Wavenumber Method Research Articles

Identification of Non-Uniform Ground Comparing Responses Function of Incident SH Wave by DWM to Resonance Frequency by HVSR

In this paper, we simulated frequency responses of subsurface due to incident SH wave by using discrete wave number method (DWM: Aki-Larner Method). It is useful in constructing the models of the non-uniform subsurface. We estimated subsurface profile based on the resonance frequency of HVSR method comparing with frequency responses obtained from SH waves incident by DWM. The only information from HVSR is the resonance-frequency of the ground. Although what obtained from the numerical analysis by DWM is a response function, it coincides with the response of the surface ground if the input motion is a white noise and the ground behaviour is a liner. In this case, the peak of response function can be considered to be a resonance frequency of the ground. Therefore, we here compared the peak frequencies of HVSR curve and response functions. To estimate the resonance frequency of ground by HVSR, the single observations of microtremor at 161 sites were carried out by using the three-component accelerometer with a data logger, GPL-6A3P, in the study area of Ende Regency that is one of five regencies in East Nusa Tenggara Province on the island of Flores, Indonesia. The results show that site response in Ende area varies the resonance frequencies span 0.7-1.4 Hz. For DWM, we assume simple two layered media with irregular boundary aimed at making a simple ground profile of the study area. The two-layered model is composed of a ‘soft basin’ on engineering bedrock. We varied the depth and the shear wave velocity of the basin and calculated response functions by using DWM. Then we selected the best fit parameters by comparing the resonance frequency of H/V result. Finally, we proposed a possible non-uniform ground model in the study area.

Hybrid broadband simulation of strong-motion records from the September 16, 1978, Tabas, Iran, earthquake (M w 7.4)

This paper presents a simulation of three components of near-field ground shaking recorded during the main shock at three stations of the September 16, 1978, Tabas (M w = 7.4), Iran, earthquake, close to the causative fault. A hybrid method composed of a discrete wavenumber method developed by Bouchon (Bouchon in Bull Seismol Soc Am 71:959–971, 1981; Cotton and Coutant in Geophys J Int 128:676–688, 1997) and a stochastic finite-fault modeling based on a dynamic corner frequency proposed by Motazedian and Atkinson (Bull Seismol Soc Am 95:995–1010, 2005), modified by Assatourians and Atkinson (Bull Seismol Soc Am 97:935–1949, 2007), is used for generating the seismograms at low (0.1–1.0 Hz) and high frequencies (1.0–20.0 Hz), respectively. The results are validated by comparing the simulated peak acceleration, peak velocity, peak displacement, Arias intensity, the integral of velocity squared, Fourier spectrum and acceleration response spectrum on a frequency-by-frequency basis, the shape of the normalized integrals of acceleration and velocity squared, and the cross-correlation with the observed time-series data. Each characteristic is compared on a scale from 0 to 10, with 10 being perfect agreement. Also, the results are validated by comparing the simulated ground motions with the modified Mercalli intensity observations reported by reconnaissance teams and showed reasonable agreement. The results of the present study imply that the damage distribution pattern of the 1978 Tabas earthquake can be explained by the source directivity effect.

IMPLEMENTATION OF A NON-SPLITTING FORMULATION OF PERFECTLY MATCHED LAYER IN A 3D – 4TH ORDER STAGGERED-GRID VELOCITY-STRESS FINITE-DIFFERENCE SCHEME

One of the major problems in numerical simulations of wave propagation in elastodynamics using grid-point methods is the truncation of the computational space by artificial boundaries. These boundaries produce spurious reflections, polluting the results with artificial noise, therefore several efforts have been realized in order to achieve transparent or non-reflecting boundaries for truncating the computational space. Perfectly Matched Layer (PML) has been one of the most efficient methods for implementing artificial boundaries at the edges of the computational models. However the application of PML requires the “tuning” of several variables, for which very limited work has been presented. In the present study we employ the Non-Splitting formulation of PML (NPML) technique presented by Wang & Tang (2003), based on the introduction of small perturbations in the wavefield. The NPML formulation shows the same accuracy with the originally introduced PML but is easier to be implemented because it does not require the field splitting. The main scope of this paper is to perform a full analysis of the efficiency of NMPL based on numerical tests using a 3D–4th order staggered-grid velocity-stress finite-difference scheme. The analysis consists of direct, quantified comparisons with reference solution waveforms from a semi-analytical method (Discrete Wavenumber Method) with synthetic waveforms produced using the most popular Absorbing Boundary Conditions (ABCs) and PML, in various canonical models (homogeneous and layer over half-space).

Constraints on the location of the 2008, MW 6.4 Achaia-Ilia earthquake fault from strong motion data.

The June 2008, Mw6.4 Achaia-Ilia earthquake was the first recorded dextral strikeslip event of considerable magnitude in western Peloponnese, which, nevertheless, could not be related to any of the known/mapped structures at the ground surface. Published locations of the mainshock focus by various agencies/researchers differ by as much as 6 km and 16 km in the horizontal and vertical dimensions, respectively, making even more difficult the accurate siting of the seismogenic fault. However, the 2008 earthquake provided a valuable set of near-fault strong motion data, which could shed some light on the problem of accurately locating the earthquake source. To this end, we use the discrete wavenumber method to forward model the strongground motion records at three stations, located close to the prolongation of the 2008 strike. We test different locations and lengths for the ruptured plane and compare synthetic polarities and amplitudes of the first strong S-wave pulse to actual data. We conclude that the line of maximum moment release (our fault models are vertical planes) during the 2008 earthquake is located to the east of the imaginary line connecting stations PAT2 and AMAA and to the west of station PYR1.

The amplitude and phase of the derivatives of the magnetic anomalies of thin dykes and contacts

If the horizontal and vertical derivatives of the total field magnetic anomalies of thin dykes and contacts (and the magnetic anomaly from a thin dyke) are put into an amplitude-phase form, then this can aid in their interpretation. First, it allows derivatives of fractional order to be calculated analytically; second, estimates of the source dip can be made; and finally, the relationships between local wavenumber and source-distance semi-automatic interpretation methods are clarified. The approach is demonstrated on synthetic data and aeromagnetic data from South Africa.

Analysis on shear wave velocity structure of a gravel landslide based on dual-source surface wave method

The depth and geometry of the potential sliding surface is the fundamental basis for evaluating the mechanism and performing mitigation measures of a landslide. The variation of shear wave velocity can directly reflect the characteristics of the strata structure in a landslide. For traditional methods (PS logging, surface exploration, H/V spectral ration and microtremor survey etc.), it is difficult to assure a large probing depth and high resolution at the same time. Joint observations were conducted using initiative-source multichannel analysis of surface wave (MASW) method and passive-source microtremor survey method (MSM) on the Xishan Village landslide located in Li County, Sichuan Province, China. Both frequency wave number method (F-K) and spatial auto correlation method (SPAC) were conducted to process the digital signal to analyze the shear wave velocity in the landslide, respectively. The Dual-source Surface Wave (DSSW) method was combined with MASW and MSM. The detected 2D profiles from the DSSW method showed that the landslide strata information was consistent with the borehole data. The results suggested that average depth of the potential sliding surface was about 50 m, of which the undulating shape was also clear. The boundary of the potential sliding surface was formed by weathered phyllite. It indicated that the DSSW method could assure both the exploration depth and enabling good resolution at the same time, which was an effective method to detect landslide structure and expected to be applied in survey of other geological hazards.

Transient analysis of concrete gravity dam-reservoir systems by Wavenumber-TD approach

The Wavenumber approach was initially introduced as an ideal substitute for the rigorous type of analysis which had been the basis of extensive studies in seismic analysis of concrete gravity dams. The former technique is formulated in the context of pure finite element programming, while the latter relies heavily on a two-dimensional semi-infinite fluid element (i.e., hyper-element). Recently, a variation of Wavenumber method was proposed which was referred to as Wavenumber-TD approach. The approximation to the original technique improves its realm of application and allows it to be carried out in time domain as well as frequency domain. In that study, the formulation was examined for harmonic type of excitation which proved to be promising. Herein, this will be evaluated for its real intended application, which is transient analysis of dam-reservoir systems. For this aim, the prepared special purpose finite element program is modified and the analysis of Pine Flat dam is considered as a typical example. Several models are considered with different values of normalized reservoir length. In each case, the reservoir truncation surface is treated by Wavenumber-TD and the extensively utilized Sommerfeld conditions. The dynamic loading considered is the S69E component of Taft earthquake record. Furthermore, two types of reservoir bottom condition of full reflective as well as absorptive, are adopted. Overall, this will allow for a thorough examination and evaluation of Wavenumber-TD approach in regard to its effectiveness.

Origin of the pulse‐like signature of shallow long‐period volcano seismicity

AbstractShort‐duration, pulse‐like long‐period (LP) events are a characteristic type of seismicity accompanying eruptive activity at Mount Etna in Italy in 2004 and 2008 and at Turrialba Volcano in Costa Rica and Ubinas Volcano in Peru in 2009. We use the discrete wave number method to compute the free surface response in the near field of a rectangular tensile crack embedded in a homogeneous elastic half space and to gain insights into the origin of the LP pulses. Two source models are considered, including (1) a vertical fluid‐driven crack and (2) a unilateral tensile rupture growing at a fixed sub‐Rayleigh velocity with constant opening on a vertical crack. We apply cross correlation to the synthetics and data to demonstrate that a fluid‐driven crack provides a natural explanation for these data with realistic source sizes and fluid properties. Our modeling points to shallow sources (<1 km depth), whose signatures are representative of the Rayleigh pulse sampled at epicentral distances >∼1 km. While a slow‐rupture failure provides another potential model for these events, the synthetics and resulting fits to the data are not optimal in this model compared to a fluid‐driven source. We infer that pulse‐like LP signatures are parts of the continuum of responses produced by shallow fluid‐driven sources in volcanoes.

S-wave velocity structure and site effect parameters derived from microtremor arrays in the Western Plain of Taiwan

In this study, microtremor array measurements were conducted at 45 sites in the Western Plain of Taiwan. The arrays were approximately 30m or 60m in radius, depending on the site. The maximum-likelihood frequency–wavenumber method was adopted to obtain the phase velocities of Rayleigh waves, and then a genetic algorithm technique based on an inversion scheme of the fundamental mode of the Rayleigh waves’ dispersion curves was applied to calculate a preliminary S-wave velocity (Vs) profile at each site. Because a layer of thick sediment covers the bedrock in the Western Plain of Taiwan, microtremor arrays in this size range cannot estimate the structure of the entire sediment. Therefore, this study implemented further inversion of the horizontal-to-vertical spectral ratios of the microtremors to estimate the deeper structures up to the bedrock of Vs greater than 1000m/s. Previously logged velocity profiles for different depths at or near our study sites were collected and compared with the Vs profiles derived from our microtremor array measurements; the results were found to be highly comparable. Therefore, we could delineate the depth distributions for the layer depths for Vs=600m/s and 1000m/s in this region. The depth for Vs=600m/s is approximately 50m in the piedmont area and approximately 300m at the coastline; moreover, the depths for Vs=1000m/s increase from 200m in the piedmont area to approximately 1000m at the coastline. The depths for Vs=1.0km/s (Z1.0), which is an important parameter that accounts for the basin effect in recent ground motion prediction equations, are consequently available at the study sites. The distribution of Z1.0 as a function of Vs30 indicates higher similarity to that in Japan than in the San Francisco Bay area.

Dynamic 2.5-D green׳s function for a poroelastic half-space

The dynamic two-and-a-half-dimensional (2.5-D) Green׳s function for a poroelastic half-space subject to a point load and dilatation source is derived based on Biot׳s theory, with the consideration of both a permeable surface and an impermeable surface. The governing differential equations for the 2.5-D Green׳s function are established by applying the Fourier transform to the governing equations of the three-dimensional (3-D) Green׳s function. The dynamic 2.5-D Green׳s function is derived in a full-space using the potential decomposition and discrete wavenumber methods. The surface terms are introduced to fulfil the free-surface boundary conditions and thereby obtain the dynamic 2.5-D Green׳s function for a poroelastic half-space with the permeable and impermeable surfaces. The half-space 2.5-D Green׳s function is verified through comparison with the 2.5-D Green׳s function regarding an elastodynamic half-space and the 3-D Green׳s function for a poroelastic half-space. A numerical case is provided to compare between the full-space solutions and the half-space solutions with two different sets of free-surface boundary conditions. In addition, a case study of efficient calculation of vibration from a tunnel embedded in a poroelastic half-space is presented to show the application of the 2.5-D Green׳s function in engineering problems.

Improvement of weighted compact scheme with multi-step strategy for supersonic compressible flow

With shock capturing capability and spectral like resolution, weighted compact schemes are good choices for supersonic turbulent flow simulation. However, because of the implicit nature of compact schemes, accuracy decrease at one point would contaminate the overall solution. The recently proposed compact-reconstructed WENO (CRWENO) scheme (Ghosh and Baeder, 2012) is an efficient weighted compact scheme. Analysis shows that the accuracy of the CRWENO scheme is only second order for points near discontinuities. In this paper, a multi-step strategy is proposed to increase the accuracy of the CRWENO scheme near discontinuities. Instead of constructing the fifth order compact scheme directly from three third order compact schemes, two fourth order compact schemes are first constructed. The final fifth order scheme is then obtained by these two fourth order schemes. In this way, the accuracy of the CRWENO scheme is increased to third order for points near discontinuities. The dissipation and dispersion properties of the new scheme are analyzed by employing the modified wave number method. Several examples, including linear advection cases, three one-dimensional shock tube problems, two-dimensional isentropic vortex convection, double Mach reflection, and shock/mixing layer interaction problems, are considered to assess the present method. Numerical results show that the present multi-step CRWENO scheme has lower dissipation and higher resolution in both smooth and discontinuous regions compared with the original scheme.

Delamination detection and quantification on laminated composite structures with Lamb waves and wavenumber analysis

Laminated composites are susceptible to delamination due to their weak transverse tensile and interlaminar shear strengths as compared to their in-plane properties. Delamination damage can occur internally, where it is not visible to the naked eye. Development of reliable, quantitative techniques for detecting delamination damage in laminated composite components will be imperative for safe and functional optimally designed next-generation composite structures. In this article, we study the potential of using Lamb waves for delamination detection and quantification, using model-assisted data acquisition. Novel wavenumber analysis approaches are developed and discussed to show how they can be used to investigate Lamb wave interactions with delaminated plies. Ultrasonic wave simulations are implemented to provide both in-plane and out-of-plane wave motion for the wavenumber studies. The out-of-plane results are verified against data obtained from experimental tests. It is found that the wavenumber methods can not only determine the delaminated region of the plate and its length, but can also identify the plies between which the delamination occurs. We envision that the wavenumber approaches can lead to a complete delamination quantification in the future.

Improving the local wavenumber method by automatic DEXP transformation

In this paper we present a new method for source parameter estimation, based on the local wavenumber function. We make use of the stable properties of the Depth from EXtreme Points (DEXP) method, in which the depth to the source is determined at the extreme points of the field scaled with a power-law of the altitude. Thus the method results particularly suited to deal with local wavenumber of high-order, as it is able to overcome its known instability caused by the use of high-order derivatives. The DEXP transformation enjoys a relevant feature when applied to the local wavenumber function: the scaling-law is in fact independent of the structural index. So, differently from the DEXP transformation applied directly to potential fields, the Local Wavenumber DEXP transformation is fully automatic and may be implemented as a very fast imaging method, mapping every kind of source at the correct depth. Also the simultaneous presence of sources with different homogeneity degree can be easily and correctly treated. The method was applied to synthetic and real examples from Bulgaria and Italy and the results agree well with known information about the causative sources.

Inverting full waveforms into 1D seismic velocity model of the upper crust by neighborhood algorithm - Corinth Gulf, Greece

We investigated inversion of full waveforms into formal 1D velocity models. ‘Formal’ means that the models are primarily intended to simulate complete seismograms close to real records, rather than to reflect the true crustal structure from the geological point of view. The method is demonstrated for a magnitude Mw 5.3 earthquake (centroid depth of 4.5 km), recorded at 8 three-component stations in the Corinth Gulf region, Greece, spanning the epicentral distance range from 15 to 102 km, and frequency range from 0.05 to 0.2 Hz. The forward problem was solved by the discrete wavenumber method, while the inversion was performed with the neighborhood algorithm. As such, not only the best-fit models, but also suites of the models almost equally well satisfying data were obtained. The best resolution was found in the topmost ∼10 km. Extensive testing of the model parametrization enabled identification of the most robust features of the solution. The P- and S-wave velocities are characterized by a strong increase with depth in the topmost ∼4–5 km. This part of the model can be approximated by a layer with constant velocity gradient. Compared to a previously existing model of the region, the satisfactory waveform match was extended from the maximum frequency of 0.1 Hz up to 0.2 Hz. This extension will improve calculation of the seismic source parameters in the region, e.g. determination of source time functions and slip distributions of potential future Mw > 6 events.

Spatio-temporal variability of seismic noise above a geothermal reservoir

Abstract We report on the application of seismic noise investigations, including H/V (horizontal to vertical) spectral ratio and array techniques, to a shallow gas-rich geothermal reservoir in Heybeli, southwestern Turkey. Fundamental resonant frequencies were determined to estimate the sediment thickness. Using small-scale seismic arrays, phase velocity dispersion curves were derived by correlating noise recordings according to the extended spatial autocorrelation method. Improved shear wave velocity profiles were estimated by combining Rayleigh wave dispersion curves and horizontal to vertical spectral ratios in a joint inversion. We found that the velocities obtained for the reservoir site are higher than those for a location outside the reservoir. In addition to the fundamental resonant peaks in the spectra, a clear 6-Hz-signal could be identified originating from the center of the geothermal field, repeatedly observed in 2010 and 2011. It had been claimed that low frequency (1–10 Hz) seismic signal anomalies were correlated with the occurrence of hydrocarbons. One of the physical mechanisms under consideration to explain these tremor-like signals above such reservoirs is resonant amplification due to the oscillation of bubbles. Based on the signal similarity with volcanic tremors, it is not a priori given that the liquid phase must be oil for resonance effects to occur. We therefore applied array techniques to identify potential noise originating from the Heybeli reservoir. In fact, the frequency–wavenumber ( f – k ) method clearly indicated a noise source coming from the main production well of the reservoir. In 2011, as part of our assessment, the operators of the spa facility stopped the extraction of thermal water for 2 h: the 6-Hz-signal disappeared after the pump had been stopped and reappeared after the pump began operating again. Thus, the 6-Hz-signal is likely of artificial origin. In addition, no natural noise source inside the reservoir could be identified.

Analytic Simulation of the Elastic Waves Propagation in the Neighborhood of Fluid Filled Wells with Monopole Sources

An analytic formulation to understand the scattering, diffraction and attenuation of elastic waves at the neighborhood of fluid filled wells is presented. An important, and not widely exploited, technique to carefully investigate the wave propagation in exploration wells is the logging of sonic waveforms. Fundamental decisions and production planning in petroleum reservoirs are made by interpretation of such recordings. Nowadays, geophysicists and engineers face problems related to the acquisition and interpretation under complex conditions associated with conducting open-hole measurements. A crucial problem that directly affects the response of sonic logs is the eccentricity of the measuring tool with respect to the center of the borehole. Even with the employment of centralizers, this simple variation, dramatically changes the physical conditions on the wave propagation around the well. Recent works in the numerical field reported advanced studies in modeling and simulation of acoustic wave propagation around wells, including complex heterogeneities and anisotropy. However, no analytical efforts have been made to formally understand the wireline sonic logging measurements acquired with borehole-eccentered tools. In this paper, the Graf’s addition theorem was used to describe monopole sources in terms of solutions of the wave equation. The formulation was developed from the three-dimensional discrete wave-number method in the frequency domain. The cylindrical Bessel functions of the third kind and order zero were re-derived to obtain a simplified set of equations projected into a bi-dimensional plane-space for displacements and stresses. This new and condensed analytic formulation allows the straightforward calculation of all converted modes and their visualization in the time domain via Fourier synthesis. The main aim was to obtain spectral surfaces of transfer functions and synthetic seismograms that might be useful to understand the wave motion produced by the eccentricity of the source and explain in detail the new arising borehole propagation modes. Finally, time histories and amplitude spectra for relevant examples are presented and the validation of time traces using the spectral element method is reported.

Rapid Discrimination of Chlorpheniramine Maleate and Assessment of Its Surface Content Uniformity in a Pharmaceutical Formulation by NIR-CI Coupled with Statistical Measurement

This study demonstrated that near infrared chemical imaging (NIR-CI) was a rapid and nondestructive technique for discrimination of chlorpheniramine maleate (CPM) and assessment of its surface content uniformity (SCU) in a pharmaceutical formulation. The characteristic wavenumber method was used for discriminating CPM distribution on the tablet surface. To assess the surface content uniformity of CPM, binary image and statistical measurement were proposed. Furthermore, high-performance liquid chromatography (HPLC) was used as reference method for accurately determining volume content of CPM in the sample. Moreover, HPLC was performed to assess volume content uniformity (VCU) of CPM in whole region and part region of the tablets. The NIR-CI result showed that the spatial distribution of CPM was heterogeneous on the tablet surface. Through the comparison of content uniformity of CPM determined by NIR-CI and HPLC, respectively, it demonstrated that a high degree of VCU did not imply a high degree of SCU of the samples. These results indicate that HPLC method is not suitable for testing SCU, and this has been verified by NIR-CI. This study proves the feasibility of NIR-CI for rapid discrimination of CPM and assessment of its SCU, which is helpful for the quality control of commercial CPM tablets.

Alternative local wavenumber methods to estimate magnetic source parameters

Three alternative local wavenumber methods are proposed to estimate the depth and the nature (structural index) of the 2D magnetic source simultaneously using various combinations of different forms of the local wavenumbers to compute the source parameters without any prior information about the source. A clustering method is also provided to get more accurate results. The proposed local wavenumber methods are demonstrated on synthetic noise-free and noise-corrupted magnetic data, and they successfully estimate the location parameters and structural index of the causative sources. The actual application of the proposed methods is demonstrated on a magnetic anomaly from southern Illinois.

Strong ground motion simulation during the November 1759 Earthquake along Serghaya Fault in the metropolitan of Damascus, Syria

The seismic hazard potential for metropolitan of Damascus, Syria is mainly controlled by earthquakes along Serghaya Fault which is a branch of Dead Sea Fault System. In this study, strong ground motion due to the November 1759 Earthquake along the fault of Serghaya was estimated with a numerical simulation technique. In the simulation, the Kostrov-like slip-velocity function was used as an input to the discrete wave number method to simulate the strong ground motions in a broadband frequency range. In order to model the incoherent rupture propagation which can excite large high-frequency waves, random numbers are added to arrival time of circular rupture front. MMI intensities calculated from the synthetic ground motions are compared with the observed values by Ambraseys and Barazangi (J Geophys Res 94:4007-4013, 1989). The calculated intensities are in good agreement with the observed ones at the most sites that validate appropriateness of the proposed source model. The PGA and PGV in the eastern region of Damascus city are higher than those in the western region due to the effects of local site amplification. The simulated high-frequency (1.0–6.0 Hz) ground motions for the sites in the Damascus city are higher than the design requirements defined by the Syrian building code. Furthermore, the simulated high-frequency ground motions for sites in the focal region are bigger than the design requirements in the case of the near-fault factors and are not considered. That demonstrates the appropriateness of considering the near-fault factors for a site near the focal region as introduced by the new building code.

Modelado numérico para estudiar interfases fluido-sólidas ante excitaciones dinámicas

This work shows the wave propagation in fluid-solid interfaces due to dynamic excitations, such interface waves are known as Scholte's waves. We studied a wide range of elastic solid materials used in engineering. The interface connects an acoustic medium (fluid) and another solid. It has been shown that by means of an analysis of diffracted waves in a fluid, it is possible to deduce the mechanical characteristics of the solid medium, specifically, its propagation velocities. For this purpose, the diffracted field of pressures and displacements, due to an initial pressure in the fluid, are expressed using boundary integral representations, which satisfy the equation of motion. The initial pressure in the fluid is represented by a Hankel's function of second kind and zero order. The solution to this problem of wave propagation is obtained by means of the Indirect Boundary Element Method, which is equivalent to the well-known Somigliana's representation theorem. The validation of the results was performed by means of the Discrete Wave Number Method. Firstly, spectra of pressures to illustrate the behavior of the fluid for each solid material considered are included, then, the Fast Fourier Transform algorithm to display the results in the time domain is applied, where the emergence of Scholte's waves and the amount of energy that they carry are highlighted.