LINEAR PHASE FILTERING OF MULTICOMPONENT SEISMIC DATA

Geophysics ◽  
1968 ◽  
Vol 33 (6) ◽  
pp. 926-935 ◽  
Author(s):  
E. J. Mercado
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Linear Phase ◽  
Linear Filtering ◽  
Linear Filters ◽  
Filtering Technique ◽  
Polarization Filtering ◽  
Phase Relationships

The phase relationships between the vertical and horizontal components of motion at a free surface differ between the various modes of propagation. These differences in phase between the components of motion may be made the basis for a linear filtering technique to separate P, S, and Rayleigh waves when the components of motion at the free surface are recorded in reproducible form. In this paper, a set of linear filters is derived and applied to some three‐component reflection seismograph field data that separate P and Rayleigh wave motion on the basis of their phase relations between horizontal and vertical components of motion at the free surface. A comparison is made between the linear phase filtering technique, and the “Polarization Filtering” technique of Shimshoni and Smith, and a multichannel Wiener deconvolution using the vertical and horizontal components of motion as input channels.

A method of ground‐roll elimination

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 894-902 ◽  
Author(s):  
Ruhi Saatçilar ◽  
Nezihi Canitez
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Wave Motion ◽  
Frequency Interval ◽  
Vertical Resolution ◽  
Matched Filters ◽  
One Dimensional ◽  
Frequency Bands ◽  
Ground Roll ◽  
Seismic Reflections

Amplitude‐ and frequency‐modulated wave motion constitute the ground‐roll noise in seismic reflection prospecting. Hence, it is possible to eliminate ground roll by applying one‐dimensional, linear frequency‐modulated matched filters. These filters effectively attenuate the ground‐roll energy without damaging the signal wavelet inside or outside the ground roll’s frequency interval. When the frequency bands of seismic reflections and ground roll overlap, the new filters eliminate the ground roll more effectively than conventional frequency and multichannel filters without affecting the vertical resolution of the seismic data.

A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

2016 ◽  
Vol 30 (08) ◽  
pp. 1650096 ◽  
Author(s):  
Shuzeng Zhang ◽  
Xiongbing Li ◽  
Hyunjo Jeong
Keyword(s):  
Rayleigh Waves ◽  
General Equation ◽  
Wave Motion ◽  
Numerical Solutions ◽  
Second Harmonic ◽  
Approximate Equation ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Quasilinear Theory ◽  
Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

Study of Noise Removal Techniques for Digital Images

Biometrics ◽  
2017 ◽  
pp. 1105-1144
Author(s):  
Punyaban Patel ◽  
Bibekananda Jena ◽  
Bibhudatta Sahoo ◽  
Pritam Patel ◽  
Banshidhar Majhi
Keyword(s):  
Image Processing ◽  
Gaussian Noise ◽  
Statistical Models ◽  
Noise Removal ◽  
Image Degradation ◽  
Linear Filters ◽  
Restoration Techniques ◽  
Filtering Technique ◽  
High Level ◽  
Camera Sensors

Images very often get contaminated by different types of noise like impulse noise, Gaussian noise, spackle noise etc. due to malfunctioning of camera sensors during acquisition or transmission using the channel. The noise in the channel affects processing of images in various ways. Hence, the image has to be restored by applying filtration process before the high level image processing. In general the restoration techniques for images are based up on the mathematical and the statistical models of image degradation. Denoising and deblurring are used to recover the image from degraded observations. The researchers have proposed verity of linear and non-linear filters for removal of noise from images. The filtering technique has been used to remove noisy pixels, without changing the uncorrupted pixel values. This chapter presents the metrics used for measurement of noise, and the various schemes for removing of noise from the images.

Study of Noise Removal Techniques for Digital Images

2016 ◽  
pp. 48-87
Author(s):  
Punyaban Patel ◽  
Bibekananda Jena ◽  
Bibhudatta Sahoo ◽  
Pritam Patel ◽  
Banshidhar Majhi
Keyword(s):  
Image Processing ◽  
Gaussian Noise ◽  
Statistical Models ◽  
Noise Removal ◽  
Image Degradation ◽  
Linear Filters ◽  
Restoration Techniques ◽  
Filtering Technique ◽  
High Level ◽  
Camera Sensors

Images very often get contaminated by different types of noise like impulse noise, Gaussian noise, spackle noise etc. due to malfunctioning of camera sensors during acquisition or transmission using the channel. The noise in the channel affects processing of images in various ways. Hence, the image has to be restored by applying filtration process before the high level image processing. In general the restoration techniques for images are based up on the mathematical and the statistical models of image degradation. Denoising and deblurring are used to recover the image from degraded observations. The researchers have proposed verity of linear and non-linear filters for removal of noise from images. The filtering technique has been used to remove noisy pixels, without changing the uncorrupted pixel values. This chapter presents the metrics used for measurement of noise, and the various schemes for removing of noise from the images.

Enhancing Signal-to-Noise Ratios of High-Frequency Rayleigh Waves Extracted from Ambient Seismic Noises in Topographic Region

2020 ◽  
Vol 110 (2) ◽  
pp. 793-802
Author(s):  
Ping Ping ◽  
Risheng Chu ◽  
Yu Zhang ◽  
Jun Xie
Keyword(s):  
Free Surface ◽  
Correlation Functions ◽  
High Frequency ◽  
Rayleigh Waves ◽  
Vertical Component ◽  
Noise Correlation ◽  
Surface Boundary ◽  
Elastic Wedge ◽  
Signal To Noise ◽  
Surface Boundary Conditions

ABSTRACT High-frequency Rayleigh waves can be extracted from ambient seismic noises through noise correlation functions (NCFs), which provides a useful tool to image shallow structures in topographic regions, for example, landslides. Topography may affect signal-to-noise ratios (SNRs) of extracted Rayleigh waves. It is necessary to investigate the propagation features of Rayleigh waves passing a 3D topography. Based on the incident and scattered waves satisfying the free surface boundary conditions, we first derive the displacement responses of Rayleigh waves across a 3D elastic wedge. The results show that the particle motions of Rayleigh waves are an ellipse whose longer axis is always perpendicular to the topographic free surface. Therefore, the Qg component, perpendicular to the topographic free surface, is a better choice to extract high-frequency Rayleigh waves than the conventional vertical component. To verify the choice, we carry out numerical simulations to extract high-frequency NCFs for a typical 3D massif model. Finally, we apply this approach to extract high-frequency Rayleigh-wave NCFs on the Xishancun landslide in southwestern China. The NCFs obtained using the Qg component have more coherent waveforms and higher SNRs than those using the vertical component. We conclude that the Qg component has advantages in extracting high-frequency Rayleigh waves over the conventional vertical component.

scholarly journals Deceleration of droplets that glide along the free surface of a bath

2016 ◽  
Vol 803 ◽  
pp. 313-331 ◽  
Author(s):  
Jacob Hale ◽  
Caleb Akers
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Droplet Diameter ◽  
Reynolds Numbers ◽  
Viscous Drag ◽  
Bath Surface ◽  
Exponential Rate ◽  
Viscous Coupling ◽  
Air Film ◽  
O 10

A droplet obliquely impacting a bath surface of the same fluid can traverse along the interface while slowing at an exponential rate. The droplet rests on a thin film of air, deforms the bath surface creating a dimple and travels along the surface similarly to a wave pulse. Viscous coupling of the droplet and bath surfaces through the air film leads to viscous drag on the bath and perturbs the wave motion of the otherwise free surface. Even though the Reynolds numbers are greater than unity ($\mathit{Re}\,O(10{-}100)$), we show that the droplet’s deceleration is only due to viscous coupling through the air gap. The rate of deceleration is found to increase linearly with droplet diameter.

Least-squares data-to-data migration: An approach for migrating free-surface-related multiples

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S83-S94 ◽  
Author(s):  
Yikang Zheng ◽  
Yibo Wang ◽  
Xu Chang
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Data Migration ◽  
Subsurface Imaging ◽  
Full Data ◽  
Recording Time ◽  
Numerical Tests ◽  
Marine Seismic

Free-surface-related multiples can provide extra illumination of the subsurface and thus can be usefully included in migration procedures. However, most multiple migration approaches require separation of primaries and free-surface-related multiples or at least prediction of multiples in advance, which is time consuming and prone to errors. The data-to-data migration (DDM) method migrates free-surface-related multiples by forward and backward propagating the recorded full data (containing primaries and free-surface-related multiples). For DDM, there is no need to predict or separate multiples, but the migration results suffer from the crosstalk generated by crosscorrelations of undesired seismic events, e.g., primaries and second-order free-surface-related multiples. We have developed least-squares DDM (LSDDM) for marine data to eliminate the crosstalk generated by DDM. In each iteration, the forward-propagated primaries and free-surface-related multiples are crosscorrelated with the backward-propagated primary and free-surface-related multiple residuals to form the reflectivity gradient. We use a three-layer model and the Marmousi model for numerical tests. The results validate that LSDDM can provide a migrated image with higher signal-to-noise ratio and more balanced amplitudes than DDM. The LSDDM approach might be valuable for general subsurface imaging for marine seismic data when the migration velocity is accurate, and the acquired data have sufficient recording time.

scholarly journals Multiple Rayleigh waves guided by the planar surface of a continuously twisted structurally chiral material

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200314
Author(s):  
Tom G. Mackay ◽  
Akhlesh Lakhtakia
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Phase Speed ◽  
Angular Frequency ◽  
Planar Surface ◽  
Fixed Frequency ◽  
Numerical Studies ◽  
Anisotropic Solid

The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending on the structural period and orientation of the CTSCM. In the case of two Rayleigh waves, each wave possesses a different wavenumber. The Rayleigh wave with the larger wavenumber is more localized to the surface and has a phase speed that changes less as the angular frequency varies in comparison with the Rayleigh wave with the smaller wavenumber.

An optimization of the inverse scattering multiple attenuation method for OBS and VC data

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1293-1303 ◽  
Author(s):  
Luc T. Ikelle ◽  
Lasse Amundsen ◽  
Seung Yoo
Keyword(s):  
Free Surface ◽  
Data Storage ◽  
Inverse Scattering ◽  
Water Depth ◽  
Seismic Data ◽  
Computation Time ◽  
Ocean Bottom ◽  
Multiple Attenuation ◽  
Obs Data ◽  
Streamer Data

The inverse scattering multiple attenuation (ISMA) algorithm for ocean‐bottom seismic (OBS) data can be formulated in the form of a series expansion for each of the four components of OBS data. Besides the actual data, which constitute the first term of the series, each of the other terms is computed as a multidimensional convolution of OBS data with streamer data, and aims at removing one specific order of multiples. If the streamer data do not contain free‐surface multiples, we found that the computation of only the second term of the series is needed to predict and remove all orders of multiples, whatever the water depth. As the computation of the various terms of the series is the most expensive part of ISMA, this result can produce significant savings in computation time, even in data storage, as we no longer need to store the various terms of the series. For example, if the streamer data contained free‐surface multiples, OBS seismic data of 6‐s duration, corresponding to a geological model of the subsurface with 250‐m water depth, require the computation of five terms of the series for each of the four components of OBS data. With the new implementation, in which the streamer data do not contain free‐surface multiples, we need the computation of only one term of the series for each component of the OBS data. The saving in CPU time for this particular case is at least fourfold. The estimation of the inverse source signature, which is an essential part of ISMA, also benefits from the reduction of the number of terms needed for the demultiple to two because it becomes a linear inverse problem instead of a nonlinear one. Assuming that the removal of multiple events produces a significant reduction in the energy of the data, the optimization of this problem leads to a stable, noniterative analytic solution. We have also adapted these results to the implementation of ISMA for vertical‐cable (VC) data. This implementation is similar to that for OBS data. The key difference is that the basic model in VC imaging assumes that data consist of receiver ghosts of primaries instead of the primaries themselves. We have used the following property to achieve this goal. The combination of VC data with surface seismic data, which do not contain free‐surface multiples, allows us to predict free‐surface multiples and receiver ghosts as well as the receiver ghosts of primary reflections. However, if the direct wave arrivals are removed from the VC data, this combination will not predict the receiver ghosts of primary reflections. The difference between these two predictions produces data containing only receiver ghosts of primaries.

Sign in / Sign up

Export Citation Format

Share Document