Dispersion and the dissipative characteristics of surface waves in the generalized S-transform domain

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. V11-V20 ◽  
Author(s):  
Roohollah Askari ◽  
Robert J. Ferguson
Keyword(s):  
Cost Function ◽  
Surface Waves ◽  
Joint Inversion ◽  
Scaling Factor ◽  
Surface Shear ◽  
Low Frequencies ◽  
Near Surface ◽  
S Transform ◽  
Generalized S Transform ◽  
The Cost

Wavenumber, group velocity, phase velocity, and frequency-dependent attenuation characterize the propagation of surface waves in dispersive, attenuating media. We use a mathematical model based on the generalized [Formula: see text] transform to simultaneously estimate these characteristic parameters for later use in joint inversion for near-surface shear wave velocity. We use a scaling factor in the generalized S transform to enable the application of the method in a highly dispersive medium. We introduce a cost function in the [Formula: see text]-domain to estimate an optimum value for the scaling factor. We also use the cost function to generalize the application of the method for noisy data, especially data with a low signal-to-noise ratio at low frequencies. In that case, the estimated wavenumber is perturbed. As a solution, we estimate wavenumber perturbation by minimizing the cost function, using Simulated Annealing. We use synthetic and real data to show the efficiency of the method for the estimation of the propagation parameters of highly dispersive and noisy media.

Joint Inversion Scheme of Dispersive Surface Waves for Near-surface Structure Estimation

2015 ◽  
Author(s):  
Tongju Gong* ◽  
Miao Liu ◽  
Yiming Wang ◽  
Zhiwei Zhu ◽  
Baoqing Zhang
Keyword(s):  
Surface Waves ◽  
Surface Structure ◽  
Joint Inversion ◽  
Near Surface ◽  
Structure Estimation

Investigation of generalized S-transform analysis windows for time-frequency analysis of seismic reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V235-V247 ◽  
Author(s):  
Duan Li ◽  
John Castagna ◽  
Gennady Goloshubin
Keyword(s):  
Temporal Resolution ◽  
Seismic Reflection ◽  
Frequency Resolution ◽  
Low Frequencies ◽  
Seismic Reflection Data ◽  
Time Frequency ◽  
Gaussian Window ◽  
Reflection Data ◽  
S Transform ◽  
Generalized S Transform

The frequency-dependent width of the Gaussian window function used in the S-transform may not be ideal for all applications. In particular, in seismic reflection prospecting, the temporal resolution of the resulting S-transform time-frequency spectrum at low frequencies may not be sufficient for certain seismic interpretation purposes. A simple parameterization of the generalized S-transform overcomes the drawback of poor temporal resolution at low frequencies inherent in the S-transform, at the necessary expense of reduced frequency resolution. This is accomplished by replacing the frequency variable in the Gaussian window with a linear function containing two coefficients that control resolution variation with frequency. The linear coefficients can be directly calculated by selecting desired temporal resolution at two frequencies. The resulting transform conserves energy and is readily invertible by an inverse Fourier transform. This modification of the S-transform, when applied to synthetic and real seismic data, exhibits improved temporal resolution relative to the S-transform and improved resolution control as compared with other generalized S-transform window functions.

Langmuir circulation due to shear flow over wavy topography

2020 ◽  
Author(s):  
Andreas H Akselsen ◽  
Andreas Brostrøm ◽  
Simen Ådnøy Ellingsen
Keyword(s):  
Boundary Layer ◽  
Surface Waves ◽  
Boundary Layer Flow ◽  
General Procedure ◽  
Bottom Topography ◽  
Langmuir Circulation ◽  
Surface Shear ◽  
Near Surface ◽  
Langmuir Circulations ◽  
Layer Flow

<p>Langmuir circulations (LC) in their traditional form are large rolling fluid flow pattern created by the interplay of surface waves and a near-surface shear current, typically both created by the wind. A celebrated theory by Craik and Leibovich (1976) describes two kinematic mechanisms which cause instabilities which grow into Langmuir rolls, both involving only the shear of the flow and the kinematic driving of flow undulations by a wavy surface, but containing no direct reference to the wind as a driving force. The same kinematic processes are present also in boundary layer flow over a wavy bottom topography in almost perfect analogy.</p><p>We present a theory of Langmuir-like circulations created by boundary layer flow over a topography in the form of a regular pattern of two monochromatic waves crossing at an oblique angle. Thus, the Craik-Leibovich instability sometimes referred to as CL1 is triggered and the close analogy with surface waves allows us to follow the general procedure of Craik (1970).</p><p>A flow of arbitrary shear profile is assumed over the bottom topography. In the opposite limits of transient inviscid flow and steady-state viscous flow simple equations for the stream function in cross-current plane can be derived and easily solved numerically. For the special case of a power-law velocity profile, explicit leading-order solutions are available. This allows us to quickly map out the circulation response to different parameters: wavelength, crossing angle and wave amplitude. The study is supplemented with direct numerical simulations which verify the manifestation of Langmuir-like circulations over wavy geometries with a no-slip boundary condition.</p><p><strong>References<br></strong>Craik, A.D.D., A wave-interaction model for the generation of windrows. J. Fluid Mech. (1970) <strong>41</strong>, 801-821.<br>Craik, A.D.D. & Leibovich, S. A rational model for Langmuir circulations. J. Fluid Mech. (1976) <strong>73</strong>, 401-426.</p>

Joint MT and CSEM data inversion using a multiplicative cost function approach

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F203-F214 ◽  
Author(s):  
A. Abubakar ◽  
M. Li ◽  
G. Pan ◽  
J. Liu ◽  
T. M. Habashy
Keyword(s):  
Cost Function ◽  
Large Scale ◽  
Joint Inversion ◽  
A Priori ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Earth Resistivity ◽  
The Cost

We have developed an inversion algorithm for jointly inverting controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data. It is well known that CSEM and MT data provide complementary information about the subsurface resistivity distribution; hence, it is useful to derive earth resistivity models that simultaneously and consistently fit both data sets. Because we are dealing with a large-scale computational problem, one usually uses an iterative technique in which a predefined cost function is optimized. One of the issues of this simultaneous joint inversion approach is how to assign the relative weights on the CSEM and MT data in constructing the cost function. We propose a multiplicative cost function instead of the traditional additive one. This function does not require an a priori choice of the relative weights between these two data sets. It will adaptively put CSEM and MT data on equal footing in the inversion process. The inversion is accomplished with a regularized Gauss-Newton minimization scheme where the model parameters are forced to lie within their upper and lower bounds by a nonlinear transformation procedure. We use a line search scheme to enforce a reduction of the cost function at each iteration. We tested our joint inversion approach on synthetic and field data.

Multiwave inversion: A key step for depth model building — Examples from the Sultanate of Oman

2021 ◽  
Vol 40 (8) ◽  
pp. 610-618
Author(s):  
Daniela Donno ◽  
Mohammad Sheryar Farooqui ◽  
Mostafa Khalil ◽  
David McCarthy ◽  
Didier Solyga ◽  
...  
Keyword(s):  
Surface Waves ◽  
Model Building ◽  
Sand Dunes ◽  
P Wave ◽  
Surface Model ◽  
Sultanate Of Oman ◽  
Surface Wave Dispersion ◽  
Low Frequencies ◽  
Near Surface ◽  
Velocity Models

The near surface in the Middle East, particularly in the Sultanate of Oman, is characterized by very shallow high-velocity carbonates and anhydrites interleaved by slow-velocity clastic layers, resulting in sharp velocity inversions in the first few hundred meters below the surface. In addition, the surface is characterized by features such as unconsolidated materials within dry riverbeds (known as “wadis”), small jebels, and sand dunes, which cause distortions in the underlying shallow and deeper seismic images. This work presents the building of a near-surface model by using multiwave inversion that jointly inverts information from P-wave first breaks and surface-wave dispersion curves. The use of surface waves in combination with first breaks captures the lateral and vertical velocity variations, especially in the shallowest parts of the near surface. This paper focuses on the analysis of two drawbacks of this technology: the picking of the input data information, which can be cumbersome and time consuming, and the limited penetration depth of surface waves at the typical frequencies of active data. To overcome these issues, an innovative workflow is proposed that combines the use of an unsupervised machine learning technique to guide the pick extraction phase and the reconstruction of ultra-low-frequency surface waves (0.5 to 1.5 Hz) through an interferometry process using information from natural and ambient noise. Deeper near-surface P- and S-wave velocity models can be obtained with multiwave inversion using these ultra-low frequencies. The integration of a near-surface model into the velocity model building workflow brings a major improvement in depth imaging from shallow to deep structures, as demonstrated on two data sets from the Sultanate of Oman.

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