Cross-correlation Of Wavefields Research Articles

Consistency of the inverse scattering imaging condition, the energy norm imaging condition and the impedance kernel in acoustic and elastic reverse-time migration

Abstract In this work, we draw connections between the imaging conditions using the impedance kernel, the inverse scattering imaging condition, and the energy norm imaging condition in acoustic and elastic reverse-time migration (RTM). Traditional RTM often introduces large low-wavenumber artifacts that degrade image quality in intricate geological structures with large velocity variations. In practice, the Laplacian filter is commonly used to remove these low-wavenumber artifacts, but it changes the image wavenumber spectrum. The advanced imaging conditions of the inverse scattering, the energy norm, and the impedance kernel can effectively remove the low-wavenumber artifacts while not changing the wavenumber spectrum. This study aims to build a connection between these three types of imaging conditions by conducting detailed analysis in the wavenumber domain for acoustic and elastic RTMs. We find that they are exactly the same except for the varying weights of the source-receiver wavefield cross-correlation. All three imaging conditions can generate clear RTM images that are not affected by low-wavenumber artifacts. Numerical examples for a simple model, Sigsbee 2a, and BP models verify the consistency of these three imaging conditions and show their advantage over conventional simple zero-lag cross-correlation imaging conditions. This is important for improving the quality and reliability of seismic imaging technology.

Parsimonious truncated Newton method for time-domain full-waveform inversion based on the Fourier-domain full-scattered-field approximation

To exploit Hessian information in full-waveform inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag crosscorrelation of the first-/second-order incident wavefields and the second-/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much more challenging because it is not affordable to store all of the time-dependent wavefields. The widely used wavefield recomputation strategy leads to computationally intensive tasks. We have developed an efficient alternative approach to computing the Hessian-vector product for time-domain FWI. In our method, discrete Fourier transform is applied to extract frequency-domain components of involved wavefields, which are used to compute wavefield crosscorrelation in the frequency domain. This makes it possible to avoid reconstructing the first- and second-order incident wavefields. In addition, a full-scattered-field approximation is proposed to efficiently simplify the second-order incident and adjoint wavefield computation, which enables us to refrain from repeatedly solving the first-order incident and adjoint equations for the second-order incident and adjoint wavefields (re)computation. With our method, the computational time can be reduced by 70% and 80% in viscous media for Gauss-Newton and full-Newton Hessian-vector product construction, respectively. The effectiveness of our method is also verified in the frame of a 2D multiparameter inversion, in which our method almost reaches the same iterative convergence of the conventional time-domain implementation.

Guided ultrasonic wavefield cross-correlation with a curved array for high-resolution plate inspection

Abstract We present in this work an ultrasonic imaging technique based on wavefield cross-correlation that has potential for high-resolution inspecting of plates and plate-like structures. A curved transmit/receive array setup is used for acquiring wide-aperture waveform data beneficial for applying the presented imaging condition. An additional dispersion analysis using waveform data received by a linear array allows one to reveal the excited guided wave modes and possibly determine the shear wave velocity as an input parameter in the 3D wavefield simulation. Using synthetic but realistic data generated by realistic 3D simulations, we demonstrate the invariance of the time reversal process and the capability of the presented imaging approach for ultrasonic testing based on Lamb waves. In addition to the ability to localise and size multiple defects simultaneously, this imaging approach does not require baseline data and involves only minimal waveform data pre-processing.

Defect mapping in pipes by ultrasonic wavefield cross-correlation: A synthetic verification

This work presents a reverse-time imaging technique by cross-correlating the forward wavefield with the reverse wavefield for the detection, localization, and sizing of defects in pipelines. The presented technique allows to capture the wavefield reflectivity at the places of ultrasonic wave scattering and reflections. Thus, the method is suitable for detecting pipe defects of either point-like or finite-size types using data from a pulse-echo setup. By using synthetic data generated by 3D spectral element pipe models, we show that the 3D wavefield cross-correlation imaging is capable in the case of cylindrical guided ultrasonic waves. With a ring setup of transducers, we analyze the imaging results obtained from the synthetic single-transducer and all-transducer firings. The presented pipe flaw imaging method is straightforward to carry out using a suitable wave equation solver. Also, the method does not suffer from long iterative runs and numerical convergence issues commonly connected with imaging methods based on either deterministic optimization or statistical inference. The imaging procedure can be fully baseline-free by performing data processing to remove direct arrivals from the ultrasound data.

Monochromatic Identities for the Green Function and Uniqueness Results for Passive Imaging

For many wave propagation problems with random sources it has been demonstrated that cross correlations of wave fields are proportional to the imaginary part of the Green function of the underlying...

Discriminating physical and non-physical diffracted energy in source–receiver interferometry

SUMMARY We show how physical and non-physical diffracted waves can be discriminated in source– receiver interferometry (SRI), a wavefield interferometric method that constructs Green’s functions between any source–receiver pair. These can be estimated by convolution and crosscorrelation of wavefields propagating to or from other sources or receivers. SRI has been observed to work surprisingly well in practical applications when theoretical requirements (e.g. complete enclosing boundaries of other sources and receivers) are contravened as is standard in practical applications. As a partial explanation to this, it has been demonstrated previouslythatSRIforsinglediffractorproblemsproducescorrectGreen’sfunctionsestimates without requiring wavefields to be generated around specific stationary-phase points in space (as is required by other forms of interferometry). In this paper, we show that also for multiplediffractorproblems,anyboundarysource–receiverpairproducesstationary,correctkinematics for singly and multiply diffracted waves. However, when multiple diffractors are present, non-physical artefacts are produced in Green’s functions estimated by SRI with incomplete boundaries. We introduce a purely data-driven algorithm that allows traveltimes of any order ofphysical, diffractedwaves tobepredicted. Thisreduces ambiguity ininterpreting wavefields generated using SRI with only partial boundaries: this also permits spurious or non-physical energy in the constructed Green’s functions to be identified and either interpreted or ignored.

Green's Function Extraction for Interfaces With Impedance Boundary Conditions

Theory and experiments to obtain the response between two receivers from cross correlations of wave fields recorded at these receivers are well established. The principle relies on mutually spatial and temporal uncorrelated contributions from sources on a boundary enclosing the two receivers, which upon cross correlation interfere only constructively for signals traveling between the two receivers. It has, therefore, become generally known as interferometry. The theory includes situations with flow, mechanical, and electromagnetic field fluctuations, and their mutual coupling. Here, we present an electromagnetic theory for Green's function retrieval from cross correlations that incorporates general bianisotropic media in which interfaces are present where bianisotropic impedance boundary conditions apply. The derived Green's function representation shows that in lossless media and for interfaces with lossless impedance boundary conditions the Green's function between two receivers is obtained by cross correlating the recordings of these receivers from sources on a boundary enclosing them. We show numerical examples in 2-D where proper solutions are numerically tractable and practical approximations illustrate that numerically less intensive algorithms lead to acceptable results and accurate extraction of reflections from impedance boundary surfaces. Because the method is data driven, it is suitable for experimental Green's function extraction from measured data.

Retrieving the exact Green’s function by wavefield crosscorrelation

Recent development on the Green's function retrieval by wavefield crosscorrelation has substantially advanced the physical research in a multidisciplinary and unprecedented fashion. However, the underlying assumption of the theory that the sources are in the far-field limits the technology to extracting only the high-frequency part of the Green's function in an open system. This critical approximation can be eliminated using the exact boundary integral equation method. A scheme involving the crosscorrelation kernel is proposed to recover the exact Green's function including all-frequency content. Symmetric difference kernels are analytically constructed for sources on a plane or on a circle and can be reduced to the known Dirac delta kernel under the far-field approximation.

Seismic interferometry of teleseicmicS-wave coda for retrieval of body waves: an application to the Philippine Sea slab underneath the Japanese Islands

SUMMARY The reconstruction of surface waves from the cross-correlation of random wavefields has recently been extensively inspected by theoretical and experimental approaches. However, the reconstruction of body waves has not been extensively studied. In this study, we present a method for extracting body waves, that is, direct P and S waves, and reflected waves from the Philippine Sea slab. We use the cross-correlation of the wavefield generated by the teleseismic S waves observed by Hi-net tiltmeters with a passband of 0.07–0.5 Hz. To enhance the contribution of the S coda, we reduced the source-time function and the deterministic phases sS, ScS and SS, and the surface wave in S coda. The records of the processed S coda observed at every station-pair are cross-correlated for each teleseismic event. The cross-correlation functions (CCFs) of different earthquakes are stacked to retrieve wavefields propagating between the station-pairs. As a result, direct P, S and the reflected waves could be extracted when the stacked CCFs are aligned as a function of distance of separation between two stations. The gradients of the traveltime curves for the direct P and S waves are approximately 5–7 and 3k m s −1 , respectively. These velocities correspond to the seismic velocities of the crust or the P-wave velocity of the uppermost mantle. In order to enhance the reflected waves, we searched for the reflection points by assuming that the later phases in the CCFs are SS reflections and map the amplitudes onto the depth sections. As a result, the negative phases dipping to the north can be traced right below the region of hypocentre distribution. These negative phases probably correspond to the oceanic Moho within the Philippine Sea slab. We also show that the oceanic Moho can also be traced by assuming PP reflections. These results indicate that the CCFs plausibly contain information regarding both P and S waves propagating between the two receivers, and are capable of detecting reflected phases in addition to the direct waves.

Interferometric imaging condition for wave-equation migration

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component of the velocity model as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e., various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by preprocessing the reconstructed wavefields prior to the imaging condition. We use Wigner distribution functions to attenuate the random noise present in the reconstructed wavefields, parameterized as a function of image coordinates. Wavefield filtering using Wigner distribution functions and conventional imaging can be lumped together into a new form of imaging condition that we call an interferometric imaging condition because of its similarity to concepts from recent work on interferometry. The interferometric imaging condition can be formulated both for zero-offset and for multioffset data, leading to robust, efficient imaging procedures that effectively attenuate imaging artifacts caused by unknown velocity models.

Seismic surface waves in a suburban environment: Active and passive interferometric methods

Seismic interferometry refers to a new range of methods where inter-receiver wavefields (those that would have been recorded if one of each pair of receivers had been a source) can be estimated by cross-correlation of wavefields recorded at each of the receivers. These methods have found many applications in different fields of seismology, including creating “virtual” sources in wells under complex overburdens, computational full-wavefield modelling, and passive construction of surface wave waveforms from background noise in the Earth. Curtis et al. (2006) provide an overview of various applications of seismic interferometry referred to herein, and more in-depth works can be found in the special supplement on Seismic Interferometry in the July-August issue of GEOPHYSICS.