Transverse Isotropic Media Research Articles

Least‐squares reverse time migration based on an efficient pure qP‐wave equation

AbstractSeismic waves propagating in anisotropic earth media suffer from waveform distortion, which leads to degraded resolution in seismic data imaging if this adverse effect is not corrected. Additionally, the wavefields simulated by the traditional coupled pseudo‐acoustic wave equations contain undesired shear wave artefacts and are unstable when Thomsen's anisotropy parameter ε is less than δ. To address these issues, many pure qP‐wave equations are proposed to describe wave propagation in anisotropic media. However, these equations are either low precision or high accuracy but computationally expensive. Considering the trade‐off between the computation efficiency and simulation accuracy, we derive a pure qP‐wave equation from the exact dispersion formula in tilted transverse isotropic media. The newly derived equation has only two higher order partial derivatives, which can better balance the accuracy and efficiency than the previous pure qP‐wave equations. The least‐squares reverse time migration method can balance amplitudes, suppress migration artefacts and improve imaging resolution. Then, based on the newly derived pure qP‐wave equation, we derive the Born modelling operator and adjoint migration operator and develop an anisotropic least‐squares reverse time migration method. To achieve the accelerated convergence, we introduce a generalized minimum residual algorithm to implement the anisotropic least‐squares reverse time migration method. Numerical simulation results show that the proposed pure qP‐wave equation outperforms the previous equations in balancing the trade‐off between accuracy and efficiency. In addition, synthetic examples demonstrate the effectiveness and robustness of our proposed anisotropic least‐squares reverse time migration method in correcting the deviations due to anisotropic effects.

Explicit finite-difference modeling for the acoustic scalar wave equation in tilted transverse isotropic media with optimal operators

We have developed an explicit finite-difference modeling scheme for the scalar acoustic wave equation in tilted transverse isotropic (TTI) media, which is computationally efficient in terms of speed and memory and can be used for reverse time migration. Our method uses local spatial operators optimized in the least-squares sense by matching the discrete operator in the wavenumber domain. The calculated operator is applied locally to the wavefield in the space-time domain when the medium is TTI and turns into a conventional finite-difference operator when the medium is isotropic. Our wavefield modeling is stable with no limits such as [Formula: see text] on anisotropic parameters and does not generate S-wave artifacts. The accuracy and the efficiency of our modeling scheme are demonstrated for homogeneous, two half-space TTI, and the BP 2007 TTI models.

Least-squares reverse-time migration in VTI media using a T-distribution-based misfit function

Abstract Anisotropy of subsurface media can affect the seismic wave travel time estimates, and then affect the imaging of target regions. To calibrate the effect of anisotropy, a VTI (transverse isotropy media with vertical symmetry axis) least-squares reverse-time migration (LSRTM) algorithm is used. However, if seismic data contains noise especially the outliers, the high-quality images cannot be produced by LSRTM based on an L2 norm. Considering that Student's t-distribution has better robustness than the L2 norm, this study derives a VTI-LSRTM algorithm based on Student's t-distribution (T-VTI-LSRTM) misfit function. The plane-wave encoding is introduced into the T-VTI-LSRTM to improve the computational efficiency. We conduct numerical tests using the complex models to illustrate the effectiveness and adaptability of the method. The sensitivity analysis of velocity and anisotropy parameters demonstrate that anisotropy and velocity parameters have a distinct effect on imaging results, in which velocity sensitivity is the strongest, then the epsilon and parameter delta sensitivity is the weakest.

Fast least‐squares reverse time migration based on stable pseudo‐acoustic wave equations for tilted transverse isotropic media

AbstractConventional tools for seismic imaging normally ignore the anisotropy of the media to produce images of the subsurface, and such omission reduces the quality of the images. Therefore, it is necessary to develop methods which account for subsurface anisotropic properties in order to produce more accurate images. In this paper, we present a least‐squares reverse time migration based on the coupled pseudo‐acoustic equations for tilted transverse isotropic media. Thus, from the stable pseudo‐acoustic wave equation for such media, we derive the linearized modelling (Born modelling) and adjoint migration operators to implement a least‐squares reverse time migration. Then, to save time and effort on development, while ensuring optimal performance of the inversion, we based our implementation on the domain‐specific language Devito, which, in turn, allowed us to easily verify the correctness of the developed operators. Synthetic examples demonstrate the validity of our approach in dealing with tilted transverse isotropic media.

Modeling 3-D Elastic Wave Propagation in TI Media Using Discontinuous Galerkin Method on Tetrahedral Meshes

Transversely isotropic (TI) medium is a widely studied anisotropic solid medium in seismology. The numerical simulation of seismic wave propagation in TI media is an effective tool to analyze the mechanism of seismic waves in complex anisotropic media. In this study, we introduce a double-weighted Runge-Kutta discontinuous Galerkin (RKDG) method for numerically solving wave propagation problems in 3D TI media with surface topography. This method incorporates the discontinuous Galerkin spatial discretization with an explicit double-weighted two-step iteration time discretization. The local Lax-Friedrichs flux is used as the numerical flux in the formulations. This method can solve the first-order velocity-stress seismic wave equations including TI media as well as more general anisotropic media. Due to the large scale of 3D problems, the parallel technology is adopted. Regions with irregular boundaries are discretized into unstructured tetrahedral meshes. Numerical experiments for various anisotropic media including the vertical and tilted TI media are presented. The results demonstrate the effectiveness of the double-weighted RKDG method in wavefield simulations in 3D complicated anisotropic media.

Automated hyperparameter optimization for simulating boundary conditions for acoustic and elastic wave propagation using deep learning

We have developed a deep learning framework to simulate the effect of boundary conditions for wave propagation in anisotropic media. To overcome the challenges associated with the stability of conventional implementation of boundary conditions for strongly anisotropic media, we develop an efficient algorithm using deep neural networks. We incorporate the hyperparameter optimization (HPO) workflow in the deep learning framework to automate the network training process. Hyperparameter selection is a crucial step in model building and has a direct impact on the performance of machine learning models. We implement three different HPO techniques, namely random search, Hyperband, and Bayesian optimization, for simulating boundary conditions and compare the strengths and drawbacks of these techniques. We train the network using a few shot locations and time slices enabling the network to learn how to remove boundary reflections and simulate wave propagation for unbounded media. The automated deep learning framework with HPO improves the performance of deep learning models by achieving the optimal minima and significantly improves the efficiency of the workflow. The benefit of this approach is its simple implementation and significant reduction of reflections at the boundaries, especially in the case of tilted transverse isotropic media. We validate our approach by comparing wave propagation at the boundaries using our algorithm with the output obtained using the unbounded media simulated by padding the model. Tests on different models with acoustic and elastic wave propagation verify the effectiveness of our approach.

Multiparameter Acoustic Inversion for Variable-Tilt Transversely Isotropic Media With Generalized Radon Transform

The pseudoacoustic approximations are commonly used for migration and inversion in transversely isotropic (TI) media, as they accurately characterize the P-wave propagation and are simpler than their elastic counterparts, resulting in computational savings. This paper is devoted to presenting an approach for generalized Radon transform (GRT) migration and inversion in acoustic TI media with a tilted symmetry axis (TTI). In parameterizing an acoustic TTI medium with the P-wave normal moveout velocity (NMO) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v_n</i> , Thomsen’s parameter δ, and anelliptic parameter η, a concise single-scattering integral for NMO pressure is obtained by perturbing the TTI medium from a background non-elliptically anisotropic medium. It results in explicitly representing the perturbation scattering patterns of each parameter ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v_n</i> , δ, η), helping us understand the scattering angular influence of the perturbed parameters. The application of GRT on this scattering integral allows a direct construction of the acoustic TTI inversion operator. Numerical examples verify the effectiveness of the proposed acoustic TTI GRT inversion method and show its considerably good performance in the presence of steeply dipping anisotropic layering.

Seismic inversion and fracture prediction in tilted transversely isotropic media

Abstract The conventional Amplitude variation with offset (AVO) inversion has been mainly developed for the isotropic media and therefore it is generally inapplicable to the anisotropic fractured formations. A set of tilted fractures in isotropic medium can be regarded as a transversely isotropic (TTI) medium. The reflection coefficient equation in TTI media contains many parameters such as anisotropic parameters, velocities, azimuth and dip angles. The selection of objective functions can significantly affect its performance in searching for the optimal solution. The seismic inversion of the TTI medium remains challenging because of its many parameters, and is very complicated after conversion into solving function problems. The genetic algorithm (GA) provides a universal framework to solve the optimization problem in complex systems, and it is independent of the types and disciplines of problems. In this study, the GA-based seismic prestack inversion of the TTI medium is implemented by constructing the objective functions of anisotropic parameters based on the TTI medium reflection coefficient approximation. The inversion performance is shown to be satisfactory on the one-dimensional well logging model, modified Hess model and the field datum. Furthermore, fracture filling materials are well predicted according to the theories of the equivalent medium for fractured materials and fracture weakness. The inversion results demonstrate the proposed method to be feasible and robust. The findings of this research are expected to provide theoretical guidance for the inversion of elastic parameters of anisotropic media and fracture type identification in hydrocarbon reservoirs.

Reflection characteristics of thin-beds with aligned fractures

Fractures are ubiquitous in rock and therefore considerably affect the overall mechanical properties of rock. In this study, effective medium theory is used to analyze the reflection characteristics of elastic waves in thin-beds containing aligned fractures. First, elastic parameters are obtained for a single thin bed containing discrete vertical fractures. Then, an exact solution is derived for the reflection coefficient of elastic waves in horizontally transverse isotropic (HTI) thin-beds using the propagation matrix method. Next, the effects of the fracture density and fillings on the reflection pattern are analyzed. Thin-beds without fractures are equivalent to a vertically transverse isotropic (VTI) medium in the long-wavelength limit. The introduction of vertical fractures makes thin-beds equivalent to a single thin bed in an orthorhombic anisotropic (ORT) medium (where the thickness of ORT thin bed is the total thickness of the original thin-beds). The ORT model of fractured thin-beds is presented by the equivalent medium theory. The results obtained using the HTI thin-beds and ORT models are compared, and the influences of the ORT model accuracy and formation parameters (such as thickness-to-wavelength ratio of a single thin bed, total thickness of thin-beds, etc.) on the ORT approximation results are analyzed. The response characteristics of elastic waves in complex thin-beds with fractures determined in this study can give an important guidance to real applications in geophysics and rock mechanics.

Earthquake Stress Drop for a Circular Crack in an Anisotropic Medium

ABSTRACT The circular-crack model has been widely used in seismology to infer earthquake stress drop. A common assumption is that the background medium is isotropic, although many earthquakes occur in geologically anisotropic settings. In this article, we study the effect of anisotropy on stress drop for a circular crack model and present explicit formalism in both static and kinematic cases. In the static case, we obtain the relationship between stress drop and slip for a circular crack model in an arbitrarily anisotropic medium. Special attention is given to the transversely isotropic (TI) medium. The static formalism is useful in understanding stress drop, but not all quantities are observables. Therefore, we resort to the kinematic case, from which we can infer stress drop using recorded far-field body waves. In the kinematic case, we assume that the crack ruptures circularly and reaches the final displacement determined by the static solutions. The far-field waveforms show that the corner frequency will change with different anisotropic parameters. Finally, we calculate the stress drops for cracks in isotropic and anisotropic media using the far-field waveforms. We find that in an isotropic medium, only shear stress acting on the crack surface contributes to shear slip. However, in a TI medium, if the anisotropy symmetry axis is not perpendicular or parallel to the crack surface, a normal stress (normal to the crack surface) can produce a shear slip. In calculating stress drop for an earthquake in an anisotropic medium using far-field body waves, a large error may be introduced if we ignore the possible anisotropy in the inversion. For a TI medium with about 18% anisotropy, the misfit of inferred stress drop could be up to 41%. Considering the anisotropic information, we can further improve the accuracy of stress-drop inversion.

3D time-domain induced polarization modelling considering anisotropy and topography

Induced polarization (IP) method is one of the most widely used techniques in mineral exploration, hydrogeology, and environmental monitoring, becoming indispensable especially for metallic ore exploration. Topography of the surface and anisotropy of the subsurface plays an important role in the IP data interpretation and modelling leading to wrong resistivity and chargeability models if they are not considered. We developed a 3D IP forward modelling considering arbitrary anisotropy and topography using the finite element method (FEM). The newly developed algorithm is compared with the numerical solutions and analytical results for classical two-layer anisotropic models successfully. By using unstructured mesh to consider complex topography, we implement 3D IP forward modelling for arbitrary anisotropic medium under the condition of uneven terrain and investigate the effect of anisotropy and topography on IP data interpretation. Topography has a decreased or reinforcing effect on time-domain induced polarization (TDIP) response. Vertical transverse isotropic (VTI) medium has a tiny effect and can accurately locate the anomaly in the subsurface while tilted transverse isotropic (TTI) medium has a very large effect and cannot be explored. Under the comprehensive influence of complex topography and anisotropy with an angle larger than 30 degrees, it is very difficult to interpret TDIP results. The 3D inversion of the synthetic data derived by the 3D anisotropic chargeability model indicates that topography weakens the TDIP response. However, VTI anisotropic anomaly can be detected accurately in the horizontal direction, the TTI anisotropic anomaly is difficult to be explored.

Near-fault broadband seismograms synthesis in a stratified transversely isotropic half-space using a semi-analytical frequency-wavenumber method

Anisotropic behavior occurs in natural soils and rocks, owing to sedimentation and weathering. However, the semi-analytical methods of near-fault broadband seismogram synthesis in the anisotropic medium are still rare. The physical-based frequency-wavenumber method was constructed for broadband seismogram synthesis due to a kinematic hybrid finite-fault source in a stratified transversely isotropic (TI) half-space for the first time. As the crucial foundation of the seismogram synthesis, the Green's function is established by the dynamic stiffness matrix method, effectively and stably modeling the broadband seismic waves propagation in a TI crust. A hybrid method of the kinematic fault source is applied to reasonably combine the low-frequency deterministic parts with the high-frequency stochastic parts, achieving a broadband waves excitation. The theoretical formulations are well-programmed by the FORTRAN code with OpenMP-based parallel technology to implement the fast solution. Compared with the two published results, the correctness of the methodology is well verified. A numerical example of an Mw7.0 scenario strike-slip earthquake is simulated to discuss the difference between TI and isotropic medium in the aspects: (i) attenuation characteristics near the fault area, (ii) rupture directional effect and velocity pulse, and (iii) response spectrum characteristics.

Generalization of Bayesian inversion with application to PP reflection in a vertical transverse isotropy medium

ABSTRACTSeismic inversion of amplitude variation with offset is an ill‐conditioned problem, in which small errors in the observed data result in large errors in the estimates, and therefore regularization functions are necessary. The Bayes' theorem regularizes ill‐posed problems using the statistical properties of the model parameters of interest; however, our knowledge of these statistical properties is poor. Meanwhile, the Bayesian framework is limited to particular forms of a priori probability distributions, due to poor knowledge of the statistical properties of individual probability distributions. Moreover, each particular a priori probability distribution requires a reformulation of the inversion under a Bayesian framework, which is not practically preferred. Here, we construct a Bayesian framework that enables the use of various types of a priori probability distributions without the need to reformulate the problem and to obtain well‐established statistical information on the model parameters of interest, specifically a lower bound on the variance of the a priori model, for example. Fisher information. Consequently, different probability distributions that best address the parameters of interest are first fitted using the maximum likelihood estimator . A lower bound on the variance of each a priori model is then estimated, which provides adequate statistical information between different model parameters; hence, it is ideally suited for the Bayesian framework. Thereafter, an iterative approach is proposed that utilizes the Hessians of the data and model spaces, and an adaptive learning rate to compute the optimal directions for model updates. The approach is applied to synthetic and real seismic data to estimate the elastic and seismic anisotropy parameters of shale formations. The regularization from the a priori probability density successfully stabilizes the updates of the variant‐sensitivity parameters by imposing the correlation information in the optimization process.

Dynamic response of a multi-layered pavement structure with subgrade modulus varying with depth subjected to a moving load

The dynamic response of a three-dimensional multi-layered pavement system subjected to a moving load is calculated by an analytical solution method. In this method, the pavement structure is assumed to be a transverse isotropic viscoelastic multi-layered structure with partially bonded interface, and the subgrade is considered to be a transverse isotropic half-space medium with its modulus varying with depth. The load is considered as a three-dimensional elliptical moving load with a constant speed. This study is divided into three key steps. Firstly, the ordinary differential equations of pavement and subgrade structures are obtained via the double Fourier transform, and the general solutions of dynamic response are obtained according to the theory of ordinary differential equations and the Frobenius method. Secondly, combined with the boundary conditions, the method of wave vector matrix, and the inverse Fourier integral transform, the dynamic responses of pavement structure in time domain are calculated. The accuracy of the analytical solution is verified by comparing against the solution from a finite element method. Lastly, the sensitivity analysis is conducted to assess the influence of four parameters on the dynamic response, namely, the horizontal load, the condition of interlayer contact, the transverse isotropy, and the non-uniform distribution of subgrade moduli. The calculation methods and the corresponding results can further develop a theory of the multi-layered system.

NMO stretch in vertical transverse isotropic media presented by nonhyperbolic approximations

Normal-moveout (NMO) correction is an inevitable part of routine seismic data processing and imaging. NMO correction suffers from an undesirable phenomenon called NMO stretching, which is more pronounced in larger emerging angles. Frequency distortions caused by NMO stretching for isotropic media have fully been studied in the literature. We express the distortions for the simplest case of anisotropy, which is vertical transverse isotropic media. This is done through different nonhyperbolic approximations, including shifted-hyperbola approximation, rational approximation, and generalized moveout approximation (GMA). To evaluate the predicted distortions, we define a trace-muting threshold and use it in the trace-muting procedure for synthetic data, as well as a field recorded example. Comparison between the results proves that the GMA has the highest accuracy among the other presented approximations. The proposed approach has an immediate potential to be used in industry and also to help to develop innovative nonstretch NMO correction workflows.

Fast wave-mode separation in anisotropic elastic reverse time migration using the phase velocity-related Poynting vector

We present a phase velocity-related Poynting vector in elastic modeling that represents the direction of the phase velocity rather than that of the group velocity as obtained by the conventional Poynting vector. This yields a highly efficient wave-mode separation scheme for vector elastic reverse time migration (ERTM), especially in anisotropic cases. We separate qP- and qSV-waves by first obtaining the polarization vector based on the proposed Poynting vector using an analytical formula and then performing a coordinate transformation based on the resulting polarization vector. Only a tiny amount of additional storage or computation is required. We provide a numerical implementation under both regular and unstructured meshes, thus allowing for spatially varying grid sizes according to the local velocities as well as accurate description of interface topographies. A Poynting vector and unstructured-mesh-based anisotropic ERTM scheme was then proposed. The resulting scheme can yield migrated opening-angle gathers related to qP- and qSV-waves without extra effort. The accuracy and efficiency of the resulting scheme are verified by several numerical examples of two-dimensional transverse isotropic media.

Method to account for natural fracture induced elastic anisotropy in geomechanical characterization of shale gas reservoirs

Shale has been usually recognized as a transverse isotropic (TI) medium in conventional geomechanical log interpretation due to its laminated nature. However, when natural fractures exist in the shale rock, additional elastic anisotropy is introduced, converting laminated Shale to an orthorhombic (OB) medium. Previous studies illustrate that neglecting the natural fracture induced anisotropy in shale geomechanical log interpretation could lead to inaccurate evaluations of elastic moduli and in-situ stresses.In this paper, a new method is developed to account for the natural fracture induced anisotropy in geomechanical log interpretation based upon the TI acoustic model developed by the author and a characterization technique of elastic wave anisotropy (Sayers, 1991). The new OB model incorporates the four acoustic log data inputs and five modeling constraints in a nonlinear optimization algorithm to solve for the nine independent stiffness coefficients of an OB rock, and further to solve for the geomechanical properties and in-situ stress profiles in an OB formation.The new method was validated with a Marcellus Gas Shale field case. Both the new OB model and the conventional TI model were applied to interpret the minimum horizontal stress profile for the same formation. By comparing the results, the OB model is more robust than the TI from two aspects. First, the average stress magnitude predicted by the OB model is closer to the one measured by the Diagnostic Fracture Injection Test (DFIT). Second, the OB model predicts a more obvious stress barrier between the lower Marcellus and upper Onondaga Limestone than the TI model does. The predicted stress barrier is consistent with the observation of the microseismic events of a horizontal well drilled and completed nearby, which reveals that no hydraulic fracture propagates downward through the bottom boundary of Marcellus Shale into the underlying Onondaga Limestone.

Smart Ultrasound Device for Non-Invasive Real-Time Myocardial Stiffness Quantification of the Human Heart.

Quantitative assessment of myocardial stiffness is crucial to understand and evaluate cardiac biomechanics and function. Despite the recent progresses of ultrasonic shear wave elastography, quantitative evaluation of myocardial stiffness still remains a challenge because of strong elastic anisotropy. In this paper we introduce a smart ultrasound approach for non-invasive real-time quantification of shear wave velocity (SWV) and elastic fractional anisotropy (FA) in locally transverse isotropic elastic medium such as the myocardium. The approach relies on a simultaneous multidirectional evaluation of the SWV without a prior knowledge of the fiber orientation. We demonstrated that it can quantify accurately SWV in the range of 1.5 to 6 m/s in transverse isotropic medium (FA < 0.7) using numerical simulations. Experimental validation was performed on calibrated phantoms and anisotropic ex vivo tissues. A mean absolute error of 0.22 m/s was found when compared to gold standard measurements. Finally, in vivo feasibility of myocardial anisotropic stiffness assessment was evaluated in four healthy volunteers on the antero-septo basal segment and on anterior free wall of the right ventricle (RV) in end-diastole. A mean longitudinal SWV of 1.08 ± 0.20 m/s was measured on the RV wall and 1.74 ± 0.51 m/s on the septal wall with a good intra-volunteer reproducibility (±0.18 m/s). This approach has the potential to become a clinical tool for the quantitative evaluation of myocardial stiffness and diastolic function.

Born Scattering Integral, Scattering Radiation Pattern, and Generalized Radon Transform Inversion in Acoustic Tilted Transversely Isotropic Media

Although the pseudo-acoustic wave equation has good accuracy in characterizing anisotropic wave propagation and obtaining interpretable seismic images, a high-precision multiparameter inversion accounting for anisotropy from compressional wavefields is still confronted with challenges, even in the simple transversely isotropic (TI) case, due to the complicated relationship between anisotropic properties and pressure data. To reduce difficulty in correctly inverting surface compressional data in anisotropic media, an appropriate parameterization for inversion is necessary. For acoustic TI media with a tilted symmetry axis (TTI), we describe the pseudo-acoustic TTI equations with the P-wave normal moveout velocity vn and anisotropic parameters η and δ, and aim to invert for this parameterization by the scattering integral method. Using perturbation theory in formulating the integral solution of the singly scattered pressure wavefield allows to acquire a scattering radiation pattern that explicitly illustrates the angular effect (including migration dip and scattering angles) of the TTI perturbation parameters, in which perturbations whether in the wavefield or anisotropic parameters are from the elliptical anisotropic background medium. Taking advantage of a ray-theoretical approximation to the background Green’s function, we can establish a relationship between the scattering integral and a form of TTI generalized Radon transform (GRT). As a result, we develop an acoustic TTI pseudoinverse GRT operator for estimating the corresponding perturbation parameters. Numerical tests on two simple models and a part of BP 2007 anisotropic benchmark model verify the effectiveness of the presented acoustic TTI GRT inverison/migration method and show its evident advantages over the conventional acoustic isotropic and TI with a vertical symmetry axis (VTI) approaches.

Acoustoelasticity in transversely isotropic soft tissues: Quantification of muscle nonlinear elasticity

Recent developments in the field of elastography aim at developing the quantification of new mechanical properties of tissues, that are complementary to the shear modulus, which is characteristic of the linear elastic properties of a quasi-incompressible medium. In this context, measurement of the elastic nonlinearity of tissues was recently proposed based on acoustoelasticity. Up to now, most of the experimental applications of acoustoelasticity theory using Landau formalism in human tissues have assumed isotropy. However, this strong hypothesis does not hold in all human tissues, such as muscles that are generally considered as transversely isotropic (TI). In this work, after reviewing the constraints imposed by TI symmetry on the linear and nonlinear elastic properties of TI media, the acoustoelasticity theory in TI incompressible media is developed and implemented experimentally on a TI polyvinyl alcohol phantom and on ex vivo muscular tissues. Based on this theory and on the evolutions of the shear wave speed, with respect to uniaxial static stress, the nonlinear elastic parameter A is experimentally quantified. The estimations of A in ex vivo bovine and porcine muscles are on the order of hundreds of kPa. This work paves the way for more thorough muscle mechanical properties characterization as well as for the development of a potential new biomarker.