Wavefield Decomposition Research Articles

Angle domain common image gathers from reverse time migration by combining the Poynting vector with directional decomposition

ABSTRACTAngle domain common image gathers are crucial for seismic applications such as the migration velocity analysis and amplitude variation with angle analysis. Angle domain common image gathers are the gather of reflection coefficients when seismic waves incident at different angles on the same image point. The curvature of gathers can be used to update the migration velocity model. The amplitude variation of gathers characterizes different rock properties. Estimating the wavefield propagation direction is the most important step in the process of generating angle domain common image gathers. The wavefront propagation direction is perpendicular to the wavefront. Accurately estimating the wavefield propagation direction is crucial for calculating the reflection angle. Existing methods cannot provide the propagation direction with the high angular resolution when the subsurface structure is complex, meaning overlapped wave events exist. We propose a new method to overcome this problem. The proposed method separates overlapped waves with a directional filter bank after the up‐going and down‐going wavefield decomposition. Then, we apply the Poynting vector method to decomposed wavefield slices to determine the propagation directions of corresponding wavefield components. The key feature of the proposed method is that it does not require spatial local windows, and it is computationally efficient. Numerical tests demonstrate that our proposed method can accurately obtain the propagation direction of seismic waves in a wavefield including overlapped waves. The angle domain common image gathers generated using our proposed method have improved image quality with more accurate amplitudes and less noise compared with the angle domain common image gathers produced by the conventional Poynting vector method. It means our proposed method provides high‐quality prestack angle gathers for seismic attribute analysis.

Reverse-Time Migration by Combining Laplacian Filtering With Wavefield Decomposition for High-Resolution Subsurface Imaging

Reverse-time migration (RTM) is considered to be one of the most accurate migration methods, especially for imaging geologically complex structures. However, the conventional RTM using cross-correlation imaging condition is subject to strong migration artifacts. Recent researches on electromagnetic wavefield decomposition exhibit that the method can greatly suppresses the internal reflection noise, however, it is still subject to residual noise. To further eliminate the low-frequency noise to obtain high-resolution subsurface image, a novel electromagnetic imaging scheme by combining a Laplacian filtering with wavefield decomposition is presented, and the pseudospectral time-domain (PSTD) method is introduced to solve the time-dependent partial differential equations efficiently. In this work, we apply the Laplacian filtering on each wavefield snapshot in space domain to sharpen the field distribution. The filtered wavefields are further decomposed into downgoing and upgoing components for final imaging. Numerical experiments show that the proposed method balances the amplitudes of reflectors, and exhibits higher resolution compared to the conventional RTM.

True Amplitude Angle Gathers from Reverse Time Migration by Wavefield Decomposition at Excitation Amplitude Time

Reservoir parameter estimation is one of the goals of amplitude-versus-angle (AVA) inversion and angle-domain common image gathers are the basis of AVA inversion. Therefore, the accuracy of kinematic and kinetic information on angle gathers is very important for reservoir characterization. Reverse time migration is one of the most physically accurate migration method. Generating angle gathers from reverse time migration with the Poynting vector method is very efficient. However, due to inaccurate angle measurement and uneven illumination, angle gathers calculated by the Poynting vector method are often not suitable for AVA inversion. In this paper, we propose an efficient method of angle gathers with accurate angular information and amplitude from reverse time migration. We firstly decompose source and receiver wavefield to their up-going and down-going parts by using analytic wavefield. We calculate propagation directions for source down-going wavefield and receiver up-going wavefield by the Poynting vector method and form the angle gathers with these angle information and decomposed wavefield. To reduce memory storage and improve computational efficiency, we decompose wavefield at excitation amplitude time by using a local spatial Fourier transform. We also use a spatial smoothed Poynting vector to improve the stability of angle measurement. We apply an illumination compensation image condition to recover the true amplitude. Numerical examples on Marmousi model and the SEAM two-dimensional (2D) model demonstrate the advantages of our proposed method. The angle gathers based on our method are cleaner with more focus on events energy and better continuity, suffering from less low-frequency noise in the shallow parts and with a distinct cutoff at large angle where reflection terminates. At last, we demonstrate the effectiveness of proposed method on a 2D marine field data example.

Ambient noise wavefield decomposition and shear-wave velocity retrieval in the south of Tehran, Iran and in the Colfiorito basin, Italy

Knowledge about ambient noise wavefield, through decomposition into different participant waves and determination of precise singularities in ellipticity curves, could be very beneficial to improve the obtained subsurface velocity structures. In this paper, two array processing methods; WaveDec and high-resolution Rayleigh three-component beamforming (RTBF) and four single-station methods; Horizontal-to-Vertical Spectral Ratio (HVSR) or H/V, HVTFA (H/V using time frequency analysis), RayDec (Random Decrement Technique) and DOP-E (Degree Of Polarization) are applied to decompose ambient noise wavefield and to extract dispersion and ellipticity curves of surface waves. Two sites with different geological and geophysical conditions are chosen to examine the results of the measurements. The first selected site is in the south of Tehran, Iran, as a site with a low impedance contrast structure. The second one is in the Colfiorito basin, Italy, as a major impedance contrast structure site. Wavefield decomposition resulted in Rayleigh and Love wave separation and also mode distinction. The decomposed modes of surface waves and ellipticity curves of Rayleigh waves are used in a joint inversion process. The retrieved shear-wave velocity profiles are in close agreement with previous studies in the mentioned sites.

Diffracted wavefield decomposition and multidimensional site effects in the Argostoli valley, Greece

SUMMARYEffects of seismic ground motion induced by surface geology and geometry are known to be associated with the generation of a substantial proportion of surface waves. As a consequence, surface waves significantly contribute to ground-motion variability and site amplification. There is a growing body of literature recognizing that an understanding of physical patterns of the wavefield crossing a site is the key aspect to characterize and quantify them. However, this task remains technically challenging due to the complexity of such effects as well as the limitations of geophysical investigations, especially in case of small sedimentary valleys. The present study attempts to investigate the waves propagating across two 2-D dense seismic arrays from a number of earthquakes and explore the extent to which they are contributing to the multidimensional site effects. The arrays were deployed in the small-size, shallow alluvial valley of Koutavos-Argostoli, located in Cephalonia Island, Greece, and consisted of three-component velocimeters with interstation distances ranging from 5 to 160 m. A set of 46 earthquakes, with magnitudes between 2 and 5 and epicentral distances up to 200 km, was analysed by using an advanced seismic array processing technique, MUSIQUE. The phase velocity, backazimuth and energy of the dominant waves crossing the array were extracted, and their identification as Love or prograde/retrograde Rayleigh waves was obtained. The results clearly indicate a predominance of scattered surface waves (up to 60 per cent of total energy), mainly from the closest valley edges, above the fundamental frequency (∼1.5 Hz) of the valley. Love waves dominate the low-frequency wavefield (<3 Hz) while Rayleigh waves dominate some high-frequency bands. An excellent consistency is observed, in a given frequency range, among the dominance of the type of diffracted surface waves, group velocities estimated from the ground velocity structure and site amplification. The outcomes of this research provide a better understanding of the contribution of edge-diffracted surface waves and the 2-D/3-D site amplification at small and shallow alluvium valleys like Argostoli. The method applied here can be used to calibrate and validate 3-D models for simulating seismic ground motion.

Suppressing residual low-frequency noise in VSP reverse time migration by combining wavefield decomposition imaging condition with Poynting vector filtering

Due to high imaging precision and adaptability for steep-dip interfaces, reverse time migration (RTM) has become the preferred choice in seismic imaging. However, low-frequency noise is a common problem in RTM and effects the clarity of the final image. The noise is formed by the cross-correlation of source and receiver wavefields that propagate along the same paths. A wavefield decomposition imaging condition (WDIC) can eliminate this low-frequency noise by separating the wavefield into up–down or left–right directions and then cross-correlating source and receiver wavefields along the different propagation paths. Nevertheless, many backscattered waves propagating along horizontal, nearly horizontal, vertical and nearly vertical directions exist in vertical seismic profile (VSP) data. These waves are difficult to separate and generate the residual low-frequency noise when applying WDIC to VSP RTM. To overcome this, Poynting vector filtering is combined with WDIC to attenuate the noise. Several numerical case studies testify to the effectiveness of the analysis and method.

Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip

In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

An improved approach for normal-incidence sound transmission loss measurement using a four-microphone impedance tube

The main aim of this study is to introduce an improved method for determining the sound properties of acoustic materials which is more precise than the common wavefield decomposition method and simpler than the common transfer matrix method. In the first part of the article, a group of formulae for calculating sound transmission loss is represented by combining the wavefield decomposition and transfer matrix methods. Subsequently, a formula for calculating sound absorption coefficients is derived from these formulae by definition. Furthermore, the present formulae are validated by comparing the experimental results achieved with the present formulae and those results obtained by other methods recorded in published articles. Eventually, it is demonstrated that the method can accurately measure the sound insulation performance of materials and the sound absorption properties of limp and lightweight materials.

Effects of Oblique Incidence of SV Waves on Nonlinear Seismic Response of a Lined Arched Tunnel

The incident direction of earthquake motion is an important factor affecting the seismic response of underground structures. In this study, a three-dimensional (3D) oblique incidence method of SV waves is proposed and the effects of incident angles of SV waves on the seismic response of a lined arched tunnel are evaluated. Based on wave field decomposition principle and equivalent node force method and together with viscous-spring artificial boundary, the oblique incidence method of SV waves is implemented by transforming seismic wave field into the equivalent nodal forces acting on the artificial boundaries. By deriving the distance of the incident waves and the reflected wave on free surface to artificial boundaries, this method can comprehensively consider the phase difference of the seismic wave propagation and the influence of the damping effect of the rock medium on the seismic wave propagation. The method is programed into a dynamic finite element program and its effectiveness is examined by a numerical example. Consequently, the oblique incidence method is applied to evaluate the seismic behaviors of the tunnel. The numerical results reveal that (1) the oblique incidence of the seismic wave results in a larger seismic response; (2) the response amplitudes of the stress and displacement increase with the increase of incident angles and reaching the maximum in the case of 30° incident angle; (3) the damage extent increases with an increase in the incident angles, and the oblique incidence of the seismic wave is believed to increase the spatial difference of damage distribution.

Reverse time migration of ground‐penetrating radar with full wavefield decomposition based on the Hilbert transform

ABSTRACTThe conventional reverse time migration of ground‐penetrating radar data is implemented with the two‐way wave equation. The cross‐correlation result contains low‐frequency noise and false images caused by improper wave paths. To eliminate low‐frequency noise and improve the quality of the migration image, we propose to separate the left‐up‐going, left‐down‐going, right‐up‐going and right‐down‐going wavefield components in the forward‐ and backward‐propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground‐penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground‐penetrating radar data of a tilt‐interface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground‐penetrating radar data, low‐frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.

Wavefield separation for shear wave reflection enhancement in seismic records

S-waves in borehole seismic data can provide velocity, attenuation, anisotropy and reflectivity information that are crucial for delineating reservoir geometry and fluid flow structures. Despite the success and other potential benefits of including shear waves in the interpretation of seismic data to discriminate gas related amplitude anomalies from non-hydrocarbon related amplitude anomalies, little efforts have been applied to the development of shear wave technology. S-waves processing is yet to become a routine in borehole geophysics. This paper describes a procedure and some techniques for processing shear waves in a multi-component borehole seismic data– as a precursor for S-wave reflection imaging. The procedure is divided into three key stages, namely: suppression of P-wavefield in the multi-component data; attenuation of non-reflection arrivals in the S-wavefield; and separation of S-S reflection into up-going and down-going components. A set of high- resolution crosswell data acquired in a west Texas Oil field, U.S.A is used to test the method. The processed data confirmed the appropriateness of the method presented in this paper. The results yielded separated up-going and down-going S-S reflections that are traceable to the various reflectors depths. Shear wave reflection processing is a key stage in the development of shear wave technology for in oil and gas application.Keyword: Crosswell seismic data, Shear waves; S-wavefield; S-S reflections processing; Wavefield decomposition

An efficient vector elastic reverse time migration method in the hybrid time and frequency domain for anisotropic media

Vector elastic reverse time migration (ERTM) produces subsurface elastic images with correct polarities using multicomponent seismic data. However, the decomposition of elastic wavefields into vector P- and S-wavefields is computationally expensive, particularly in heterogeneous and complex anisotropic media. We have developed a computationally efficient vector ERTM method in the hybrid time and frequency domain by combining three existing techniques. Rather than decomposing elastic wavefields into vector qP- and qS-wavefields during time-domain wavefield propagation, we conduct the wavefield decomposition in the frequency domain for several selected frequencies. In general, the number of selected frequencies needed for migration imaging is much smaller than the number of time steps during forward and backward wavefield propagation, leading to greatly reduced computational costs associated with the qP-/qS-wavefield vector separation in complex heterogeneous anisotropic media. We further combine an implicit directional wavefield separation into the vector ERTM to enhance the image quality. The numerical results demonstrate that our method produces high-quality elastic-wave migration images with notably reduced computational costs compared to the conventional vector ERTM method.

Frequency-dependent reflection wave-equation traveltime inversion from walkaway vertical seismic profile data

To accurately image the geologic structures from walkaway vertical seismic profile (VSP) data, it is necessary to estimate the subsurface velocity field with high resolution and enhanced illumination of deep reservoirs. Because full-waveform inversion (FWI) suffers from cycle skipping when the initial model is far from the true model, we have adopted frequency-dependent reflection wave-equation traveltime inversion (FRWT) to generate the background velocity model for VSP migration. The upgoing reflection data are separated from the original shot gathers, and dynamic warping is used to evaluate the traveltime differences between the observed data and the calculated data. Different frequency bands of the data are inverted in sequence to reconstruct the velocity model with higher resolution. We also implement wavefield decomposition on the gradient field to extract the contributions of reflection components and improve the updated model. The inverted results obtained from FRWT can be used as the initial model for conventional FWI or the velocity model for reverse time migration. The experiments on synthetic data and field data demonstrate that our approach can effectively recover the background velocity model from walkaway VSP data.

2D least-squares elastic reverse time migration of multicomponent seismic data

Elastic reverse time migration (ERTM) is a state-of-the-art imaging technique used for determining complicated subsurface structures. However, the migrated images often suffer from low spatial resolution, low signal-to-noise ratio (S/N), and unbalanced amplitudes because the theoretical hypothesis of ERTM cannot be satisfied in practice. Although elastic least-squares reverse time migration (ELSRTM) has been proposed to address the issues of ERTM, the resulting images are generally represented by parameter perturbations such as P- and S-velocity perturbations, which have the different physical meanings from the ERTM images. To produce improved ERTM images, we used a least-squares RTM method for elastic data in isotropic media by applying least-squares inversion to ERTM. In the least-squares ERTM method, the forward operator generates multicomponent seismic data from the migrated images by applying elastic wavefield decomposition, scalar wavefield extrapolation, and wavefield recomposition operators. Additionally, the adjoint operator generates PP and PS images using ERTM, at which point the wavefield decomposition operator and scalar imaging condition are applied in the imaging process. Compared to conventional ERTM, our least-squares ERTM method enables us to produce improved ERTM images with higher resolution, more balanced amplitudes, and fewer artifacts. Several synthetic and field data examples were used to validate the effectiveness of the proposed least-squares ERTM method.

Stable and High-Efficiency Attenuation Compensation in Reverse-Time Migration Using Wavefield Decomposition Algorithm

Q -compensated reverse time migration ( Q -RTM) can compensate seismic attenuation caused by the anelastic behavior of subsurface media. Although, the traditional Q -RTM has high computational efficiency, it is instable because the high frequency or wavenumber ambient noise is exponentially boosted during forward and backward seismic wavefield propagation. The existing stable Q -RTM method costs twice as much computing time and memory compared to the traditional Q -RTM. In this letter, we propose a new Q -RTM method to address the above issues simultaneously. First, a new viscoacoustic wave equation is derived based on a wavefield decomposition method to obtain the velocity-dispersion-only and viscoacoustic wavefields efficiently. Then, a theoretical framework of stable and high-efficiency Q -RTM method is proposed based on the velocity-dispersion-only and viscoacoustic wavefields. The synthetic example shows that the new stable Q -RTM results match well with the reference images (without attenuation images). Moreover, the field data images also demonstrate the stability and high-efficiency of our proposed Q -RTM method.

Passive multiple reverse time migration imaging based on wave decomposition and normalized imaging conditions

With the development of seismic exploration, passive-source seismic data has attracted increasing attention. Ambient noise passive seismic sources exists widely in nature and industrial production. Passive seismic data is important in logging while drilling (LWD), large-scale structural exploration, etc. In this paper, we proposed a passive multiple reverse time migration imaging (PMRTMI) method based on wavefield decomposition and normalized imaging conditions method. This method differs from seismic interferometry in that it can use raw passive seismic data directly in RTM imaging without reconstruction of virtual active gather, and we use the wavefield decomposition method to eliminate the low frequency noise in RTM. Further, the energy normalized imaging condition is used in full wavefield decomposition, which can not only enhance the image quality of both edge and deep information but also overcome the wrong energy problem caused by uneven distribution of passive sources; furthermore, this method exhibits high efficiency. Finally, numerical examples with the Marmousi model show the effectiveness of the method.

Source-side spatial wavefield gradients in land seismic exploration

The recording of seismic data using arrays of densely spaced receivers enables the estimation of the spatial gradient components of the wavefield, in addition to the acquisition of conventional translational motion. We have extended the concept of array-based receiver-side gradiometry to the source-side and investigated the potential of combining source- and receiver-side gradient estimates for land seismic exploration. The robustness of array-based gradient source formation is demonstrated with a field data reciprocity experiment. We apply a gradient-based elastic wavefield decomposition technique to small arrays of densely spaced vertically and horizontally oriented force sources and determine with synthetic and field data examples that the processing of data obtained from multicomponent source arrays allows us to simulate a composite source that theoretically only emits S-waves at all emergence angles. A promising application of the gradient-based S-wave source is downhole S-wave imaging. Finally, by combining source- and receiver-side gradient estimates, 49C seismic data can be obtained comprising three translational components, three rotational components, and one divergence component on the source and receiver side. This concept could have a significant potential to enhance the acquisition and processing of data from locally dense arrays in land seismic exploration.

Energy Flow Domain Reverse-Time Migration for Borehole Radar

A modified 2-D reverse-time migration algorithm in the energy flow domain, called EF-RTM, is proposed for short impulse borehole radar (BHR) imaging. The key of the approach is based on Poynting's theorem, which allows decomposition of the energy flux density (EFD) derived from the source and receiver wave fields in different wave-propagation directions. Then, imaging conditions, for example, zero-lag cross correlation (prestack migration) and zero-time imaging principle (poststack migration), are applied to the decomposed EFD-field components to obtain the migrated sections. The characteristics of the resulting images can be optionally combined or separately used for better BHR data imaging, interpretation, and analysis. In this paper, the EF-RTM algorithm is validated by numerical modeling and real field data and compared with the conventional RTM algorithm. All the results show that this new EF-RTM method is superior to the conventional RTM method: it inherits the high precision of RTM with additional imaging advantages, such as natural wave-field decomposition in different directions, improved migrated cross-range resolution, a better focus of the target's shape, and migration noise reduction.

A causal imaging condition for reverse time migration using the Discrete Hilbert transform and its efficient implementation on GPU

Abstract Reverse time migration (RTM) has shown a significant advantage over other imaging algorithms for imaging complex subsurface structures. However, low-wavenumber noise severely contaminates the image, which is one of the main issues in the RTM algorithm. To attenuate the undesired low-wavenumber noise, the causal imaging condition based on wavefield decomposition has been proposed. First, wavefield decompositions are performed to separate the wavefields as up-going and down-going wave components, respectively. Then, to preserve causality, it constructs images by correlating wave components that propagate in different directions. We build a causal imaging condition in this paper. Not only does it consider the up/down wavefield decomposition, but it also applies the decomposition on the horizontal direction to enhance the image quality especially for steeply dipping structures. The wavefield decomposition is conventionally achieved by the frequency-wavenumber (F-K) transform that is very computationally intensive compared with the wave propagation process of the RTM algorithm. To improve the efficiency of the algorithm, we propose a fast implementation to perform wavefield separation using the discrete Hilbert transform via the Graphics Processing Unit. Numerical tests on both the synthetic models and a real data example demonstrate the effectiveness of the proposed method and the efficiency of the optimized implementation scheme. This new imaging condition shows its ability to produce high image quality when applied to both the RTM stack image and also the angle domain common image gathers. The comparison of the total elapsed time for different methods verifies the efficiency of the optimized algorithm.

Surface impedance properties of a wire grid embedded in a chiral medium

AbstractThe surface impedance characteristics of a wire grid composed of infinitely long parallel conducting wires embedded in lossless and lossy frequency-dispersive chiral background media have been investigated. Using wavefield decomposition approach for a chiral background and with the application of impedance boundary conditions for a wire grid, an analytic expression for the surface impedance of a wire grid with a chiral background has been derived. It is shown that the surface impedance magnitude of a wire grid with chiral nihility background is close to zero and almost independent of incident polar angles. A strong chiral background significantly enhances the surface impedance magnitude of a wire grid for incident polar angles closer to right angle as compared to the free space background. The same electromagnetic appearance of a wire grid with frequency-dispersive chiral and free space background media at some critical frequency has also been discussed which may find applications in electromagnetic illusions. It is also shown that if the value of incident polar angles are closer to right angle then the impedance magnitude of a wire grid embedded in the realistic chiral background is smaller as compared to the same wire grid when placed in the free space background.