Monte Carlo Inversion Technique Research Articles

Comparison of Holocene temperature reconstructions based on GISP2 multiple-gas-isotope measurements

Nitrogen and argon stable isotope data obtained from ancient air in ice cores provide the opportunity to reconstruct past temperatures in Greenland. In this study, we use a recently developed fitting-algorithm based on a Monte Carlo inversion technique coupled with two firn densification and heat diffusion models to fit several Holocene gas-isotope data measured at the GISP2 ice core and infer temperature variations.We present for the first time the resulting temperature estimates when fitting δ15N, δ40Ar, and δ15Nexcess as individual targets. While the comparison between the reconstructions using δ15N and δ40Ar shows high agreement, the use of δ15Nexcess for temperature reconstruction is problematic because the statistical and systematic data uncertainty is higher and has a particular impact on multi-decadal to multi-centennial signals.Our analyses demonstrate that T(δ15N) provides the most robust estimate. The T(δ15N) estimate is in better agreement with Buizert et al. (2018) than with the temperature reconstruction of Kobashi et al. (2017). However, all three reconstruction strategies lead to different temperature realizations.

Trans-dimensional Markov chain Monte Carlo inversion of sound speed and temperature: Application to Yellow Sea multichannel seismic data

Abstract Understanding the oceanographic features of the sea water is important for ecosystem studies. In seismic oceanography, structures are imaged and physical properties, such as the sound speed, temperature, or salinity, are calculated using multichannel seismic data. These data provide high lateral resolution information at the full depth of the ocean. However, when the sea water depth is shallow, such as in shallow basins, conventional seismic oceanographic data processing techniques might not provide accurate inversion results for oceanographic properties or accurate images of the sea water structures. In this study, we use the trans-dimensional Markov chain Monte Carlo inversion technique, which assumes both the dimension and properties of the model as unknowns in inversion problems, to estimate the sound speed and define the locations of layer interfaces of the Yellow Sea, which is a semi-enclosed shallow basin. The ocean temperature is calculated using the estimated sound speed and the sound speed-temperature relationship. The estimated sound speed and temperature are compared with the true sound speed and temperature obtained from an expendable bathythermograph. The result shows that the proposed algorithm correctly estimates the sound speed and temperature and accurately images the oceanic structure. As a result, the trans-dimensional Markov chain Monte Carlo inversion can accurately identify the distribution of the Yellow Sea bottom cold water.

Global Analysis of Experimental Data on the Rheology of Olivine Aggregates

AbstractFollowing the reanalysis of individual experimental runs of some widely cited studies (Jain et al., 2018, https://doi.org/10.1002/2017JB014847), we revisit the global data analysis of Korenaga and Karato (2008, https://doi.org/10.1029/2007JB005100) with a significantly improved version of their Markov chain Monte Carlo inversion. Their algorithm, previously corrected by Mullet et al. () to minimize potential parameter bias, is further modified here to estimate more efficiently interrun biases in global data sets. Using the refined Markov chain Monte Carlo inversion technique, we simultaneously analyze experimental data on the deformation of olivine aggregates compiled from different studies. Realistic composite rheological models, including both diffusion and dislocation creep, are adopted, and the role of dislocation‐accommodated grain boundary sliding is also investigated. Furthermore, the influence of interrun biases on inversion results is studied using experimental and synthetic data. Our analysis shows that existing data can tightly constrain the grain‐size exponent for diffusion creep at ∼2, which is different from the value commonly assumed (p = 3). Different data sets and model assumptions, however, yield nonoverlapping estimates on other flow‐law parameters, and the flow‐law parameters for grain boundary sliding are poorly resolved in most cases. We thus provide a few plausible candidate flow‐law models for olivine rheology to facilitate future geodynamic modeling. The availability of more data that explore a wider range of experimental conditions, especially higher pressures, is essential to improve our understanding of upper mantle rheology.

A three-step maximum a posteriori probability method for InSAR data inversion of coseismic rupture with application to the 14 April 2010Mw6.9 Yushu, China, earthquake

[1] We develop a three-step maximum a posteriori probability method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic deformation solutions of earthquake rupture. The method originates from the fully Bayesian inversion and mixed linear-nonlinear Bayesian inversion methods and shares the same posterior PDF with them, while overcoming difficulties with convergence when large numbers of low-quality data are used and greatly improving the convergence rate using optimization procedures. A highly efficient global optimization algorithm, adaptive simulated annealing, is used to search for the maximum of a posterior PDF (“mode” in statistics) in the first step. The second step inversion approaches the “true” solution further using the Monte Carlo inversion technique with positivity constraints, with all parameters obtained from the first step as the initial solution. Then slip artifacts are eliminated from slip models in the third step using the same procedure of the second step, with fixed fault geometry parameters. We first design a fault model with 45° dip angle and oblique slip, and produce corresponding synthetic interferometric synthetic aperture radar (InSAR) data sets to validate the reliability and efficiency of the new method. We then apply this method to InSAR data inversion for the coseismic slip distribution of the 14 April 2010 Mw 6.9 Yushu, China earthquake. Our preferred slip model is composed of three segments with most of the slip occurring within 15 km depth and the maximum slip reaches 1.38 m at the surface. The seismic moment released is estimated to be 2.32e+19 Nm, consistent with the seismic estimate of 2.50e+19 Nm.

Assessing a multilayered dynamic firn-compaction model for Greenland with ASIRAS radar measurements

AbstractA method to assess firn compaction using data collected with the Airborne SAR (Synthetic Aperture Radar)/Interferometric Radar Altimeter System (ASIRAS) is developed. For this, we develop a dynamical firn-compaction model that includes meltwater retention. Based on the ASIRAS data, which show internal layers as annual horizons in the uppermost firn, the method relies on inferring the age/ depth (internal layers) information from the radar data using a Monte Carlo inversion technique to tune in parallel both the firn model and the atmospheric forcing parameters (temperature and accumulation). The model is validated against two firn cores, and it is shown that applying both firn densities and age/ depth information for the inversion gives the most accurate understanding of model biases. The method is then applied to a 67 km section of the EGIG line forced by atmospheric output from a regional climate model using only age/depth information in the inversion step. The layers traced by the ASIRAS data are modeled with a root-mean-square error of 9 cm, which is within the estimated error of the layer tracing. This gives us confidence in applying observed annual layering from firn radar data to assess firn compaction; however, the study also indicates that our firn-model-tuning parameters are site-dependent and cannot be parameterized by temperature and accumulation alone.

The Medieval Climate Anomaly in Greenland ice core data

Temperature signals in ice core data Greenland ice core data can be used to derive information on past climatic conditions in the Greenland area. Recently, Vinther et al. (2010) demonstrated a high correlation between δ18O data and Greenland coastal temperature observations even on seasonal timescales, reaffirming the ability of ice core δ18O to capture local temperatures, first proposed by Dansgaard (1954). The Vinther et al. (2010) analysis of the seasonal ice core δ18O data showed that the winter δ18O contains the strongest temperature signal, and that even annual average Greenland temperatures are more accurately captured in the winter δ18O rather than annual average δ18O data. This surprising fact is partly explained by the observation that Greenland winter temperatures are much more variable than summer temperatures and thus dominate the annual average variability (Vinther et al., 2010). Past Greenland climatic conditions can also be derived directly from Greenland ice core borehole temperature observations, by solving the equation of heat conduction in moving ice and firn (Dahl-Jensen et al., 1998). Using a Monte Carlo inversion technique, Dahl-Jensen et al. (1998) derived temperature histories from both southern and central Greenland from high precision borehole temperature measurements obtained at the DYE-3 and GRIP ice core drill sites. A third way of estimating past Greenland temperature conditions is to measure isotopes on nitrogen and argon trapped in air-bubbles within the ice (Severinghaus et al., 1998). These gases undergo a temperature dependent mass fractionation in the snow column before the air-bubbles are formed in the ice, thus retaining a retrievable temperature signal.

Differences in optical properties between healthy and pathological human colon tissues using a Ti:sapphire laser: an in vitro study using the Monte Carlo inversion technique

The purpose of the study is to analyze and compare differences in the optical properties between normal and adenomatous human colon tissues in vitro at 630-, 680-, 720-, 780-, 850-, and 890-nm wavelengths using a Ti:sapphire laser. The optical parameters of tissue samples are determined using a double integrating sphere setup at seven different laser wavelengths. The inverse Monte Carlo simulation is used to determine the optical properties from the measurements. The results of measurement show that the optical properties and their differences vary with a change of laser wavelength for normal and adenomatous colon mucosa/submucosa and normal and adenomatous colon muscle layer/chorion. The maximum absorption coefficients for normal and adenomatous human colon mucosa/submucosa are 680 nm, and the minimum absorption coefficients for both are 890 nm. The maximum difference of the absorption coefficients between both is 56.8% at 780 nm. The maximum scattering coefficients for normal and adenomatous colon mucosa/submucosa are 890 nm, and the minimum scattering coefficients for both are 780 nm. The maximum difference of the scattering coefficients between both is 10.6% at 780 nm. The maximum absorption coefficients for normal and adenomatous colon muscle layer/chorion are 680 nm, and the minimum absorption coefficients for both are 890 nm. The maximum difference of the absorption coefficients between both is 47.9% at 780 nm. The maximum scattering coefficients for normal and adenomatous colon muscle layer/chorion are 890 nm, and the minimum scattering coefficients for both are 680 nm. The maximum difference of the scattering coefficients between both is 9.61% at 850 nm. The differences in absorption coefficients between normal and adenomatous tissues are more significant than those in scattering coefficients.

Near-infrared optical properties of ex vivo human uterus determined by the Monte Carlo inversion technique

The optical properties, absorption (µa) and reduced scattering coefficient (µs´), of ex vivo human myometrium and leiomyoma (fibroid) have been determined by the Monte Carlo inversion technique over the wavelength range 600 - 1000 nm. This region is currently of interest for new, minimal-access, surgical laser procedures such as photodynamic therapy (PDT) for abnormalities of the uterus, and interstitial laser photocoagulation (ILP) for the thermal ablation of fibroids. In the region 630 - 675 nm (corresponding to PDT), the optical coefficients of myometrium are µa = 0.041±0.012 mm-1 and µs´ = 1.37±0.19 mm-1. For the wavelength range 800-1000 nm (associated with infrared lasers for ILP), the optical coefficients of fibroid were found to be µa = 0.020±0.003 mm-1 and µs´ = 0.56±0.03 mm-1. Overall, the optical properties of fibroid were found to be lower than myometrium, and this was attributed to the differences in both anatomy and vascularity. The results show that PDT for ablation of the uterine endometrium is most unlikely to affect any tissues beyond the myometrium, and that the region around 800 nm is the most effective for ablation of fibroids using ILP as the penetration depth of light is greatest at this wavelength.

Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique

The absorption and transport scattering coefficients of caucasian and negroid dermis, subdermal fat and muscle have been measured for all wavelengths between 620 and 1000 nm. Samples of tissue 2 mm thick were measured ex vivo to determine their reflectance and transmittance. A Monte Carlo model of the measurement system and light transport in tissue was then used to recover the optical coefficients. The sample reflectance and transmittance were measured using a single integrating sphere `comparison' method. This has the advantage over conventional double-sphere techniques in that no corrections are required for sphere properties, and so measurements sufficiently accurate to recover the absorption coefficient reliably could be made. The optical properties of caucasian dermis were found to be approximately twice those of the underlying fat layer. At 633 nm, the mean optical properties over 12 samples were and for absorption coefficient and and for transport scattering coefficient for caucasian dermis and the underlying fat layer respectively. The transport scattering coefficient for all biological samples showed a monotonic decrease with increasing wavelength. The method was calibrated using solid tissue phantoms and by comparison with a temporally resolved technique.

Estimating Lithospheric Properties at Atla Regio, Venus

Magellan spherical harmonic gravity and topography models are used to estimate lithospheric properties at Atla Regio, Venus, a proposed hotspot with dynamic support from mantle plume(s). Global spherical harmonic and local representations of the gravity field share common properties in the Atla region in terms of their spectral behavior over a wavelength band from ∼2100 to ∼700 km. The estimated free-air admittance spectrum displays a rather featureless long-wavelength portion followed by a sharp rise at wavelengths shorter than about 1000 km. This sharp rise requires significant flexural support of short-wavelength structures. The Bouguer coherence also displays a sharp drop in this wavelength band, indicating a finite flexural rigidity of the lithosphere. A simple model for lithospheric loading from above and below is introduced (D. W. Forsyth, 1985, J. Geophys. Res. 90, 12,623-12,632) with four parameters: f, the ratio of bottom loading to top loading; Z m , crustal thickness; Z l, depth to bottom loading source; and T e, elastic lithosphere thickness. No model is found that fits simultaneously the estimated free-air admittance and Bouguer coherence across the entire spectrum. A dual-mode compensation model is introduced in which the shorter wavelengths (λ ⪉ 1000 km) might be explained best by a predominance of top loading by the large shield volcanoes Maat Mons, Ozza Mons, and Sapas Mons, and the longer wavelengths (λ ⪊ 1500 km) might be explained best by a deep depth of compensation, possibly representing bottom loading by a dynamic source. A Monte Carlo inversion technique is introduced to thoroughly search out the four-space of the model parameters and to examine parameter correlations in the solutions. It is shown that simultaneous inversion on admittance and Bouguer coherence in the short-wavelength band constrains the elastic thickness to a range of approximately 40 to 50 km. Introduction of the free-air coherence as an observable in the inversion narrows the estimates of the other three parameters ( f = 0.10 ± 0.01, Z m = 30 ± 13 km, Z l = 7 ± 5 km) and provides a solution T e = 45 ± 3 km. In the long-wavelength band, Z l is found to be about 150 km, and this is the only parameter that can be estimated robustly. Crustal thickness, Z m , is unbounded, and the solutions are degenerate in that there is no discrimination between top and bottom loading. Acceptable elastic thicknesses range from 0 to 140 km. The elastic thickness results from both wavelength bands are corroborated in the spatial domain by examining residual standard deviations for a range of T e values. The results found here are consistent with the results of Smrekar (1994) for wavelengths longer than 600 km. Values of Z l are consistent with other analyses that exclude wavelengths longer than about 2,000 km. Inclusion of wavelengths longer than about 3000 km leads to compensation depths of approximately 200 km. Moment-curvature relationships based on yield strength envelopes are used to constrain temperature gradient. Average curvature is obtained from the flexurally deformed Moho surface by Fourier transform techniques. Surface temperature gradients are obtained in the range 7-10 K km -1, depending on the strain rate adopted. The relationship between elastic thickness and temperature gradient is calibrated by comparing elastic thickness estimates of two East African hotspots with measured heat flow. The excess heat flow at the East African hotspots over the African continental mean, if applicable to Venus, can be used to show that the globally averaged heat flow on Venus must be much lower than the Earth-scaled value predicts. A thick (∼350-km) ambient thermal lithosphere, as proposed by A. B. Kucinskas and D. L. Turcotte in this issue, and interpretable from the long-wavelength depth of compensation at Atla Regio, provides an acceptable background temperature gradient. When it is added to the excess heat flow or temperature gradient, the predicted heat flow at Atla Regio is consistent with the moment-curvature results. The thermal lithosphere beneath Atla Regio may be about 100 km thick and this answer can be obtained by two independent methods: from the ambient thermal lithosphere thickness and simple elevation scaling (result dependent on long gravity wavelengths) and from the elastic thickness estimate converted to temperature gradient (result dependent on short gravity wavelengths). Either Venus is considerably deficient in heat sources relative to Earth, or the thermal lithosphere is overthickened in response to an earlier episode of significant heat loss from the planet.