Spatial Distribution Of Elastic Properties Research Articles

Low-Frequency Elastic Properties of a Polymineralic Carbonate: Laboratory Measurement and Digital Rock Physics

We demonstrate that the static elastic properties of a carbonate sample, comprised of dolomite and calcite, could be accurately predicted by Digital Rock Physics (DRP), a non-invasive testing method for simulating laboratory measurements. We present a state-of-the-art algorithm that uses X-ray Computed Tomography (CT) imagery to compute the elastic properties of a lacustrine rudstone sample. The high-resolution CT-images provide a digital sample that is used for analyzing microstructures and performing quasi-static compression numerical simulations. Here, we present the modified Segmentation-Less method withOut Targets method: a combination of segmentation-based and segmentation-less DRP. This new method assigns the spatial distribution of elastic properties of the sample based on homogenization theory and overcomes the monomineralic limitation of the previous work, allowing the algorithm to be used on polymineralic rocks. The method starts by partitioning CT-images of the sample into smaller sub-images, each of which contains only two phases: a mineral (calcite or dolomite) and air. Then, each sub-image is converted into elastic property arrays. Finally, the elastic property arrays from the sub-images are combined and fed into a finite element algorithm to compute the effective elastic properties of the sample. We compared the numerical results to the laboratory measurements of low-frequency elastic properties. We find that the Young’s moduli of both the dry and the fully saturated sample fall within 10% of the laboratory measurements. Our analysis also shows that segmentation-based DRP should be used cautiously to compute elastic properties of carbonate rocks similar to our sample.

Multimodal Evaluation of the Spatiotemporal Variations of Periprosthetic Bone Properties.

Titanium implants are widely used in dental and orthopedic surgeries. However, implant failures still occur because of a lack of implant stability. The biomechanical properties of bone tissue located around the implant need to be assessed to better understand the osseointegration phenomena and anticipate implant failure. The aim of this study was to explore the spatiotemporal variation of the microscopic elastic properties of newly formed bone tissue close to an implant. Eight coin-shaped Ti6Al4V implants were inserted into rabbit tibiae for 7 and 13 weeks using an in vivo model allowing the distinction between mature and newly formed bone in a standardized configuration. Nanoindentation and micro-Brillouin scattering measurements were carried out in similar locations to measure the indentation modulus and the wave velocity, from which relative variations of bone mass density were extracted. The indentation modulus, the wave velocity and mass density were found to be higher (1) in newly formed bone tissue located close to the implant surface, compared to mature cortical bone tissue, and (2) after longer healing time, consistently with an increased mineralization. Within the bone chamber, the spatial distribution of elastic properties was more heterogeneous for shorter healing durations. After 7 weeks of healing, bone tissue in the bone chamber close to the implant surface was 12.3% denser than bone tissue further away. Bone tissue close to the chamber edge was 16.8% denser than in its center. These results suggest a bone spreading pathway along tissue maturation, which is confirmed by histology and consistent with contact osteogenesis phenomena.

Volcano deformation source parameters estimated from InSAR: Sensitivities to uncertainties in seismic tomography

AbstractThe eruption cycle of a volcano is controlled in part by the upward migration of magma. The characteristics of the magma flux produce a deformation signature at the Earth's surface. Inverse analyses use geodetic data to estimate strategic controlling parameters that describe the position and pressurization of a magma chamber at depth. The specific distribution of material properties controls how observed surface deformation translates to source parameter estimates. Seismic tomography models describe the spatial distributions of material properties that are necessary for accurate models of volcano deformation. This study investigates how uncertainties in seismic tomography models propagate into variations in the estimates of volcano deformation source parameters inverted from geodetic data. We conduct finite element model‐based nonlinear inverse analyses of interferometric synthetic aperture radar (InSAR) data for Okmok volcano, Alaska, as an example. We then analyze the estimated parameters and their uncertainties to characterize the magma chamber. Analyses are performed separately for models simulating a pressurized chamber embedded in a homogeneous domain as well as for a domain having a heterogeneous distribution of material properties according to seismic tomography. The estimated depth of the source is sensitive to the distribution of material properties. The estimated depths for the homogeneous and heterogeneous domains are 2666 ± 42 and 3527 ± 56 m below mean sea level, respectively (99% confidence). A Monte Carlo analysis indicates that uncertainties of the seismic tomography cannot account for this discrepancy at the 99% confidence level. Accounting for the spatial distribution of elastic properties according to seismic tomography significantly improves the fit of the deformation model predictions and significantly influences estimates for parameters that describe the location of a pressurized magma chamber.

Joint stochastic inversion of 3D prestack seismic-amplitude data and well logs for high-resolution reservoir characterization of deepwater hydrocarbon reservoirs

A new algorithm for joint stochastic inversion of well logs and multiple-angle stacks of migrated 3D prestack seismic data is based on a Bayesian statistical search criterion implemented with fast Markov-chain Monte Carlo updates. It enforces a priori measures of spatial correlation as well as geometric structural and stratigraphic embedding. Results consist of spatial distributions of elastic properties with a vertical resolution intermediate between that of seismic-amplitude data and well logs. In addition, the algorithm provides quantitative estimates of nonuniqueness based on statistical distribution of multiple spatial realizations derived from random initial models. It is also possible to estimate lithology and petrophysical properties such as porosity by enforcing multidimensional statistical correlations between elastic and petrophysical properties sampled from well logs. Results are described from the successful application of the inversion algorithm to the high-resolution characterization of hydrocarbon-producing units of a deepwater reservoir in the central Gulf of Mexico. Sensitivity analyses of resolution and non-uniqueness at blind-well locations corroborate the reliable estimation of elastic and petrophysical properties. Estimated distributions of lithology and elastic properties are influenced only marginally by the choice of inversion parameters and the assumed measures of spatial correlation.

Sensitivity analysis of data-related factors controlling AVA simultaneous inversion of partially stacked seismic amplitude data: Application to deepwater hydrocarbon reservoirs in the central Gulf of Mexico

We consider the inversion of synthetic and recorded seismic amplitude variation with angle AVA data to appraise the influence of several data-related factors that control the vertical resolution and accuracy of the estimated spatial distributions of elastic properties. We use measurements acquired in deepwater hydrocarbon reservoirs in the central Gulf of Mexico to generate synthetic seismic amplitude data and evaluate inversion results with both synthetic and recorded seismic amplitudes. Detailed sensitivity analysis of synthetic amplitude data indicates that, even in the most ideal scenario (perfectly migrated data, isotropic media, noise-free seismic amplitude data, sufficient far-angle coverage, and accurate estimates of angle-dependent wavelets and low-frequency components), input elastic models are not reconstructedaccurately by the inversion of synthetic seismic amplitudes. We attribute this result to the relatively low vertical resolution of the seismic amplitude data. P-wave impedance is the most accurate of the inverted properties, followed by S-impedance and bulk density. Additionally, sufficient far-angle coverage is crucial for the accurate estimation of 1D distributions of S-impedance and bulk density. We show that time alignment of partial-angle stacks for correcting residual NMO effects improves the vertical resolution of the estimated spatial distributions of elastic parameters and consistently decreases the data misfit. Finally, we found that the accuracy of the inverted distributions of elastic parameters is improved substantially by (1) increasing the preserved AVA information via multiple single-angle stacks, (2) correcting the P-wave velocity field used for calculating angles in partial-angle stacking, and (3) excluding far-angle data with low signal-to-noise ratios.

Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force

Bubble-based acoustic radiation force aims to measure highly localized tissue viscoelastic properties. In the current investigation, acoustic radiation force was applied to laser-induced bubbles to measure age-related changes in the spatial distribution of elastic properties within in vitro porcine lenses. A potential in vivo technique to map lens elasticity is crucial to understanding the onset of presbyopia and develop new treatment options. Bubble-based acoustic radiation force was investigated as a technique to measure the spatial elasticity distribution of the lens in its natural state without disrupting the lens capsule. Laser-induced optical breakdown (LIOB) generated microbubbles in a straight line across the equatorial plane of explanted porcine lenses with 1mm lateral spacing. Optical breakdown occurs when sufficiently high threshold fluence is attained at the focus of femtosecond pulsed lasers, inducing plasma formation and bubble generation. A two-element confocal ultrasonic transducer applied 6.5 ms acoustic radiation force-chirp bursts with the 1.5 MHz outer element while monitoring bubble position within the lens using pulse-echoes with the 7.44 MHz inner element. A cross-correlation method was used to measure bubble displacements and determine exponential time constants of the temporal responses. Maximum bubble displacements are inversely proportional to the local Young's modulus, while time constants are indicative of viscoelastic properties. The apparent spatial elasticity distributions in 41 porcine lenses, ranging from 4 months to 5 years in age, were measured using bubble-based acoustic radiation force. Bubble displacements decrease closer to the porcine lens center, suggesting that the nucleus is stiffer than the cortex. Bubble displacements decrease with increasing lens age, suggesting that porcine lenses become stiffer with age. Bubble-based acoustic radiation force may be well-suited as a potential in vivo technique to spatially map elastic properties of the lens and guide therapeutic procedures aimed at restoring accommodation.