Acoustic Approximation Research Articles

Single-Shot Time-Lapse Target-Oriented Velocity Inversion Using Machine Learning

In this study, we used machine learning (ML) to estimate time-lapse velocity variations in a reservoir region using seismic data. To accomplish this task, we needed an adequate training set that could map seismic data to velocity perturbation. We generated a synthetic seismic database by simulating reservoirs of varying velocities using a 2D velocity model typical of the Brazilian pre-salt ocean bottom node (OBN) acquisition, located in the Santos basin, Brazil. The largest velocity change in the injector well was around 3% of the empirical velocity model, which mimicked a realistic scenario. The acquisition geometry was formed by the geometry of 1 shot and 49 receivers. For each synthetic reservoir, the corresponding seismic data were obtained by estimating a one-shot forward-wave propagation using acoustic approximation. We studied the reservoir illumination to optimize the input data of the ML inversion. We split the set of synthetic reservoirs into two subsets: training (80%) and testing (20%) sets. We point out that the ML inversion was restricted to the reservoir zone, which means that it was inversion-oriented to a target. We obtained a good similarity between true and ML-inverted reservoir anomalies. The similarity diminished for a situation with non-repeatability noise.

An approximation method to determine the travel time in total focusing imaging of carbon fiber-reinforced laminates

Abstract It is critical to accurately determine the propagation time in testing objects for ultrasonic array imaging using the Total Focusing Method (TFM). However, it poses challenges for the calculation of wave propagation time in carbon fiber reinforced polymer (CFRP) laminates because of the material anisotropy and inhomogeneity. This paper introduces a novel approach for computing ultrasonic wave travel time to enhance the TFM image of CFRP laminates. This method, termed the layer-by-layer acoustic travel time approximation (L-L TravelTimeAppro), considers the anisotropy within each monolayer and the heterogeneity of CFRP. It approximates the propagation path as straight throughout the material and computes the wave propagation duration utilizing the group velocity in each ply. The application of this method to TFM imaging is referred to as TravelTimeAppro-TFM. Experiments were conducted in a specially designed CFRP laminate. Subsequently, TFM imaging was processed by using propagation time calculated by isotropic, Dijkstra, and L-L TravelTimeAppro methods, respectively. The results indicate that TravelTimeAppro-TFM outperforms isotropic-TFM in terms of imaging amplitude gain with a maximum gain of 4.67 dB. Furthermore, it offers superior computational efficiency compared to Dijkstra-TFM.

3D reverse-time migration for pure P-wave in orthorhombic media

Compared with the transverse isotropic (TI) medium, the orthorhombic anisotropic medium has both horizontal and vertical symmetry axes and it can be approximated as a set of vertical fissures developed in a group of horizontal strata. Although the full-elastic orthorhombic anisotropic wave equation can accurately simulate seismic wave propagation in the underground media, a huge computational cost is required in seismic modeling, migration, and inversion. The conventional coupled pseudo-acoustic wave equations based on acoustic approximation can be used to significantly reduce the cost of calculation. However, these equations usually suffer from unwanted shear wave artifacts during wave propagation, and the presence of these artifacts can significantly degrade the imaging quality. To solve these problems, we derived a new pure P-wave equation for orthorhombic media that eliminates shear wave artifacts while compromising computational efficiency and accuracy. In addition, the derived equation involves pseudo-differential operators and it must be solved by 3D FFT algorithms. In order to reduce the number of 3D FFT, we utilized the finite difference and pseudo-spectral methods to conduct 3D forward modeling. Furthermore, we simplified the equation by using elliptic approximation and implemented 3D reverse-time migration (RTM). Forward modeling tests on several homogeneous and heterogeneous models confirm that the accuracy of the new equation is better than that of conventional methods. 3D RTM imaging tests on three-layer and SEG/EAGE 3D salt models confirm that the ORT media have better imaging quality.

Elastodynamic shape derivative: focus on the sampling of a circular distribution

The detection and quantification of defects plays a crucial role in several industries. Assessing the severity enables to schedule maintenance appropriately, optimizing costs and reducing risks. Guided elastic waves are particularly suitable for Structural Health Monitoring applications on thin structures thanks to their long range and high sensitivity. Guided wave tomography, based on an acoustic propagation hypothesis, has been studied over the last decade to quantitatively image defects in waveguides. The acoustic approximation of this family of methods allows fast computation and good estimation of defects for simple geometries such as plates or pipes. However, this hypothesis induces that a single guided mode is considered, without mode conversion, which limits its use to defects larger than two wavelengths in structures close to ideal waveguides. Hence the need of new imaging algorithms for smaller defects in less ideal structures such as pipes with welded supports. We present here an adaptation of the shape derivative method to ultrasounds in order to reconstruct surface defect on structures with complex geometries. The physical model used is the full elastodynamic problem. It allows taking into account all physical phenomena occuring during wave propagation. Iterative methods such as shape derivative are well known to give precise results but at a high computational cost as the method needs to solve the full elastodynamic problem at each iteration, and a sensitivity to local minima, which may prevent convergence toward the true defect. To suppress these two drawbacks, a spectral finite element method is used to reduce the computation and memory costs. The result of acoustic guided wave tomography is also used as a first guess to reduce the number of iterations and the sensitivity to local minima. After explaining the principle of the shape derivative, validations on simulated and experimental data will be presented in this talk.

Full Dispersion‐Spectrum Inversion of Surface Waves

AbstractNowadays, the most successful applications of full‐waveform inversion (FWI) involve marine seismic data under acoustic approximations. Elastic FWI of land seismic data is still challenging in theory and practice. Here, we propose a full dispersion spectrum inversion method and apply it to seismic data acquired in West Antarctica. Inspired by the conventional surface wave dispersion curve inversion method, we propose to invert the surface wave dispersion spectrum instead of the complicated waveforms. We compare the frequency‐velocity, frequency‐slowness, and frequency‐wavenumber spectra in terms of their ability to resolve dispersion modes and the feasibility of their adjoint updates and conclude that the frequency‐slowness spectrum is the best for our inversion objectives. We test four objective functions, subtraction, zero‐lag crosscorrelation, optimal transport, and the local‐crosscorrelation to quantify the spectrum mismatch and provide the corresponding adjoint source. We then theoretically analyze the convexity of the proposed objective functions and examine their convergence behavior using numerical examples. We also compare the proposed method with the classic FWI method and the traditional surface wave dispersion curve inversion method and discuss the strengths and weaknesses of each method. This technique is employed to evaluate the shallow velocity structures beneath a seismic array stationed in West Antarctica. Our proposed inversion scheme is also useful for more general applications such as imaging the shallow subsurface of the critical zones, like geothermal reservoirs, and CO2 storage sites.

Molecular dynamics simulation of spall behavior of amorphous/crystalline composites under shock loading

The industrial application of metallic glass (MG) is greatly limited due to its poor ductility and susceptibility to catastrophic fracture. The mechanical properties of MG can be effectively improved by adding crystal phases to make amorphous/crystalline composites. Meanwhile, spallation is a typical form of dynamic failure of materials under shock loading. However, the spall behavior of amorphous /crystalline composites has been rarely studied. In this work, the shock induced spallation process of Cu50Zr50/copper (Cu) composite materials was investigated through molecular dynamics (MD) simulations. It is found that stress waves transmit and reflect at interface due to the mismatch of acoustic impedance. Besides, MG is “softer” than the single crystal Cu from the perspective of stress wave propagation. By changing the loading direction, it was found that classical spall is more likely to occur in the Cu phase, while micro-spall is more likely to occur in the MG phase. However, as the loading velocity increases, the spall form in the Cu phase will also transform into micro-spall. The spall strength and strain rate through acoustic approximation and MD simulations were also obtained. Finally, it was observed that the tensile stress superposition region caused by interface reflection waves may form new danger points where spallation may initiate, thereby resulting in complex spall phenomena in composite materials. The conclusions obtained reveal the characteristics of the spall phenomenon in Cu50Zr50/Cu composite materials, which is beneficial to further understanding the spall mechanism and providing guidance for designing amorphous/crystalline composite materials under shock loading.

Analysis of natural vibration of truncated conical shells partially filled with fluid

AbstractIn this paper, we study the vibrational behavior of shells in the form of truncated cones containing an ideal compressible fluid. The sloshing effect on the free surface of the fluid is neglected. The dynamic behavior of the elastic structure is investigated based on the classical shell theory, the constitutive relations of which represent a system of ordinary differential equations written for new unknowns. Small fluid vibrations are described in terms of acoustic approximation using the wave equation for hydrodynamic pressure written in spherical coordinates. Its transformation into the system of ordinary differential equations is carried out by applying the generalized differential quadrature method. The formulated boundary value problem is solved by Godunov's orthogonal sweep method. Natural frequencies of shell vibrations are calculated using the stepwise procedure and the Muller method. The accuracy and reliability of the obtained results are estimated by making a comparison with the known numerical and analytical solutions. The dependencies of the lowest frequency on the fluid level and cone angle of shells under different combinations of boundary conditions (simply supported, rigidly clamped, and cantilevered shells) have been studied comprehensively. For conical straight and inverted shells, a numerical analysis has been performed to estimate the possibility of finding configurations at which the lowest natural frequencies exceed the corresponding values of the equivalent cylindrical shell.

A new highly accurate and efficient pure visco‐acoustic wave equation for tilted transversely isotropic attenuating media

AbstractThe propagation of seismic waves in attenuating anisotropic media exhibits amplitude dissipation and phase dispersion. To describe its effects, the fractional Laplacian pure visco‐acoustic wave equations capable of producing stable and noise‐free wavefields have been derived. However, except for acoustic approximation, previous wave equations utilize the approximations with lower accuracy in simplifying the denominator of the approximate complex‐valued dispersion relation, resulting in reduced accuracy. To address this concern, we use a combination of complex stiffness coefficients to replace the denominator term of the approximate complex‐valued dispersion relation. This approximation effectively reduces the loss of accuracy caused by ignoring the influence of the velocity anisotropy parameter ε and the attenuation anisotropy parameter εQ in the denominator term, leading to a wave equation with high accuracy in media with large anisotropic parameters ε and δ. In addition, the new wave equation only contains two high‐order spatial partial derivatives and has high computational efficiency. Theoretical analysis and numerical examples demonstrate that the proposed pure visco‐acoustic tilted transversely isotropic wave equation outperforms the previous pure visco‐acoustic wave equation in terms of simulation accuracy. The newly developed wave equation is well suited for the application of Q‐compensated reverse time migration and full waveform inversion in attenuating anisotropic media.

A wave model of high frequency vibrational energy transfer in a wedge-shaped combined plate structure

Wedge shaped combined plate structure (WCPS) is broadly applied in large-sized transport equipment such as aerospace and shipping. However, with the increase of equipment operating running, it is easy to cause high-frequency vibration of structure components. Therefore, studying the energy transfer and vibration response of high-frequency vibration in WCPS is significant for the structural design of aerospace and shipping. The promising method is energy finite element analysis (EFEA). However, the energy transfer coefficient at joint of WCPS is needed in EFEA. The current studies about the energy transfer coefficients are focus on the joint between two uniform thickness plate. But it is some different that getting the energy transfer coefficient for WCPS, because the near-field solve representation for wedge-shaped plate is complicated due to the non-uniform thickness of wedge-shaped plate member in WCPS. In this research, geometric acoustic approximation and an equilibrium equation on both ends of joints were used to derive the equation of the energy transfer coefficient for the WCPS. Then by setting coupling nodes, construction of a coupling matrix to characterize discontinuity of energy density at the coupling position of the WCPS and energy density governing equation of wedge-shaped plates were integrated. In doing so, the EFEA modeling of the WCPS was developed and the energy density distribution on each node of the WCPS could be obtained. Same-sized uniformly coupled structures is analyzed, the vibration energy distribution characteristics of two types of coupling structures were compared. The results show that the energy density value of the wedge plate member attenuate more slowly than that of the uniform plate member due to the acoustic black hole aggregation effect in the wedge plate part, and there is an abrupt change in the energy density value at the joint of WCPS. As a result, the factors influencing high-frequency vibration energy transfer were investigated.

Wavefield simulation of acoustic VTI wave equation based on adaptive-coefficient finite-difference frequency-domain method

Abstract Many simulation methods have been developed for P-waves in vertically transversely isotropic (VTI) media. These methods are based on the acoustic approximation. The finite-difference frequency-domain (FDFD) method stands out for its ability to simulate multi-shot or narrowband seismic data. It has no temporal dispersion, facilitates attenuation modelling, and enables parallelization. The optimal FDFD method is commonly used to simulate the acoustic VTI wave equation, but it applies the same FDFD coefficients for different frequencies and model velocities, which cannot fully minimize the numerical dispersion error. To enhance its accuracy and effectiveness, we develop an adaptive-coefficient FDFD method specifically for the acoustic VTI wave equation. The FDFD coefficients depend on two factors: the number of wavelengths in each grid and the Thomsen parameters. The dispersion analysis reveals that the proposed FDFD method can achieve a reduction in the necessary number of grid points from 4 to 2.5 compared to the optimal 9-point average derivative method (ADM), while maintaining a maximum dispersion error of 1%. From three numerical examples, the developed FDFD method can obtain more accurate wavefield results than the ADM optimal FDFD method, while taking comparable computational time and memory.

ON THE POSSIBILITY OF ESTIMATING THE RADIUS OF A CYLINDRICAL REFLECTOR BY THE TIME OF THE DELAY OF THE PULSE OF THE PASSING WAVE IN RELATION TO THE MIRROR-REFLECTED PULSE OF THE SHEAR WAVE DURING ULTRASONIC METAL INSPECTION BY AN ANGLE PROBE

Modeling of the electro-acoustical channel of an angle probe for a side drilled hole type reflector made it possible to calculate the forms of the run round pulse generated by the radiation of a surface Rayleigh wave propagating along a concave cylindrical cavity and the wave pulse when reflected in the geometric acoustics approximation (mirror) for different radii of the hole and to obtain estimates of the ratio of the amplitudes of these pulses and the difference in their registration time. Comparison of the experimental results with those obtained by calculation for holes with radii of 2 and 3 mm showed their quite good qualitative and satisfactory quantitative coincidence. Estimates of the radius of a cylindrical hole are given based on the experimental delay time of the run round pulse and the Rayleigh wave velocity for a flat surface using a simple ratio; the range of the ratio of the diameter of the hole to the length of the transverse wave in the medium in which such an assessment is advisable is indicated, and an example of the values of the lag time in this range is given.

Wavefield simulation and reverse time migration for acoustic TTI media

Seismic imaging necessitates precisely separating P and S waves to mitigate undesirable crosstalk between them. Failure to properly handle this crosstalk can lead to distorted or misinterpreted images. In an elastic anisotropic medium, the polarization of a P wave is not necessarily parallel to its propagating direction, making the separation of P and S waves more difficult than in the case of an elastic isotropic medium. A pure acoustic transversely isotropic (TI) wave equation involves a mixed-domain problem. This usually means the space dependencies and wavenumbers are coupled in the wavefield extrapolator. An efficient solution to the wavefield requires a separation between the space dependencies and wavenumbers in the extrapolator. There are two primary approaches: (1) an analytical separation of the mixed-domain term; and (2) a numerical solution to the mixed-domain term, such as low-rank and Poynting vector methods. In this study, the acoustic approximation is derived by setting the S-wave phase velocity to zero in all phase directions. An analytical separation is developed in this study by employing a Taylor series to linearize the anellipticity term, thereby decoupling the space-dependent and wavenumber-dependent variables within the wavefield extrapolator. The kinematics analysis demonstrates that our method has competitive phase velocity accuracy compared with existing methods. Moreover, the corresponding TI acoustic wave equation can be efficiently solved by the hybrid finite-difference/pseudospectral method. In a 2D case, it only requires one fast Fourier transform, two inverse Fourier transforms, and a few additional spatial differentiations at each time step. Remarkably, our wavefield solution remains independent of the wavefield heterogeneity (as observed in the low-rank approach) and is immune to wavefield interference (as encountered in the Poynting vector method). The developed acoustic approximation ensures the absence of any S-wave artifacts with relatively cheap computation. Numerical examples indicate our acoustic tilted transversely isotropic wave equation is reliable for accurate wavefield modeling and reverse time migration.

2D multiple waves scattering for active detection of a dummy human body in a low frequency range and for various boundary conditions

This paper investigates the results of simulations devoted to the acoustic field variation caused by different boundary conditions applied to the backscattering of the acoustic wave in both low and moderately low frequency ranges. The goal is to analyse the object behaviour and the detection ability of the 2D acoustic field approximations when the simulation data of the scattered sound field is available. The plane waves are backscattered by a dummy human body, positioned in a cabin which has a defined size. The dummy human body is created by using clusters of finite and disjointed but tangent circular cylinders. Each cylinder is a scatterer that emulates various boundary conditions i.e., the scatterers can be sound-soft (Dirichlet boundary condition) and sound-hard scatterers (Neumann boundary condition). The cylinders are filled with biological tissue (i.e., fat). The exterior scattering problem is solved using the preconditioned Krylov subspace iterative solvers (GMRES), as a computationally cheaper alternative. We use the hypothesis that the mass density of the obstacle and wave speed in the obstacle are both constant. During the simulation experiments, we neglected the interactions among scatterers. A frequency range from 100 Hz to 1000 Hz is analysed. Both the Sound Pressure Level (SPL) and Radar Cross Section (RCS) are used to analyse the numerical simulation of the sound field.

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain.

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. These results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

Simplified TTI pure qP-wave equation implemented in the space domain and applied for reverse time migration in TTI media

The assumption that the earth’s subsurface is a homogeneous and isotropic medium enables the imaging of important geologic structures but results in information loss, especially in more complex geologic media. Therefore, considering anisotropy is crucial for seismic imaging, particularly the most common anisotropy in geophysics: the transversely isotropic medium. However, this also means a considerable increase in the computational cost of reverse time migration (RTM). Thus, a new pseudoacoustic wave equation for pure qP-wave in tilted transversely isotropic (TTI) media, which can also be efficiently implemented using the finite-difference (FD) method with the unit vector method (UVM), is proposed, aiming to reduce the computational cost of the RTM. The proposed equation solved with fast Fourier transforms is exact and faster for seismic migration than the base equations found in the literature; however, a greater efficiency is achievable by using FD to compute the second derivatives. In contrast, when solved with the UVM, it is kinematically accurate and significantly faster, although dynamically inaccurate as it is an acoustic approximation. The efficiency and efficacy of this new equation are demonstrated by modeling and migrating synthetic TTI data found in the literature.

Mesoscale modelling of the dynamic tensile strength enhancement of concrete in spalling tests using interface elements

The dynamic tensile strength of concrete has been experimentally reported to increase significantly with the increase of imposed strain rates. However, the intrinsic mechanisms accounting for the strength increase are not well understood so far. This paper presented numerical simulations based on the spalling technique to further explore mechanisms of the dynamic responses of concrete under impact loadings. Numerical results have been verified and validated against experimental evidence with various strain rates. The validity of utilizing the Novikov acoustic processing approximation for obtaining the spalling strength of concrete is identified and discussed. Results demonstrate that this indirect processing approach could overestimate the spalling strength because real material behavior tends to deviate from its basic assumption. Mechanisms accounting for the spalling strength increase from key aspects including the meso-structure, the strain rate-dependent material behaviour, the micro-crack inertia, and the structural inertial are also identified accordingly. Results demonstrate that the increment of concrete dynamic tensile strength in spalling tests is mainly caused by the strain rate-dependent material behaviour which should be incorporated in the material constitutive description. Besides that, the material heterogeneity also makes a considerable contribution to the increase of dynamic tensile strength in spalling tests and this contribution becomes increasingly prominent with the increase of the imposed strain rates. On the other hand, the structure inertial and the micro-crack inertial have little effect on the increase of spalling strength of concrete and thus may be ignored within the imposed strain rate range in spalling tests.

Pressure dynamics of an internal shock wave emission inside a water droplet and potential cavitation

Shock reflected by a spherical interface is involved in shock-droplet interaction. Here, we investigate the pressure dynamics of an internal spherical shock wave and the potential cavitation inside a spherical water droplet. We conduct hydrodynamic simulation and employ the linear geometrical acoustics approximation to analyze the negative pressure and the wavefront at different intervals d between the source point of the shock and the droplet surface. Studies indicate that the negative pressure at a very large d is primarily attributed to the focusing effect of the droplet surface, whereas the collision of the reflected waves contributes to negative pressure at a small d. The caustic, which is the locus of the cusps (singular points) on the shock wavefront is determined by the parametric equations. Notably, the caustic also has singular points owing to the off-axis reflection. Finally, we evaluate the cavitation inside the droplet. Cavitation occurs on the opposite side of the droplet and moves away from the surface with d increasing, which agrees with previous experimental results. Additionally, we demonstrate that cavitation can occur with less damage to the droplet compared to a planar shock impact on a water droplet.

An open benchmark to assess the effects of underwater explosions on steel panels using the volume of fluid approach

Despite the underwater explosion phenomena (UNDEX) have been studied for decades and several numerical methods have been proposed in literature, the simulation of the whole phenomenon in issue is even nowadays a matter of research. In this paper, a Volume of Fluid (VOF) approach, which allows the simulation of Fluid-Structure Interaction (FSI), including the effects of seawater and vapor of cavitation on structures, is calibrated according to theory and experimental data. As a benchmark, a parallelepiped of fluid is built, verifying the effectiveness of the method with reference to some close-in explosions available in literature. In addition, VOF results are compared with the ones achieved from other researchers using the acoustic approximation. Strengths and limits of VOF coupling method are pointed out. In the end, the modelling strategy proposed and validated can be considered a suitable tool for the design of naval structures subject to underwater explosions.

Layer-by-layer acoustic travel time approximation using ray theory for total focusing method imaging in carbon fiber reinforced polymer

This paper proposes a layer-by-layer acoustic travel time approximation method based on ray theory for total focusing method (TFM) imaging in carbon fiber reinforced polymer (CFRP) laminates. The method considers the anisotropy in every monolayer and heterogeneity of CFRP, which approximates the path of propagation as straight in the whole material. The application of this method to TFM imaging is called TravelTimeAppro-TFM. In comparison to isotropic-TFM and Dijkstra-TFM, the experimental results indicated that TravelTimeAppro-TFM outperforms isotropic-TFM in terms of imaging amplitude gain with a maximum gain of 4.67 dB. On the other hand, this approach reduces the computational work compared to Dijkstra-TFM. The proposed method demonstrates significant improvements in both focusing performance and the speed of calculation. This paper also investigates the effective angular range of the layer-by-layer acoustic travel time approximation method through experimental and finite element simulation analysis.

Acoustic error approximation due to Gouy phase in the sea

In order to estimate the statistical phase of underwater propagation for coherent acoustic systems, a calculation of background structure functions, based on wavespeeds, provides a wavefront distortion metric that excludes the phase due to focusing. In 1890, Gouy measured a phase change through the focus that differs for spherical vs cylindrical convergence by a factor of 2 from π/2. Statistics for the locations of the probable focus waist can use structure functions based on the measured sound speed profiles. Phase estimates are susceptible to errors in phase estimation unless results consider the Gouy phase while passing through focus waists. These foci may counteract or average with other errors of estimation, including scattering, type of spreading (cylindrical vs spherical foci), and reflections from the surface and bottom. Oceans have a sufficient range for the spatial derivatives of sound speed profiles to contribute persistently to foci that we show have coherence time and cross-sectional spatial (imaging) coherence. As an alternative, specular point theory can estimate deterministic pressure solutions. Convergence of these ray models that violate the stationary phase requires methods such as catastrophe theory to estimate the focal effects. Sommerfeld had an early comprehensive ray theory description that includes the Gouy phase. Using Flatté’s data, the foci are clearly time and length coherent. Statistically, the mutual coherence function for the Atlantic, Caribbean, and Gulf of Mexico regions shows that even distorted and out-of-phase convergence has full spatial coherence.