Prestack reverse time imaging in tunnels based on the decoupled nonconversion elastic-wave equation

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. S371-S383
Author(s):  
Yuxiao Ren ◽  
Zhichao Yang ◽  
Bin Liu ◽  
Xinji Xu ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Accurate Method ◽  
Wave Mode ◽  
P Wave ◽  
Tunnel Construction ◽  
Reverse Time ◽  
S Wave ◽  
Tunnel Face ◽  
Time Migration ◽  
Converted Waves

The safety and efficiency of tunnel construction depend on the knowledge of complex geologic conditions. Hence, an accurate forward-prospecting technique is required to detect unexpected inhomogeneous geologic structures ahead of tunnel construction. As an accurate method to image geologic heterogeneities, elastic reverse time migration (ERTM) is introduced to the field of tunnel forward prospecting. However, in the tunnel environment, ERTM images may suffer from the interference of crosstalk artifacts, which are caused by converted waves on tunnel surfaces. Therefore, considering the actual influence of the tunnel body, the decoupled nonconversion elastic equation was incorporated into traditional ERTM. This method prevents the generation of converted waves but ensures independent P- and S-wave propagation. In addition, wave-mode separation for raw seismic data is required in our approach. Synthetic examples based on the real geologic environment of tunnels show that our method produces satisfactory results for P-wave and S-wave imaging and the S-wave can produce a better imaging effect in tunnels. Finally, we apply our method to the seismic data obtained from a real highway tunnel construction site to demonstrate its performance in real-world applications. The results indicate that the migrated images can help to accurately constrain the geologic formations ahead of the tunnel face.

A new decoupling and elastic propagator for efficient elastic reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. A31-A36
Author(s):  
Qizhen Du ◽  
Qiang Zhao ◽  
Qingqing Li ◽  
Liyun Fu ◽  
Qifeng Sun
Keyword(s):  
Heterogeneous Media ◽  
Compressional Wave ◽  
Wave Mode ◽  
P Wave ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Energy Leakage

Methods to decompose the elastic wavefield into compressional wave (P-wave) and shear wave (S-wave) components in heterogeneous media without wavefield distortions or energy leakage are the key issues in elastic imaging and inversion. We have introduced a decoupled P- and S-wave propagator to form an efficient elastic reverse time migration (RTM) framework, without assuming homogeneous Lamé parameters. Also, no wave-mode conversions occur using the proposed propagator in the presence of strong heterogeneities, which avoids the potential imaging artifacts caused by wave-mode conversions in the receiver-side backward extrapolation. In the proposed elastic RTM framework, the source-side forward wavefield is simulated with a P-wave propagator. The receiver-side wavefield is back extrapolated with the proposed propagator, using the recorded multicomponent seismic data as input. Compared to the conventional elastic RTM, the proposed framework reduces the computational complexity while preserving the imaging accuracy. We have determined its accuracy and efficiency using two synthetic examples.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

Direct vector-field method to obtain angle-domain common-image gathers from isotropic acoustic and elastic reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB135-WB149 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Direct Method ◽  
Incident Angle ◽  
Field Method ◽  
Propagation Direction ◽  
P Wave ◽  
Common Source ◽  
Spatial Gradient ◽  
Reverse Time ◽  
S Wave ◽  
Time Migration

We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in angle domain, we use the crosscorrelation image condition, which is substantially more efficient. This is a direct method, and is less dependent on the data quality than the space-shift method. The concepts were successfully implemented and tested with 2D synthetic acoustic and elastic examples, including a complicated (Marmousi2) model that illustrates effects of multipathing in angle-domain common-image gathers.

On plane‐wave decomposition: Alias removal

Geophysics ◽  
1989 ◽  
Vol 54 (10) ◽  
pp. 1339-1343 ◽  
Author(s):  
S. C. Singh ◽  
G. F. West ◽  
C. H. Chapman
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Time Distance ◽  
P Domain ◽  
Wave Decomposition ◽  
Rapid Modeling

The delay‐time (τ‐p) parameterization, which is also known as the plane‐wave decomposition (PWD) of seismic data, has several advantages over the more traditional time‐distance (t‐x) representation (Schultz and Claerbout, 1978). Plane‐wave seismograms in the (τ, p) domain can be used for obtaining subsurface elastic properties (P‐wave and S‐wave velocities and density as functions of depth) from inversion of the observed oblique‐incidence seismic data (e.g., Yagle and Levy, 1985; Carazzone, 1986; Carrion, 1986; Singh et al., 1989). Treitel et al. (1982) performed time migration of plane‐wave seismograms. Diebold and Stoffa (1981) used plane‐wave seismograms to derive a velocity‐depth function. Decomposing seismic data also allows more rapid modeling, since it is faster to compute synthetic seismograms in the (τ, p) than in the (t, x) domain. Unfortunately, the transformation of seismic data from the (t, x) to the (τ, p) domain may produce artifacts, such as those caused by discrete sampling, of the data in space.

Elastic inversion of near- and postcritical reflections using phase variation with angle

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R149-R159 ◽  
Author(s):  
Xinfa Zhu ◽  
George A. McMechan
Keyword(s):  
Wave Velocity ◽  
Spherical Wave ◽  
Phase Variation ◽  
P Wave ◽  
Wide Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Elastic Inversion

Near- and postcritical (wide-angle) reflections provide the potential for velocity and density inversion because of their large amplitudes and phase-shifted waveforms. We tested using phase variation with angle (PVA) data in addition to, or instead of, amplitude variation with angle (AVA) data for elastic inversion. Accurate PVA test data were generated using the reflectivity method. Two other forward modeling methods were also investigated, including plane-wave and spherical-wave reflection coefficients. For a two half-space model, linearized least squares was used to invert PVA and AVA data for the P-wave velocity, S-wave velocity, and the density of the lower space and the S-wave velocity of the upper space. Inversion tests showed the feasibility and robustness of PVA inversion. A reverse-time migration test demonstrated better preservation of PVA information than AVA information during wavefield propagation through a layered overburden. Phases of deeper reflections were less affected than amplitudes by the transmission losses, which makes the results of PVA inversion more accurate than AVA inversion in multilayered media. PVA brings useful information to the elastic inversion of wide-angle reflections.

Amplitude-preserving scalar PP and PS imaging condition for elastic reverse time migration based on a wavefield decoupling method

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S113-S125 ◽  
Author(s):  
Xiyan Zhou ◽  
Xu Chang ◽  
Yibo Wang ◽  
Zhenxing Yao
Keyword(s):  
Wave Vector ◽  
Numerical Models ◽  
P Wave ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Decoupling Method ◽  
Time Migration ◽  
Imaging Results

To eliminate crosstalk within the imaging results of elastic reverse time migration (ERTM), we can separate the coupled P- and S-waves from the forward source wavefield and the backpropagated receiver wavefield. The P- and S-wave decoupling method retains the original phase, amplitude, and physical meaning in the separated wavefields. Thus, it is a vital wavefield separation method in ERTM. However, because these decomposed wavefields are vectors, we could consider how to retrieve scalar images that reveal the real reflectivity of the subsurface. For this purpose, we derive a scalar P-wave equation from the velocity-stress relationship for PP imaging. The phase and amplitude of this scalar P-wave are consistent with the scalarized P-wave. Therefore, this scalar P-wave can be exploited to perform PP imaging directly, with the imaging result retaining the amplitude characteristics. For PS imaging, it is difficult to calculate a dynamic preserved scalar S-wave. However, we have developed a scalar PS imaging method that divides the PS image into energy and sign components according to the geometric relationship between the wavefield vibration and propagation directions. The energy is calculated through the amplitude crosscorrelation of the forward P-wave and backpropagated S-wave from the receivers. The sign is obtained from the dot product of the forward P-wave vector and the backpropagated S-wave vector. These PP and PS imaging methods are suitable for 2D and 3D isotropic media and maintain the correct amplitude information while eliminating polarity-reversal phenomena. Several numerical models are used to verify the robustness and effectiveness of our method.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

Amplitude effect of the free surface in elastic reverse-time extrapolation

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S177-S184 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Free Surface ◽  
Computational Model ◽  
P Wave ◽  
Surface Boundary ◽  
Reverse Time ◽  
S Wave ◽  
Elastic Data ◽  
Converted Waves ◽  
Incident Waves ◽  
Time Extrapolation

We evaluate the physical validity of surface boundary conditions of the computational model in reverse-time extrapolation of 3D, three-component (3-C) elastic seismic data acquired at the earth’s free surface by using mathematical derivations and numerical simulations. Reverse-time extrapolation of elastic data assumes that only the incident P- or S-waves are reconstructed during extrapolation into the computational grid. However, superposition of the (upgoing) incident waves and the (downgoing) reflected and converted waves generated at the free surface also is recorded in data acquisition and is input into reverse-time extrapolation. In elastic reverse-time extrapolation, the computational model needs to have an absorbing top boundary. When the 3D, 3-C elastic data are inserted into the computational model during reverse-time extrapolation, the originally incident P- or S-wave is reconstructed. In addition, the free-surface P-to-P reflected and P-to-S converted waves recombine to reconstruct a second incident P-wave, and the free-surface S-to-S reflected and S-to-P converted waves recombine to reconstruct a second incident S-wave. Therefore, 3D elastic reverse-time extrapolation reconstructs the incident waves with displacement amplitudes increased by a fixed factor of exactly two when free-surface reflections and conversions are in the data. In this implementation, reconstructed (virtual) waves propagating upward from the free surface enter an absorbing zone and disappear.

Prestack scalar reverse-time depth migration of 3D elastic seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S199-S207 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan ◽  
Chen-Shao Lee ◽  
Jinder Chow ◽  
Chen-Hong Chen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Seismic Data ◽  
P Wave ◽  
Scalar Wave ◽  
Reverse Time ◽  
S Wave ◽  
Absolute Value ◽  
S Waves ◽  
Finite Difference Solution

Using two independent, 3D scalar reverse-time depth migrations, we migrate the reflected P- and S-waves in a prestack 3D, three-component (3-C), elastic seismic data volume generated with a P-wave source in a 3D model and recorded at the top of the model. Reflected P- and S-waves are extracted by divergence (a scalar) and curl (a 3-C vector) calculations, respectively, during shallow downward extrapolation of the elastic seismic data. The imaging time for the migrations of both the reflected P- and P-S converted waves at each point is the one-way P-wave traveltime from the source to that point.The divergence (the extracted P-waves) is reverse-time extrapolated using a finite-difference solution of the 3D scalar wave equation in a 3D P-velocity modeland is imaged to obtain the migrated P-image. The curl (the extracted S-waves) is first converted into a scalar S-wavefield by taking the curl’s absolute value as the absolute value of the scalar S-wavefield and assigning a positive sign if the curl is counterclockwise relative to the source or a negative sign otherwise. This scalar S-wavefield is then reverse-time extrapolated using a finite-difference solution of the 3D scalar wave equation in a 3D S-velocity model, and it is imaged with the same one-way P-wave traveltime imaging condition as that used for the P-wave. This achieves S-wave polarity uniformity and ensures constructive S-wave interference between data from adjacent sources. The algorithm gives satisfactory results on synthetic examples for 3D laterally inhomogeneous models.

Multidirectional-vector-based elastic reverse time migration and angle-domain common-image gathers with approximate wavefield decomposition of P- and S-waves

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S57-S79 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Time Migration ◽  
Mode Separation ◽  
Reflection Image ◽  
Wavefield Decomposition ◽  
Imaging Conditions

Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the traditional scheme of P/S-wave mode separation is based on Helmholtz’s equations, which ignore the conversion between P- and S-waves at the current separation time. Thus, it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition. Second, the vector-based imaging condition needs to use the reflection-image normal, and it also cannot give the correct polarity of the PP image in all possible conditions. Third, the angle-domain common-image gathers (ADCIGs) calculated using the Poynting vectors (PVs) do not consider the wave interferences that happen at each reflector. Therefore, smooth models are often used for E-RTM. We relax this condition by proposing an improved data flow that involves three new contributions. The first contribution is an improved system of P/S-wave mode separation that considers the converted wave generated at the current time, and thus it does not require the constant-shear-modulus assumption. The second contribution is the new elastic imaging conditions based on multidirectional vectors; they can give the correct image polarity in all possible conditions without knowledge of the reflection-image normal. The third contribution is two methods to calculate multidirectional propagation vectors (PRVs) for RTM images and ADCIGs: One is the elastic multidirectional PV, and the other uses the sign of wavenumber-over-frequency ([Formula: see text]) ratio obtained from an amplitude-preserved approximate-propagation-angle-based wavefield decomposition to convert the particle velocities into multidirectional PRVs. The robustness of the improved data flow is determined by several 2D numerical examples. Extension of the schemes into 3D and amplitude-preserved imaging conditions is also possible.

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