rename backstress url to be more informative

content/blog/diede-backstress-2025/index.md → content/blog/dislocations-transient-creep/index.md

@@ -15,15 +15,15 @@ Traditionally, transient creep in the upper mantle has been attributed to diffus
 
 We performed high-temperature (900–1200°C), high-pressure (\~5 GPa), and high-stress forced-oscillation experiments on polycrystalline olivine in a multi-anvil apparatus called a deformation-DIA. In these experiments we applied a sinusoidal force to our samples. We then used the bright X-rays produced by the APS to measure the deformation (also referred to as ‘strain’) of our samples from digital image correlation of radiographs. We measured the stress that the rock experienced by diffracting X-rays through the crystal lattice of the sample and converting the elastic lattice strains to stresses using Hooke’s law. The time delay between the imposed sinusoidal stress and the measured sinusoidal strain is directly related to a quantity known as the inverse quality factor, *Q*\-1, that is commonly used by seismologists to quantify the attenuation of seismic waves traveling through the mantle after earthquakes. By changing the stress amplitude of the imposed oscillations we were able to observe that *Q*\-1 increased with amplitude (Figure 1), which is diagnostic of attenuation produced by dislocations.
 
-![Figure 1 shows a logspace graph of attenuation as a function of amplitude in which measurments from our deformation-DIA experiments indicate a linear positive correlation at amplitudes of 200 to 250 MPa with attenuation values between 1 and 10.](/images/blog/diede-backstress-2025/invQvA.png "Figure 1: Positive correlation between attenuation and stress amplitude observed in one of our experiments at 1150°C that featured 4 steps of increasing amplitude, all at a period of 300 seconds. Symbology represents measurements from different lattice planes of olivine and two different olivine samples that were deformed in the same experiment.")
+![Figure 1 shows a logspace graph of attenuation as a function of amplitude in which measurments from our deformation-DIA experiments indicate a linear positive correlation at amplitudes of 200 to 250 MPa with attenuation values between 1 and 10.](/images/blog/dislocations-transient-creep/invQvA.png "Figure 1: Positive correlation between attenuation and stress amplitude observed in one of our experiments at 1150°C that featured 4 steps of increasing amplitude, all at a period of 300 seconds. Symbology represents measurements from different lattice planes of olivine and two different olivine samples that were deformed in the same experiment.")
 
 To confirm that the trend we observed could not be attributed to changes in grain size or crystallographic orientations over the course of our experiments, we characterized the microstructure of our samples before and after deformation by electron backscatter diffraction using a scanning electron microscope. These analyses confirmed that the evolution of grain size and crystallographic orientations could not explain our observations. Therefore, our measurements of *Q*\-1 provide a first-of-its-kind dataset to compare to the predictions of the plastic-anisotropy and backstress models.
 
 Because there are no analytical solutions to the constitutive equations of these models, we performed numerical simulations of our experiments, solving the equations for the strain produced by a sinusoidally varying stress. Figure 2 presents a comparison of the attenuation from our experiments to the attenuation predicted by the plastic-anisotropy and backstress models. The comparison clearly illustrates that the plastic-anisotropy model underpredicts the amount of attenuation observed in our experiments, especially at lower temperatures. As such, we conclude that the plastic-anisotropy of olivine did not dominate the behavior of the olivine in our experiments.
 
-![Figure 2 presents a comparison of deformation-DIA data obtained at 1150 and 900 degrees Celcius to predictions of the plastic anisotropy and backstress models at a period of 300 seconds that indicates that attenuation in our deformation-DIA experiments exceeds predictions of the plastic-anisotropy model by up to two orders of magnitude at 900 degrees celcius and is within error of those predictions at 1150 degrees celcius. The data fall within error of the predictions of the backstress model for both temperatures. Attenuation data fall between 0.1 and 10 over amplitudes between 100 and 1000 MPa.](/images/blog/diede-backstress-2025/ModelComparison.png "Figure 2: Comparison of experimental data (symbols), and predictions of the backstress and plastic anisotropy models (solid and dotted lines, respectively) at a period (*p*) of 300 s. Colors refer to temperatures and shaded areas represent the approximate error of experimental results due to the temperature-uncertainty in the deformation-DIA apparatus.")
+![Figure 2 presents a comparison of deformation-DIA data obtained at 1150 and 900 degrees Celcius to predictions of the plastic anisotropy and backstress models at a period of 300 seconds that indicates that attenuation in our deformation-DIA experiments exceeds predictions of the plastic-anisotropy model by up to two orders of magnitude at 900 degrees celcius and is within error of those predictions at 1150 degrees celcius. The data fall within error of the predictions of the backstress model for both temperatures. Attenuation data fall between 0.1 and 10 over amplitudes between 100 and 1000 MPa.](/images/blog/dislocations-transient-creep/ModelComparison.png "Figure 2: Comparison of experimental data (symbols), and predictions of the backstress and plastic anisotropy models (solid and dotted lines, respectively) at a period (*p*) of 300 s. Colors refer to temperatures and shaded areas represent the approximate error of experimental results due to the temperature-uncertainty in the deformation-DIA apparatus.")
 
 
-![Figure 3 presents a logspace graph of attenuation as a function of frequency on which solid lines (one each for 1300, 1400, and 1500 degrees Celcius) indicate the prediction of the linearized backstress model that peak at an attenuation of approximately 0.3 around 0.1 to 1 mHz and have a slope of -1 in logspace at higher frequencies. The position of the peak increases approximately one order of magnitude in frequency for a temperature increase of 100 degrees. The prediction for 1400 degrees celcius matches the attenuation values of the PREM and NoMelt models given a grain size of 1 mm, a bias stress of 3 MPa, and a stress amplitude of 100 kPa. Dashed lines indicate the attenuation predicted by the extended Burgers model of Qu (2022) that fall about 1.5 orders of magnitude below the attenuation values of the PREM and NoMelt models. The extended Burgers model of Qu (2022) is much less sensitive to temperature than the linearized backstress model.](/images/blog/diede-backstress-2025/Extrapolation.png "Figure 3: Extrapolation of the backstress model to conditions of seismic-wave propagation in the upper mantle (*d* is grain size, \\(\sigma_{\mathrm{dc}}\\) is the tectonic background stress, \\(\sigma_{\mathrm{A}}\\) is the amplitude of the seismic wave, increasing temperature is indicated by colors of increasing warmth, \\(\omega\\) is frequency). Seismological constraints on attenuation in upper oceanic mantle (PREM, NoMelt) are plotted for comparison, as well as an extrapolation of the recent recalibration of a popular grain-boundary sliding model (dashed lines).")
+![Figure 3 presents a logspace graph of attenuation as a function of frequency on which solid lines (one each for 1300, 1400, and 1500 degrees Celcius) indicate the prediction of the linearized backstress model that peak at an attenuation of approximately 0.3 around 0.1 to 1 mHz and have a slope of -1 in logspace at higher frequencies. The position of the peak increases approximately one order of magnitude in frequency for a temperature increase of 100 degrees. The prediction for 1400 degrees celcius matches the attenuation values of the PREM and NoMelt models given a grain size of 1 mm, a bias stress of 3 MPa, and a stress amplitude of 100 kPa. Dashed lines indicate the attenuation predicted by the extended Burgers model of Qu (2022) that fall about 1.5 orders of magnitude below the attenuation values of the PREM and NoMelt models. The extended Burgers model of Qu (2022) is much less sensitive to temperature than the linearized backstress model.](/images/blog/dislocations-transient-creep/Extrapolation.png "Figure 3: Extrapolation of the backstress model to conditions of seismic-wave propagation in the upper mantle (*d* is grain size, \\(\sigma_{\mathrm{dc}}\\) is the tectonic background stress, \\(\sigma_{\mathrm{A}}\\) is the amplitude of the seismic wave, increasing temperature is indicated by colors of increasing warmth, \\(\omega\\) is frequency). Seismological constraints on attenuation in upper oceanic mantle (PREM, NoMelt) are plotted for comparison, as well as an extrapolation of the recent recalibration of a popular grain-boundary sliding model (dashed lines).")