simple pathway to estimate appropriate uncertainty intervals is suggested. These results demonstrate that the interpretation of uncertainty in residual strain is strongly dependent on intrinsic sample-dependent effects, and that oversampling orientations and statistical analysis can give more accurate results with realistic uncertainties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A New Residual Strain Mapping Program Using Energy Dispersive X-Ray Diffraction at the Advanced Photon Source

Here, the ability to non-destructively map the residual strain field inside an engineering component is important for predicting its fatigue life or developing processing methods to prevent failure or enhance performance. In this paper, we describe a new residual strain mapping program at the Advanced Photon Source, Argonne National Laboratory. The new program is based on energy dispersive x-ray diffraction (EDXRD). It is capable of non-destructively penetrating a several- cm thick polycrystalline sample fabricated from engineering alloys using high-energy x-rays and measuring the residual strain field with mm or better spatial resolution and approximately ±1 x 10 -4 strain resolution. A multi-element detector array is employed to measure multiple strain components simultaneously. The residual strain mapping setup is augmented with a high-energy tomography capability, allowing precise alignment of the material volume of interest for residual strain mapping and providing a complementary view of the structure to understand the measured strain field. These measurement capabilities are demonstrated using several strain mapping examples ranging from polycrystalline structural alloys to biological materials. We also provide some guidance for the future users of the program for a successful residual strain mapping experiment. We are expanding the capabilities of the new setup with various in situ capabilities including thermo-mechanical loading.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Neutron Diffraction Analysis of Residual Strain in High-Pressure Die Cast A383 Engine Blocks

The residual strains in three high-pressure die cast A383 engine blocks were measured using neutron diffraction. Residual strains and stresses can be generated during high-pressure die casting process due to high thermal gradients and may cause fatigue failure or dimensional distortion. Neutron diffraction can measure the residual strain distributions deep inside castings with complex geometries, because neutrons can penetrate substantially more material than x-rays. In this paper, the residual strains (in the axial and hoop directions) along the whole cylinder bridge of high-pressure die cast A383 engine blocks in as-cast and heat-treated conditions were measured by neutron diffraction methods. The effect of heat treatment on the distribution and magnitude of residual strains was also investigated. The results indicate that the residual strain in the cylinder bridge is tensile in both the axial and hoop components for both the as-cast and the heat-treated engine blocks. The residual strain in the hoop direction is bigger in magnitude than the residual strain in the axial direction. Heat treatment significantly relaxes the residual strain in the axial direction but only slightly relaxes the residual strain in the hoop direction.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

We report the fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10 -3 s -1 to 10 3 s -1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2022

High strain-rate compression behavior of polymeric rod and plate Kelvin lattice structures

The compressive high strain-rate behavior of polymeric Kelvin lattice structures with rod-based or plate-based unit cells was investigated through experimental techniques and finite element simulations. Polymeric lattice structures with 5x5x5 unit cell geometries were manufactured on the millimeter scale using vat polymerization additive manufacturing and tested at low (0.001/s) and high (1000/s) strain-rates. High strain-rate experiments were performed and validated for a viscoelastic split-Hopkinson (Kolsky) pressure bar system (SHPB) coupled with high-speed imaging and digital image correlation (DIC). Experimental results at both low and high strain-rates show the formation of a localized deformation band which was more prevalent in low relative density specimens and low strain-rate experiments. Strain-rate effects of lattice specimens strongly correlate with effects of the base polymer material; both bulk polymer and lattice specimen demonstrated strain-rate hardening, strain-rate stiffening, and decreased fracture strain under dynamic loading. Results show mechanical failure properties and energy absorption depended strongly on the relative density of the lattice specimen and exhibited distinct scaling between relative density and geometry type (rod, plate) and loading rate. High relative density plate-lattices demonstrated inferior mechanical properties to rod-lattices; however, there exists a critical relative density for a given mechanical property (17%- 28%) below which plate-lattices outperform rod-lattices of similar mass. As a result, high strain-rate explicit finite element simulations were performed and showed good agreement with the mechanical failure trends and deformation modes observed in the experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Strain-Induced Shifts in Defective Graphite Phonon Modes Predicted by Density Functional Theory

Carbon fiber composites have gained attention as a structural material because of their high strength-to-weight ratio, and understanding the effect of defects on reactivity and mechanical properties is important for the longevity and safety of the composite. Although it is known that strain causes the underlying graphitic vibrational modes to redshift, it is not clear how strain may alter reactivity and defect-induced vibrational changes. To investigate the strain-induced phonon changes of defective carbon fiber composites, density functional theory calculations of graphite are used, including intercalated hydrogen and fluorine defects. By comparing changes in the bond lengths, formation energies, and phonon density of states for uniaxially and biaxially strained graphite, strain was found to generally make defect formation more favorable and the specific behavior changes are dependent on the strain direction and defect identity. Specifically, intercalated fluorine phonons are more sensitive to strain than hydrogen intercalation phonons, and strain applied along the zigzag direction alters the calculated properties more than strain along the armchair direction. Finally, these results highlight the importance of understanding the microstructural effect of deviations from the ideal material because small changes in strain or defect type can significantly alter the behavior of the carbon fiber composite core.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Direct strain correlations at the single-atom level in three-dimensional core-shell interface structures

Abstract Nanomaterials with core-shell architectures are prominent examples of strain-engineered materials. The lattice mismatch between the core and shell materials can cause strong interface strain, which affects the surface structures. Therefore, surface functional properties such as catalytic activities can be designed by fine-tuning the misfit strain at the interface. To precisely control the core-shell effect, it is essential to understand how the surface and interface strains are related at the atomic scale. Here, we elucidate the surface-interface strain relations by determining the full 3D atomic structure of Pd@Pt core-shell nanoparticles at the single-atom level via atomic electron tomography. Full 3D displacement fields and strain profiles of core-shell nanoparticles were obtained, which revealed a direct correlation between the surface and interface strain. The strain distributions show a strong shape-dependent anisotropy, whose nature was further corroborated by molecular statics simulations. From the observed surface strains, the surface oxygen reduction reaction activities were predicted. These findings give a deep understanding of structure-property relationships in strain-engineerable core-shell systems, which can lead to direct control over the resulting catalytic properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Strain-insensitive intrinsically stretchable transistors and circuits

An all-elastomer strain engineering approach, which uses patterned elastomer layers with tunable stiffnesses, can be used to create intrinsically stretchable transistor arrays with a device density of 340 transistors cm -2 and strain insensitivity of less than 5% performance variation when stretched to 100% strain. Intrinsically stretchable electronics can form intimate interfaces with the human body, creating devices that could be used to monitor physiological signals without constraining movement. However, mechanical strain invariably leads to the degradation of the electronic properties of the devices. Here we show that strain-insensitive intrinsically stretchable transistor arrays can be created using an all-elastomer strain engineering approach, in which the patterned elastomer layers with tunable stiffnesses are incorporated into the transistor structure. By varying the cross-linking density of the elastomers, areas of increased local stiffness are introduced, reducing strain on the active regions of the devices. This approach can be readily incorporated into existing fabrication processes, and we use it to create arrays with a device density of 340 transistors cm -2 and a strain insensitivity of less than 5% performance variation when stretched to 100% strain. We also show that it can be used to fabricate strain-insensitive circuit elements, including NOR gates, ring oscillators and high-gain amplifiers for the stable monitoring of electrophysiological signals.

42 ENGINEERING↗
DOE OSTI2025

Enabling room-temperature ferromagnetism in few-layered MoS 2 films via strain engineering

Strain engineering presents a promising pathway for modulating the physical properties of two-dimensional (2D) transition metal dichalcogenides materials. Here, in this study, we investigate the strain-induced magnetic behavior of diamagnetic MoS 2 films prepared by the DC magnetron sputtering technique. By applying +1% tensile strain to few-layered MoS 2 films (∼3.5 nm), we observe the emergence of room-temperature ferromagnetism with a magnetization saturation of about ∼130 emu/cm 3 , in stark contrast to bulk films (∼40 nm), which remain diamagnetic under similar conditions. Raman spectroscopy reveals a pronounced reduction in the intensity and the splitting of the E′ mode in 1% strained few-layered films, indicating a possible bond elongation and symmetry breaking under tensile stress. Additionally, x-ray absorption spectroscopy at the Mo M 3 edge further confirms a strain-induced electronic structure modification in few-layered films, with no corresponding shift observed in bulk counterparts. Moreover, the strain-induced magnetic and structural changes are largely reversible upon strain release. We attribute the origin of ferromagnetism in few-layered films to the combined influence of tensile strain and defect-assisted bond weakening, which facilitates crystal field transitions within the Mo 4d orbitals. These findings demonstrate that strain engineering can effectively induce and modulate magnetism in 2D materials, providing opportunities for developing strain-controlled spintronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Crustal Strain Rates in the Western United States and Their Relationship with Earthquake Rates

Abstract We present a suite of strain rate models for the western United States based on geologic and geodetic data. The geologic data consist of Quaternary fault-slip rates and the geodetic data consists of a new compilation of Global Positioning System (GPS) velocities derived from continuous, semicontinuous, and campaign measurements. We remove postseismic deformation from the GPS time series in order for our geodetic strain rate model to best capture the interseismic strain accumulation rate. We present models based on either geologic or geodetic data, but also create a hybrid model. Although there are some differences between the models, the large-scale features are the same, with the noticeable exception for the Pacific Northwest where interseismic strain is naturally more distributed than the long-term strain release. We also present a map of earthquake rate densities based on mainshocks, and the result has similar spatial features similar to the strain rate models (at least in the southwestern United States). We perform a general correlation analysis between strain rate and seismicity rate (south of Cascadia) and find a change in linearity between seismicity and strain rates from slow to faster deforming areas with seismicity rates relatively lower for the latter. The extent of that change depends a bit on assumptions made on the declustering and completeness of the catalog, but the finding of a change in slope is robust across the different strain rate models. Linearity for all areas is only expected when Gutenberg–Richter parameters and parameters involved in the conversion from strain to moment rate are uniform across the study area. We discuss these qualifications, but find no single satisfactory explanation for our observation. Moreover, when considering a rather short time and space, theoretical considerations of sampling from a power-law distribution actually predict there to be a power law instead of a linear relationship, generally consistent with our observation.

Geochemistry & Geophysics↗