Plane Wave Reflection Coefficient Research Articles

Numerical Integration and Angular Spectrum Modeling of Resonant and Non-Resonant Wave Interaction with a Solid Plate

The angular spectrum (AS) model is widely used to calculate the pressure transmitted through, and reflected from, a fluid-immersed solid plate, using a baffled piston as source. However, narrow peaks (infinite peaks for the lossless case) in the piston aperture function and in the plane wave transmission and reflection coefficients, in addition to a highly oscillatory integrand, cause challenges in the numerical integration. To overcome the challenges related to the aperture function peak, the AS model is reformulated using integration by parts. The peaks in the transmission and reflection coefficients are identified as symmetric and antisymmetric Scholte modes, and a numerical integration method is provided enabling integration over these peaks. The AS-model is also used to obtain the full-wave diffraction correction for a pulse-train transmitted through, or reflected from, the plate, which is highly relevant in pulse-transmit or pulse-receive measurements. The diffraction effects caused by the plate are calculated by suppressing resonance effects in the plate and obtaining the corresponding plane wave pressure transmission and reflection coefficients. A hybrid Gauss-Filon adaptive numerical integration method is used to calculate the pressure. These calculations are conducted in APAS, a MATLAB program developed in the current work and provided as open-source supplementary material.

Complex spherical-wave seismic inversion in anelastic media for the P-wave minimum quality factor

Attenuation always exists when seismic waves propagate in underground anelastic media, especially in hydrocarbon-bearing reservoirs. Quality factor Q or attenuation factor 1/ Q can be used to quantify the seismic wave attenuation and has become an important hydrocarbon indicator. The relationship between the plane-wave reflection coefficient ([Formula: see text]) in anelastic media and P- and S-wave quality factors has been widely used in the plane-wave seismic inversion to estimate the quality factors. The [Formula: see text] provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the [Formula: see text] is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient ([Formula: see text]) in anelastic media is used here. Considering that having too many parameters to be inverted will lead to unstable and inaccurate inversion results, we further derive an approximate anelastic [Formula: see text] and anelastic spherical-wave impedance ([Formula: see text]), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor ([Formula: see text]). Finally, a complex spherical-wave seismic inversion approach in anelastic media for the P-wave minimum quality factor is developed. Using the Bayesian inversion approach and complex convolution model, we first estimate the multilayer [Formula: see text] from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent [Formula: see text], the P- and S-wave velocities, density, and P-wave minimum quality factor are further estimated using a nonlinear inversion tool. Synthetic examples verify the feasibility and robustness of the complex spherical-wave seismic inversion approach in anelastic media. In the shallow subsurface, the spherical-wave inversion is superior to plane-wave inversion. A field example further demonstrates the accuracy and great potential of our approach in hydrocarbon-bearing reservoir prediction.

Spherical-wave elastic inversion in transversely isotropic media with a vertical symmetry axis

SUMMARY Although subsurface media are usually assumed to be isotropic, anisotropy is ubiquitous in crustal rocks and leads to the variation of seismic response with direction. Transversely isotropic media with a vertical symmetry axis (VTI media) are widely found in the real world, such as in textured shale reservoirs. Plane-wave reflection coefficients (PRCs) in VTI media have been widely exploited in amplitude variation with offset (AVO) inversion to estimate the elastic and anisotropy parameters of subsurface media. However, the PRCs in VTI media meet some fundamental problems, especially at near-critical or post-critical incidence angles where the spherical-wave effect is significant. To consider the wave front curvature, a complex spherical-wave reflection coefficient (SRC) in VTI media is derived. To better understand the spherical-wave seismic response in VTI media, we investigate the dependence of the complex SRC on frequency, reflector depth and Thomsen anisotropy parameters ($\varepsilon $ and $\delta $). Based on a complex convolution model, a spherical-wave AVO inversion approach in VTI media is proposed to estimate the vertical (symmetry-axis) compressional and shear wave velocities (P and S waves), density and Thomsen anisotropy parameters from observed seismic data with different incidence angle and frequency components. Synthetic data with Gaussian random noise are used to verify the robustness of the spherical-wave AVO inversion approach in VTI media. Field data examples show that the proposed approach can produce reasonable inversion results that match well with the well-logging data.

Reflection of Plane Waves in Nonlocal Fractional-Order Thermoelastic Half Space

The problem of plane waves in nonlocal fractional-order thermoelasticity has been studied. We have considered the x-y plane for the governing equation of nonlocal fractional thermoelasticity and solved these governing equations to calculate the equation in terms of frequency. This frequency shows that three sets of waves exist, in which two are coupled and one is uncoupled. The reflection coefficient of plane waves for classical theory and LS theory has been calculated. The effect of phase speeds, specific losses, and attenuation coefficients with respect to the frequency and nonlocal parameter for the two theories (LS theory and the classical theory of thermoelasticity) has been studied numerically for all propagating waves, and the same has been plotted graphically and explained thoroughly.

Range-Dependent Inversion for Seabed Parameters Using Vector Acoustic Measurements of Underwater Ship Noise

The Intensity Vector Autonomous Recorder (IVAR) measures acoustic particle velocity and pressure simultaneously. IVAR was deployed on the seabed during the 2017 Seabed Characterization Experiment (SBCEX) with the primary objective to study sound propagation within underwater waveguides for which the seabed consists of fine-grained, muddy sediments. In this study, a Bayesian framework is applied to underwater noise recorded by IVAR from a cargo ship traversing the central region of the SBCEX2017 area for the purpose of inversion to characterize sediment properties. The vector acoustic data are in the form of a bounded, nondimensional form known as circularity, a quantity that is independent of the ship noise-source spectrum and that can be interpreted as the normalized curl of active intensity. The inversion model space for the seabed consists of a low-compressional speed layer and underlying basement half-space, with each having compressional and shear components. The interpretative model for producing a replica of the data is based on the plane wave reflection coefficient for a layered, elastic seabed in conjunction with the depth-dependent Green’s function that is integrated in the complex wave number plane to obtain pressure and particle velocity fields. The small change in water depth between the location of the ship source and IVAR is addressed using adiabatic mode theory. The inversion results exhibit slow variation over the 20-min observation period, representing approximately 5 km of travel by the ship source.

Complex spherical-wave elastic inversion using amplitude and phase reflection information

Unlike the real-valued plane wave reflection coefficient (PRC) at the pre-critical incident angles, the frequency-and depth-dependent spherical-wave reflection coefficient (SRC) is more accurate and always a complex value, which contains more reflection amplitude and phase information. In near field, the imaginary part of complex SRC (phase) cannot be ignored, but it is rarely considered in seismic inversion. To promote the practical application of spherical-wave seismic inversion, a novel spherical-wave inversion strategy is implemented. The complex-valued spherical-wave synthetic seismograms can be obtained by using a simple harmonic superposition model. It is assumed that geophone can only record the real part of complex-valued seismogram. The imaginary part can be further obtained by the Hilbert transform operator. We also propose the concept of complex spherical-wave elastic impedance (EI) and the complex spherical-wave EI equation. Finally, a novel complex spherical-wave EI inversion approach is proposed, which can fully use the reflection information of amplitude, phase, and frequency. With the inverted complex spherical-wave EI, the velocities and density can be further extracted. Synthetic data and field data examples show that the elastic parameters can be reasonably estimated, which illustrate the potential of our spherical-wave inversion approach in practical applications.

Stochastic-Deterministic Assessment of Electric Field Radiated by Base Station Antenna above a Two-Layered Ground

The paper deals with stochastic-deterministic modelling of radiated electric field by base station antennas (BSAs) operating in GSM frequency range. Within the framework of deterministic analysis, the total electric field above a two-layered lossy ground is obtained by considering the incident and reflected ray in the far field zone. The influence of nonhomogeneous lower medium is taken into account via two approaches: Fresnel plane wave reflection coefficient (FRM) and simplified reflection coefficient stemming from Modified Image Theory (MIT). Antenna height, relative conductivity, and permittivity of each ground layer, as well as the thickness of the upper ground layer, are considered as input parameters with inherent uncertainty. To quantify the uncertainty of output electric field, deterministic models are treated as black boxes by two stochastic methods, Monte Carlo (MC) and Stochastic Collocation (SC), respectively. Stochastic mean and standard deviation of the output are computed, and sensitivity analysis is carried out in order to analyze the impact of input parameters’ variations on the resulting electric field variance. The presented results expose weakness and strength of the two stochastic methods, particularly identifying the cases when the preferred SC method fails to converge. Furthermore, sensitivity analysis reveals that despite the smallest variation around its respective average value, the antenna height has the highest impact on the output variance at observation points in the vicinity of the antenna. However, as the distance from the antenna increases, the 1st layer depth and its relative electric permittivity become the most significant parameters.

On acoustic reflection from a seabed exhibiting a non-uniform sound speed profile, with relevance to fine-grained sediments.

An analysis of the plane wave reflection coefficient of the seabed, R, is developed for two upward-refracting sediment sound speed profiles: the two-parameter linear and the three-parameter inverse-square, both extending to infinite depth. For the linear profile, it turns out that |R| = 1, representing total reflection for all grazing angles and all frequencies, signifying that in this special case, |R| is insensitive to the gradient. The implication is that if |R| is to return information about the shape of a profile, the gradient must change with depth, either smoothly through the presence of second- and/or higher-order depth derivatives or discontinuously at, say, an interface between sediment layers. The inverse-square is an example of a profile with a smoothly varying gradient, for which a general, closed-form expression for R is derived, valid for all grazing angles and all frequencies. When the sound speed ratio is less than unity, representative of a fine-grained sediment (mud), |R| exhibits two frequency regimes, designated high and low, separated by a transition frequency, fT. In each of these regimes, |R| exhibits a frequency-dependent angle of intromission, which exhibits high- and low-frequency limiting values, differing by approximately 3.5°, depending on the geo-acoustic parameters of the sediment.

Reflection and Transmission of Inhomogeneous Plane Waves in Thermoelastic Media

We study the reflection and transmission coefficients of plane waves incident at an interface between two isotropic thermoelastic half spaces and compare them with those of the elastic case. The models include the classical-Biot (B) and extended Lord-Shulman (LS) theories, and predict reflected and transmitted fast-compressional (P), thermal (T) and shear (S) waves. The coefficients are formulated in terms of incidence and inhomogeneity angles, medium properties and potential functions. We consider different incident wave types and inhomogeneity angles to analyze the magnitude, phase and energy ratio of the plane waves, and perform a comparison with the isothermal (elastic) theory. The thermoelastic and elastic models predict different energy partitions between the P and S modes, satisfying the conservation of energy. The LS model exhibits higher T-wave thermal attenuation with increasing inhomogeneity angle at high frequencies, accordingly predicting more interference energy. The angle affects the energy partitions, particularly at the critical angle and near grazing incidence for an incident P wave, which satisfies the conservation of energy. Beyond the critical angle, the energy flux perpendicular to the interface of the isothermal model vanishes, while it is significant in the thermoelastic case. The T-wave magnitudes increase when the thermal conductivity (relaxation time) increases.

Seismic inversion using complex spherical-wave reflection coefficient at different offsets and frequencies

Compared with the plane-wave reflection coefficient, the spherical-wave reflection coefficient (SRC) can more accurately describe the reflected wavefield excited by a point source, especially in the case of low seismic frequency and short travel distance. However, unlike the widely used plane-wave amplitude-variation-with-offset/frequency (AVO/AVF) inversion, the practical application of spherical-wave AVO/AVF inversion in multilayer elastic media is still in the exploratory stage. One of the difficulties is how to fully use the amplitude and phase information of the complex-valued SRC and the spherical-wave response property of each frequency component to obtain the spherical-wave synthetic seismogram in multilayer elastic media. In view of this, we have developed a complex convolution model considering the amplitude and phase information of an SRC to obtain the complex synthetic seismogram of a certain frequency component. A simple harmonic superposition method is further developed. By superposing the complex synthetic seismograms of different frequency components, the synthetic seismogram of the full-frequency band can be obtained. In addition, a novel three-parameter SRC in terms of P- and S-wave moduli and density is derived. Based on the SRC and complex seismic traces with different offsets (or incidence angles) and frequency components, an inversion approach of complex spherical-wave amplitude and phase variation with offset and frequency is proposed. A noisy synthetic data example verifies the robustness of our complex spherical-wave inversion approach. Field data examples indicate that the P- and S-wave moduli estimated by the complex spherical-wave inversion approach can reasonably match the filtered well-logging data. Considering spherical waves rather than plane waves can improve the accuracy of seismic inversion results.

Propagation and reflection of plane waves in biological tissue based on nonlocal TPL thermoelasticity

The investigation for propagation and reflection of plane waves is carried out based on three-phase-lag (TPL) thermoelasticity with the aids of Eringen's nonlocal theory in a special medium - biological tissue. The scalar and vector potential functions of Helmhotz decomposition are adopted to obtain the propagation speeds, attenuation coefficients and reflection coefficients of plane waves analytically. There are two sets of dispersive attenuated longitudinal waves whose speeds of propagation are associated with angular frequency, and independent transverse elastic shear wave which exhibits no attenuation. It is found that the blood perfusion rate has few effects on wave propagation speed and attenuation coefficient and the phase lag of temperature gradient is negligible in present configuration. The effects of working angular frequency, nonlocal parameters, phase lag times, reflecting thermal boundaries and the type of incident waves on the propagation speeds, attenuation coefficients and reflection coefficients of harmonic waves are discussed and investigated graphically.

Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media.

There has been an increase in the use of ultrasonic arrays for the detection of defects in composite structures used in the aerospace industry. The response of a defect embedded in such a medium is influenced by the inherent anisotropy of the bounding medium and the layering of the bounding medium and hence poses challenges for the interpretation of the full matrix capture (FMC) results. Modeling techniques can be used to understand and simulate the effect of the structure and the defect on the received signals. Existing modeling techniques, such as finite element methods (FEM), finite difference time domain (FDTD), and analytical solutions, are computationally inefficient or are singularly used for structures with complex geometries. In this paper, we develop a novel model based on the Gaussian-based recursive stiffness matrix approach to model the scattering from a side-drilled hole embedded in an anisotropic layered medium. The paper provides a novel method to calculate the transmission and reflection coefficients of plane waves traveling from a layered anisotropic medium into a semi-infinite anisotropic medium by combining the transfer matrix and stiffness matrix methods. The novelty of the paper is the developed model using Gaussian beams to simulate the scattering from a Side Drilled Hole (SDH) embedded in a multilayered composite laminate, which can be used in both immersion and contact setups. We describe a method to combine the scattering from defects with the model to simulate the response of a layered structure and to simulate the full matrix capture (FMC) signals that are received from an SDH embedded in a layered medium. The model-assisted correction total focusing method (MAC-TFM) imaging is used to image both the simulated and experimental results. The proposed method has been validated for both isotropic and anisotropic media by a qualitative and quantitative comparison with experimentally determined signals. The method proposed in this paper is modular, computationally inexpensive, and is in good agreement with experimentally determined signals, and it enables us to understand the effects of various parameters on the scattering of a defect embedded in a layered anisotropic medium.

Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of fluid-loaded functionally gradient plates

Based on the Legendre orthogonal polynomial series expansion and the partial wave theory, a Legendre orthogonal polynomial method (LOPM) is proposed to calculate the reflection and transmission coefficients of plane waves at the liquid/solid interface of a liquid-loaded functionally gradient material (FGM) plate. The displacement solutions in FGM plate are fitted approximately by Legendre orthogonal polynomial series. The stresses and the governing differential equations of the FGM plate are derived. Based on the boundary conditions of the liquid/solid interface and the governing differential equations, the linearly independent equations are set up to calculate the reflection and transmission coefficients. Meanwhile, the expansion coefficients of the Legendre orthogonal polynomials are also obtained. The power function establishes the gradient model of the mechanical parameters along the thickness direction. The angular spectrums of reflection and transmission coefficients from LOPM are in well agreement with the calculation results from the transfer matrix method. By analyzing the convergence of the reflection coefficient spectrum, the critical value of the truncated order of Legendre orthogonal polynomials is determined. The mapping relationship between the FGM gradient models and the reflection coefficient angular spectrum, also the frequency spectrums and the displacement/stress distributions can be demonstrated simultaneously, which provides the theoretical fundamentals of the ultrasonic non-destructive testing for the mechanical properties of FGM and extends the application of the LOPM.

Optimal Design Parameters for a Phased-Array-Based Ultrasonic Polar Scan.

In the context of designing a next-generation ultrasonic polar scan (UPS) measurement system for viscoelastic material characterization, a novel approach is proposed, which draws on a set of cylindrically focused emitters in conjunction with a circular phased array (C-PA) receiver in order to create a portable measurement system while improving the data quality and ease the data interpretation. To explore the potential of the new approach and determine its optimal design parameters, a 3-D analytical model is presented to numerically simulate UPS experiments with the proposed system. Furthermore, a postprocessing procedure is worked out to treat the acquired raw data with the aim to deal with the integrating effect of finite size transducers and directly reconstruct the angle-dependent plane wave reflection coefficients of the sample under study. As the accuracy of the reconstruction heavily depends on various design parameters, a parameter study focusing on the influence of three main experimental parameters is performed to guide the optimal design. For each of these parameter studies, the UPS simulation results have been inverted, and the errors on the estimated C-tensor parameters have been deduced. First, it is shown that, for a given frequency, the radius of the C-PA must be large enough to capture both the specular and nonspecular reflected field, which is crucial to assure a correct reconstruction of the plane wave characteristics and find proper estimates of the C-tensor parameters. Second, the impact of the emitter and receiver lengths on the quality of the reconstruction and the C-tensor parameters has been investigated, yielding superior results upon increasing either of them. Finally, a dedicated study of the pitch of the C-PA elements and the angular range of the cylindrically focused emitters shows that aliasing effects disturb the results if the pitch is too large. However, this effect can somewhat be mitigated by employing multiple emitters with a restricted angular range. Using the knowledge of the abovementioned parameter studies, a simulated UPS experiment using a proper set of design parameters is performed for a cross-ply carbon epoxy laminate. The postprocessed reconstruction based on these data shows an excellent agreement with the theoretical plane wave results.

Permittivity Extraction From Synthetic Aperture Radar (SAR) Images of Multilayered Media

A method to extract the complex permittivity from synthetic aperture radar (SAR) images of multilayered structures is proposed. Specifically, a three-term one-port calibration method is implemented to compensate for issues such as wave attenuation, antenna pattern, and multiple reflection effect between the antenna and the material under test (MUT) at each measurement frequency within a wideband operating frequency range. These issues are usually not considered by the $\omega $ - $k$ SAR algorithm used here. The ability of SAR imaging to focus the beam at any location within the MUT, representing a plane-wave at that location, so that the calibrated SAR image can then be used in conjunction with a plane-wave reflection coefficient model for a multilayered structure to calculate the complex permittivity of a certain layer in the MUT through an inverse optimization procedure. Measurement results conducted on a number of multilayered dielectric sheets with finite thicknesses and different complex permittivities confirm the validity of the proposed method. The results also indicate that using a wide operating frequency range can help mitigate measurement variations, leading to more accurate results. Finally, the possible limitations of this method are also discussed, and a sensitivity analysis is conducted to show the accuracy of this proposed method for materials with different loss factors. All these together indicate the potential of the proposed method to accurately extract the complex permittivity distribution of a multilayer structure for nondestructive evaluation (NDE) purposes.

Reflection and transmission coefficient approximations for P, S1 and S2 waves in triclinic media

SUMMARY The conventional assumptions, in most published approximations of the reflection and transmission (R/T) coefficients of plane waves at a plane interface between two anisotropic half-spaces, confine their applications to weakly anisotropic and/or weak contrast models. We consider the horizontal interface enclosed by two triclinic half-spaces to approximate the R/T coefficients normalized by the vertical energy flux. The homogeneous background medium can be anisotropic with arbitrary symmetry to better simulate the strongly anisotropic media. The second-order approximations are proposed to accommodate the strong contrast interface. We also consider an isotropic background medium under the weak anisotropy assumption. The obtained approximations can be applied to P, S1 and S2 waves, except for the transmission coefficients between the S1 and S2 waves. The S-wave transmission coefficients are insensitive to the model parameter contrasts and predominately rely on the S-wave polarization directions in the half-spaces above and below the interface. The proposed approximations are tested numerically.

Amplitude and phase changes for reflected and transmitted waves from a curved interface in anisotropic media

SUMMARYIt is well known that seismic data that have been recorded in complex geological environments must be compensated for geometrical spreading before AVO/AVA (amplitude-versus-offset/amplitude-versus-angle) analysis, in order to avoid erroneous imaging interpretation. By investigating analytically both the effect of the geometrical spreading and the effect of the reflector curvature on amplitude and phase changes for reflected and transmitted waves between anisotropic media, using ray theory, we show that these data should be compensated for interface effects as well. In order to gain insight more specifically in the focusing effect of the interface, the special case of homogeneous isotropic media separated by a curved interface of syncline type is discussed and compared to the case of a plane interface. 3-D numerical simulations of wave reflection from curved interfaces using a spectral element method validate our analytical derivations. In particular, numerical seismograms obtained at a vertical receiver array highlight that the effect of interface curvature on the reflected events is much more pronounced in a restricted area associated with the existence of caustics, which is consistent with our analytical predictions. Moreover, comparisons between the numerical and the analytical results confirm the fact that using plane-wave reflection coefficients without correction for the interface effect may lead to wrong interpretation of AVA/AVO analysis.

Frequency-dependent spherical-wave nonlinear AVO inversion in elastic media

SUMMARY The plane-wave reflection coefficient (PRC) plays a remarkable role in conventional amplitude variation with offset (AVO) analysis and inversion. Compared with the widely exploited PRC that breaks down at the near- and supercritical incidence angles, the spherical-wave reflection coefficient (SRC) can overcome the influence of wide-angle reflection and give an accurate description of the actual seismic wave reflection phenomenon based on spherical-wave fronts. However, SRC is not widely used in AVO inversion due to its nonlinearity and computational complexity. In our study, the characteristics of frequency–depth-dependent monochromatic SRC are discussed and a novel three-parameter SRC is derived. Compared with the conventional six-parameter SRC, the novel three-parameter SRC improves the stability of spherical-wave AVO inversion. In addition, the concept of SRC within the Fresnel zone is proposed, and the accuracy of SRC within the Fresnel zone in the deep subsurface is tested. Finally, a nonlinear spherical-wave AVO inversion method for elastic media is proposed, which can make full use of all frequency components of wavelet. The robustness of the proposed method is verified by the application on synthetic seismogram with white Gaussian noise. The feasibility and practicability of this method are verified by comparing the spherical-wave AVO inversion results with the filtered well logs at the known well location.

Propagation of blasting seismic wave in viscoelastic full space and half space under infinitely long cylindrical charge

The analytical solution of blasting seismic waves induced by cylindrical charge in a viscoelastic half space was lacked. In this study, an approximate analytical solution of this problem is proposed, with the combination of the exact analytical solution of the blasting seismic wave in viscoelastic full space and the reflection coefficients of plane waves in viscoelastic half space. To verify the accuracy of the proposed analytical solution, the finite difference method is employed and the numerical results is found well matched the theoretical analysis. The results indicate that the blast load parameters and the mechanical parameters of medium have predominant impact on the propagation of blasting seismic wave, the vibration attenuation on free surface can be divided into near field and far field according to charge depth. In the near field, the vibration amplitude decreases in the vertical direction but increases in the horizontal direction. In the far field, the vibration amplitude decreases in both the vertical and horizontal directions.

Frequency-dependent spherical-wave reflection coefficient inversion in acoustic media: Theory to practice

As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.