Adaptive wavelets for analyzing dispersive seismic waves

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
A. Kritski ◽  
A. P. Vincent ◽  
D. A. Yuen ◽  
T. Carlsen
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Shear Wave ◽  
Primary Objective ◽  
Sediment Surface ◽  
Horizontal Distance ◽  
Time Frequency ◽  
Interface Waves ◽  
Adaptive Wavelets ◽  
Wave Modes

Our primary objective is to develop an efficient and accurate method for analyzing time series with a multiscale character. Our motivation stems from the studies of the physical properties of marine sediment (stiffness and density) derived from seismic acoustic records of surface/interface waves along the water-seabed boundary. These studies depend on the dispersive characteristics of water-sediment surface waves. To obtain a reliable retrieval of the shear-wave velocities, we need a very accurate time-frequency record of the surface waves. Such a time-frequency analysis is best carried out by a wavelet-transform of the seismic records. We have employed the wavelet crosscorrelation technique for estimating the shear-wave propagational parameters as a function of depth and horizontal distance. For achieving a greatly improved resolution in time-frequency space, we have developed a new set of adaptive wavelets, which are driven by the data. This approach is based on a Karhunen-Loeve (KL) decomposition of the seismograms. This KL decomposition allows us to obtain a set of wavelet functions that are naturally adapted to the scales of the surface-wave modes. We demonstrate the superiority of these adaptive wavelets over standard wavelets in their ability to simultaneously discriminate the different surface-wave modes. The results can also be useful for imaging and statistical data analysis in exploration geophysics and in other disciplines in the environmental sciences.

Improving surface‐wave group velocity measurements by energy reassignment

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 677-684 ◽  
Author(s):  
Helle A. Pedersen ◽  
Jérôme I. Mars ◽  
Pierre‐Olivier Amblard
Keyword(s):  
Surface Waves ◽  
Dispersion Curve ◽  
Group Velocity ◽  
Shear Wave ◽  
Group Velocity Dispersion ◽  
Seismic Survey ◽  
Earth Model ◽  
Velocity Measurements ◽  
Time Frequency ◽  
Shallow Seismic

Surface waves are increasingly used for shallow seismic surveys—in particular, in acoustic logging, environmental, and engineering applications. These waves are dispersive, and their dispersion curves are used to obtain shear velocity profiles with depth. The main obstacle to their more widespread use is the complexity of the associated data processing and interpretation of the results. Our objective is to show that energy reassignment in the time–frequency domain helps improve the precision of group velocity measurements of surface waves. To show this, full‐waveform seismograms with added white noise for a shallow flat‐layered earth model are analyzed by classic and reassigned multiple filter analysis (MFA). Classic MFA gives the expected smeared image of the group velocity dispersion curve, while the reassigned curve gives a very well‐constrained, narrow dispersion curve. Systematic errors from spectral fall‐off are largely corrected by the reassignment procedure. The subsequent inversion of the dispersion curve to obtain the shear‐wave velocity with depth is carried out through a procedure combining linearized inversion with a nonlinear Monte Carlo inversion. The diminished uncertainty obtained after reassignment introduces significantly better constraints on the earth model than by inverting the output of classic MFA. The reassignment is finally carried out on data from a shallow seismic survey in northern Belgium, with the aim of determining the shear‐wave velocities for seismic risk assessment. The reassignment is very stable in this case as well. The use of reassignment can make dispersion measurements highly automated, thereby facilitating the use of surface waves for shallow surveys.

Errors Introduced in Estimation of Surface Wave Phase and Group Velocities Due to Wrong Assumptions: An Assessment Using a Simple Model For Love Wave

2021 ◽  
Author(s):  
Akash Kharita ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Love Wave ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Horizontal Distance ◽  
Wave Analysis ◽  
Time Period ◽  
Phase And Group Velocities ◽  
Group Velocities

<p>The surface wave phase and group velocities are estimated by dividing the epicentral distance by phase and group travel times respectively in all the available methods, this is based on the assumptions that (1) surface waves originate at the epicentre and (2) the travel time of the particular group or phase of the surface wave is equal to its arrival time to the station minus the origin time of the causative earthquake; However, both assumptions are wrong since surface waves generate at some horizontal distance away from the epicentre. We calculated the actual horizontal distance from the focus at which they generate and assessed the errors caused in the estimation of group and phase velocities by the aforementioned assumptions in a simple isotropic single layered homogeneous half space crustal model using the example of the fundamental mode Love wave. We took the receiver locations in the epicentral distance range of 100-1000 km, as used in the regional surface wave analysis, varied the source depth from 0 to 35 Km with a step size of 5 km and did the forward modelling to calculate the arrival time of Love wave phases at each receiver location. The phase and group velocities are then estimated using the above assumptions and are compared with the actual values of the velocities given by Love wave dispersion equation. We observed that the velocities are underestimated and the errors are found to be; decreasing linearly with focal depth, decreasing inversely with the epicentral distance and increasing parabolically with the time period. We also derived empirical formulas using MATLAB curve fitting toolbox that will give percentage errors for any realistic combination of epicentral distance, time period and depths of earthquake and thickness of layer in this model. The errors are found to be more than 5% for all epicentral distances lesser than 500 km, for all focal depths and time periods indicating that it is not safe to do regional surface wave analysis for epicentral distances lesser than 500 km without incurring significant errors. To the best of our knowledge, the study is first of its kind in assessing such errors.</p>

Observation of Higher-Mode Surface Waves from an Active Source in the Hutubi Basin, Xinjiang, China

2021 ◽  
Author(s):  
Zhanbo Ji ◽  
Baoshan Wang ◽  
Wei Yang ◽  
Weitao Wang ◽  
Jinbo Su ◽  
...  
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Seismic Waves ◽  
Velocity Structure ◽  
Group Velocity Dispersion ◽  
S Wave ◽  
Contributing Factors ◽  
Low Velocity ◽  
Time Frequency ◽  
Wave Modes

ABSTRACT Basins with thick sediments can amplify and prolong the incoming seismic waves, which may cause serious damage to surface facilities. The amplification of seismic energy depends on the shear-wave velocity of the uppermost layers, which is generally estimated through surface wave analysis. Surface waves may propagate in different modes, and the mechanism of the mode development is not well understood. Exploiting a recently deployed permanent airgun source in the Hutubi basin, Xinjiang, northwest China, we conducted a field experiment to investigate the development of multimode surface waves. We observed surface waves at the frequency of 0.3–5.0 Hz with apparent group velocities of 200–900  m/s, and identified five modes of surface waves (three Rayleigh-wave modes and two Love-wave modes) through time–frequency and particle-motion analyses. We then measured 125 group velocity dispersion curves of the fundamental- and higher-mode surface waves, and further inverted the 1D S-wave velocity structure of the Hutubi basin. The S-wave velocity increases abruptly from 238  m/s at the surface to 643  m/s at 300 m depth. Synthetic seismograms with the inverted velocity structure capture the main features of the surface waves of the different modes. Synthetic tests suggest that the low velocity, high velocity gradient, and shallow source depth are likely the dominant contributing factors in the development of higher-mode surface waves.

Multichannel analysis of surface waves

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 800-808 ◽  
Author(s):  
Choon B. Park ◽  
Richard D. Miller ◽  
Jianghai Xia
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Dispersion Curve ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Frequency Component ◽  
Multichannel Recording ◽  
Phase Velocities ◽  
Ground Roll

The frequency‐dependent properties of Rayleigh‐type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface‐wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental‐mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source‐generated noise inhibits the reliability of shear‐wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental‐mode Rayleigh waves (noise) are body waves, scattered and nonsource‐generated surface waves, and higher‐mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear‐wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace‐to‐trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable‐frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real‐time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface‐wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single‐measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a swept‐frequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear‐wave velocity ([Formula: see text]) profile with a downhole [Formula: see text] profile.

scholarly journals A high-resolution dispersion imaging method of seismic surface waves based on chirplet transform

2021 ◽  
Vol 18 (6) ◽  
pp. 908-919
Author(s):  
Qin Su ◽  
Xingrong Xu ◽  
Zhinong Wang ◽  
Chengyu Sun ◽  
Yaozong Guo ◽  
...  
Keyword(s):  
Surface Wave ◽  
Frequency Domain ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Phase Function ◽  
Imaging Method ◽  
Dispersion Energy ◽  
Time Frequency ◽  
Seismic Surface Waves

Abstract The surface-wave analysis method is widely adopted to build a near-surface shear-wave velocity structure. Reliable dispersion imaging results form the basis for subsequent picking and inversion of dispersion curves. In this paper, we present a high-resolution dispersion imaging method (CSFK) of seismic surface waves based on chirplet transform (CT). CT introduces the concept of chirp rate, which could focus surface-wave dispersion energy well in time-frequency domain. First, each seismic trace in time-distance domain is transformed to time-frequency domain by CT. Thus, for each common frequency gather, we obtain a series of 2D complex-valued functions of time and distance, which are called pseudo-seismograms. Then, we scan a series of group velocities to obtain the slanting-phase function and perform a spatial Fourier transform on the slanting-phase function to get its amplitude. In addition, power operation is adopted to increase the amplitude difference between dispersion energy and noise. Finally, we generate the dispersion image by searching for the maximum amplitude of a slanting-phase function. Because the CSFK method considers the position of surface-wave energy in the time-frequency domain, this largely eliminates the noise interference from other time locations and improves the resolution and signal-to-noise ratio of the dispersion image. The results of synthetic test and field dataset processing demonstrate the effectiveness of the proposed method. In addition, we invert all 120 sets of dispersion curves extracted from reflected wave seismic data acquired for petroleum prospecting. The one-dimensional inversion shear-wave velocity models are interpolated into a two-dimensional profile of shear-wave velocity, which is in good agreement with the borehole data.

Application of constrained polarization filtering for surface-wave mitigation: Three case studies

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. V169-V181 ◽  
Author(s):  
Mamadou S. Diallo ◽  
Warren S. Ross ◽  
Andrew P. Shatilo ◽  
Inmaculada Dura-Gomez ◽  
Gary C. Szurek
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Case Studies ◽  
Data Sets ◽  
Velocity Amplitude ◽  
Time Frequency ◽  
Frequency Information ◽  
Straightforward Application ◽  
F Region ◽  
Polarization Filtering

We applied constrained polarization filtering (CPF) to surface-wave mitigation on data sets from different geologic settings. The method derives from the application of polarization filtering in the time-frequency (t-f) domain and introduces new constraints to effectively detect and mitigate surface waves while protecting the signal. We use these constraints that we derive from velocity, amplitude, time, and frequency information to delineate the t-f region dominated by surface-wave noises. Then, we restrict the application of polarization filtering to this region to avoid damaging the signal. Straightforward application of polarization filtering without these constraints results in ineffective filtering or damage to the signal, due to the complexity of surface-wave wavetrains. The performance of CPF with these various data sets is demonstrably superior compared to the unconstrained approach. There are some of the issues that may affect performance of the CPF, but they can be overcome.

Ground roll extraction using the Karhunen-Loeve transform in the time-frequency domain

Geophysics ◽  
2021 ◽  
pp. 1-22
Author(s):  
Aleksander S. Serdyukov
Keyword(s):  
Surface Wave ◽  
Data Processing ◽  
Surface Waves ◽  
Frequency Domain ◽  
Band Frequency ◽  
Time Frequency ◽  
S Transform ◽  
Ground Roll ◽  
Karhunen Loeve Transform ◽  
Complex Valued

Ground roll suppression is critical for seismic reflection data processing. Many standard methods, i.e., FK filtering, fail when spatially aliased surface wave interference is present in the data. Spatial aliasing is a common problem; receiver spacing is often not dense enough to extract wavenumbers of low-velocity surface waves. It has long been known that the Karhunen-Loeve transform can be used to suppress aliased ground roll. However, the ground roll should be flattened before suppression, which is challenging due to the dispersion of surface wave velocities. I propose to solve this problem via the time-frequency domain. I apply the S-transform, which was previously shown to perform well in the multichannel analysis of surface waves. A simple complex-valued constant phase shift is a suitable model of surface wave propagation in common-frequency S-transform gathers. Therefore, it is easy to flatten the corresponding S-transform narrow-band frequency surface wave packet and extract it from the data by principal component analysis of the corresponding complex-valued data-covariance matrix. As the result, the proposed S-transform Karhunen-Loeve (SKL) method filters the aliased ground roll without damaging the reflection amplitudes. The advantages of SKL filtering have been confirmed by synthetic- and field-data processing.

scholarly journals Joint analysis of refractions with surface waves: An inverse solution to the refraction-traveltime problem

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. R131-R138 ◽  
Author(s):  
Julian Ivanov ◽  
Richard D. Miller ◽  
Jianghai Xia ◽  
Don Steeples ◽  
Choon B. Park
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Reference Model ◽  
Real Data ◽  
Joint Analysis ◽  
Basic Principles ◽  
Refraction Tomography

We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. The application of the joint analysis of refractions with surface waves (JARS) method provided a more realistic solution than the conventional refraction/tomography methods, which did not benefit from a reference model derived from real data. This confirmed our conclusion that the proposed method is an advancement in the IRTP analysis. The unique basic principles of the JARS method might be applicable to other inverse geophysical problems.

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