Dispersion Estimation From Linear Array Data in the Time-Frequency Plane

International audienceWe consider the problem of estimating the dispersion of a wave field from data recorded by a linear array of geophones. The fact that the data we are looking at may contain several propagating waves make this even more challenging. In this paper, a new algorithm is proposed to solve this issue. Currently, there are two methods for estimating wave dispersion described in the literature. The first method estimates the group delay function from the time-frequency representation (TFR) of each sensor separately. It is efficient as long as the patterns of the different waves do not overlap in the time-frequency plane. The second method estimates the dispersion from the two-dimensional (2-D) Fourier transform of the profile (or more generally from a velocity-frequency representation). This assumes that the dispersion is constant along the entire sensor array. It is efficient as long as the patterns of the waves do not overlap in the frequency domain. Our method can be thought of as a hybrid of the above two methods as it is based on the construction of a TFR where the energy of waves that propagate at a selected velocity are amplified. The primary advantage of our algorithm is the use of the velocity variable to separate the patterns of the propagating waves in the time-frequency plane. When applied to both synthetic and real data, this new algorithm gives much improved results when compared with other standard methods

Impact of water saturation on seismoelectric transfer functions: a laboratory study of coseismic phenomenon

Seismic waves propagating in a porous medium, under favourable conditions, generate measurable electromagnetic fields due to electrokinetic effects. It has been proposed, following experimental and numerical studies, that these so-called ‘seismoelectromagnetic' couplings depend on pore fluid properties. The theoretical frame describing these phenomena are based on the original Biot's theory, assuming that pores are fluid-filled. We study here the impact of a partially saturated medium on amplitudes of those seismoelectric couplings by comparing experimental data to an effective fluid model. We have built a 1-m-length-scale experiment designed for imbibition and drainage of an homogeneous silica sand; the experimental set-up includes a seismic source, accelerometers, electric dipoles and capacitance probes in order to monitor seismic and seismoelectric fields during water saturation. Apparent velocities and frequency spectra (in the kiloHertz range) are derived from seismic and electrical measurements during experiments in varying saturation conditions. Amplitudes of seismic and seismoelectric waves and their ratios (i.e. transfer functions) are discussed using a spectral analysis performed by continuous wavelet transform. The experiments reveal that amplitude ratios of seismic to coseismic electric signals remain rather constant as a function of the water saturation in the Sw=[0.2-0.9] range, consistently with theoretically predicted transfer function

A STUDY OF FRACTAL ANALYSIS AND SINGULARITY SPECTRUM AND ITS POTENTIAL APPLICATION IN THE OIL AND GAS INDUSTRY

The world is made up of various irregular objects and signals. Although traditional mathematical techniques are not able to analyse these signals, it has been identified that these signals show common features such as singularities at various scales of observation. This indicates the existence of fractals within these signals. In the oil and gas industry, seismic data is a collection of reflected audio signals and is an example of irregular signals that could also have fractal features. Even though we know that global petroleum resources are on the decline, oil and gas still remains the main source of energy throughout the world. This makes seismic exploration activities all the more important. Present indirect hydrocarbon detection techniques using seismic are costly and do not guarantee detection of oil or gas. Therefore, a technological advancement in the field of seismic exploration is evidently needed. Therefore, this study aims to develop a method for direct detection and delineation of hydrocarbons from seismic data. In order to analyse the fractal nature of signals, a collection of mathematical steps known as fractal analysis is applied to generate a singularity spectrum. Although importance has been given on the methods of computing the singularity spectrum, there is little study on the effects of different types of singularities on the singularity spectrum. This study aims to understand how the singularity spectrum is affected by changes applied to input signals. It is by acquiring this knowledge first that the study also intends to develop an algorithm for direct detection of hydrocarbons. The Fraclab toolbox in MATLAB will be extensively used to achieve both of these goals. From the study of the changes to singularity spectrum due to change in signals, it was observed that the square wave is the most irregular signal when compared with sine wave and sawtooth wave. Meanwhile, it was also discovered that a change in the amplitude of the periodic signal does not play a part in the final result of the singularity spectrum. The study has also observed that when two regular waves concatenate, the singularity spectrum produces more than one point due to the existence of a singularity or singularities at the point where the two signals concatenate. In direct comparison, when two periodic signals are added to one another, they only produce a dot on the singularity spectrum indicating that the end signal is still monofractal

AN INVESTIGATION OF SEISMIC ATTENUATION IN MARINE SEDIMENTS

There have been relatively few investigations into the attenuation properties of unconsolidated sediments using marine surface seismic data. Several methods of measuring attenuation were assessed for reliability in a noise-free case and with the addition of noise using a set of synthetically absorbed and dispersed wavelets. Wavelet modelling proved to be superior to the other techniques, followed by spectrum modelling and the spectral ratios method. Complex trace analysis using the analytical signal proved to be unreliable for non-sinusoidal wavelets, whilst the risetime method was found to be very susceptible to noise for practical purposes. Numerical modelling was carried out to assess the spectral effects of layering on a propagating pulse. The thin layer / peg-leg phenomenon has varying filtering effects on the propagating pulse. In particular, layers which are less than the "tuning thickness" of the propagating pulse have a low-pass effect. The quality factor, Q, was measured in two case studies. In the first, the mean Q was determined from wavelet and spectrum modelling and found to be 60 for fine sands and 47 for coarse sands in the 1 kHz to 3 kHz frequency band. In the second, Q was determined as 59 for poorly sorted sandy diamicts in the 100 Hz to 240 Hz frequency band. The close fit between synthesised spectra and wavelets and observed data showed that a constant- Q mechanism would account for the spectral changes between the seabed and the deeper target reflection events in the two case studies. The spectra of the target reflection events in both case studies were lacking in low frequencies which is likely to be due to low-pass filtering from composite reflection events due to thin bed layering. For practical purposes, the determination of Q from a mean normalised seismic trace yielded the same result as measuring a mean Q from individual traces. In a third case study, the seabed multiple was compared to the seabed reflection using wavelet and spectrum modelling. A lack of low frequencies in the seabed multiple showed that the seabed can act as a low-pass filter to an incident pulse. As the numerical methods rely on the seabed as having a white reflection and transmission response, the low-pass effect will result in erroneous estimates of the quality factor, Q

Near-Surface Shear-Wave Velocity Measurements in Unlithified Sediment

Shear-wave (S-wave) velocity can be directly correlated to material stiff¬ness making it a valuable physical property that has found uses in construction, engineering, and envi-ronmental projects. This study compares three different methods, Multi¬channel Analysis of Surface Waves (MASW), S-wave tomography, and downhole seismic for measuring S-wave velocities, investigates and identi¬fies the differences among the methods' results, and pri¬oritizes the different methods for S-wave use at the U. S. Army's Yuma Proving Grounds (YPG) north of Yuma, AZ. A large signal-to-noise ratio and a layered depositional architecture at the study site gives the MASW method much potential, but higher-mode energy resulting from velocity discontinuities reduces the effectiveness of the method shallower than 20 ft. First arrival analysis provides evidence of a velocity discontinuity within the first 10 feet of unconsolidated sediment. S-wave first arrivals were picked using impulsive sledgehammer data which were then used for both tomographic inversion and refraction analysis. Three-component downhole seismic data were collected by using a locking geophone coupled with the borehole casing to estimate seismic velocities directly. This study helps to identify the strengths and weaknesses of each of these methods at sites similar to YPG. MASW results show a low-velocity layer at a depth of about 50 feet that is verified by downhole seismic data and is undetectable through traditional refraction tomography. However S-wave refraction tomography provides more convincing results at shallow depths where the MASW method fails. Using both methods in an integrated fashion provide the most accurate depiction of S-wave velocity characteristics in the shallow unconsolidated sediments at YPG

Étude numérique de l'interaction des ondes de surface avec les cavités souterraines

L’effondrement des remblais routiers causé par le développement de cavités souterraines autour des ponceaux pose un risque majeur pour la sécurité des usagers et les installations à proximité. La détection de vides peu profonds est devenue l'une des missions récurrentes difficiles en génie civil à cause de la complexité de la réponse sismique d’un remblai routier en présence d’un ponceau et d’éventuelles cavités. Bien que les méthodes non intrusives basées sur les ondes de surface permettent d’estimer efficacement la vitesse des ondes de cisaillement des dépôts de sol, de nombreux défis sont rencontrés lorsqu'il s'agit de juger de la présence d'une inhomogénéité latérale locale en raison de la résolution limitée des approches géophysiques appliquées. Par conséquent, une étude numérique a été entreprise pour étudier la sensibilité des deux composantes des ondes de Rayleigh (la composante horizontale et la composante verticale désignées X et Z respectivement dans cette étude) et la seule composante des ondes de Love (désignée Y dans cette étude) à un contraste de rigidité (vide) dans différents contextes géologiques. Les accélérations des trois composants sont simulées au moyen du programme de modélisation numérique par éléments finis FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) pour différentes configurations de modèles en présence et en absence de cavité. Les données sismiques sont traitées avec la transformée de Stockwell généralisée (GST) dans le domaine temps-fréquence. Les résultats sont présentés sous forme des tomographies des courbes de dispersion des vitesses de groupe et de phase pour évaluer l'effet de la cavité et la localiser par rapport à la source. La signature de la cavité a également été étudiée à deux différentes profondeurs à partir du modèle parfaitement homogène. Les distributions de vitesse des trois composants ont révélé des changements négligeables après la création de la plus profonde cavité. Les observations numériques ont démontré que les vitesses de phase sont plus sensibles que la vitesse de groupe aux variations latérales de densité. De plus, on peut conclure que les trois composants ont révélé des distributions de vitesse de phase perceptibles et distinctes en présence d’un vide. La composante X s'est également avérée plus efficace pour localiser la cavité. Les résultats de cette étude numérique suggèrent l’acquisition des trois composantes lors des relevés sismiques sur terrain et d’intégrer simultanément ses trois composantes lors de l’analyse pour une plus grande fiabilité.Abstract : A road collapse caused by the development of near-surface cavities surrounding buried culverts poses a major hazard to road users’ safety and nearby facilities. The complexity of the road embankment seismic response has made it a challenging recurring mission in civil engineering to detect shallow voids. Although non-intrusive surface wave methods afford reliable shear wave velocity estimates of the subsurface materials, many challenges are encountered when judging the presence of a local lateral heterogeneity due to the limited resolution of the applied geophysical approaches. Therefore, a numerical study was conducted to investigate the sensitivity of the two Rayleigh waves components (the horizontal and vertical components, designed as X-component and Z-components, respectively in this study) and the only Love waves component (designed as Y-component in this study) to a contrast of rigidity (void) in different geological contexts. The accelerations of the three components are computed using a finite element commercial code FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) for different model configurations both with and without a cavity. The seismic data are processed using the Generalized Stockwell transform (GST) in the time-frequency domain. To evaluate the effect of the cavity and locate it with respect to the source offset, the results are presented in the form of tomography maps and the group and phase velocity dispersion curve variations along the inspected array. The cavity signature was also studied at two depths relying on a perfectly homogeneous model. The velocity distribution change of the three components revealed minor changes after creating the deeper cavity. Moreover, the numerical observations demonstrated that the phase velocity is considerably more susceptible to lateral density variations than the group velocity. It was concluded that the three components revealed perceptible and distinct phase velocity changes in the presence of the void. The X-component was also found to be more effective in localizing the near and far boundaries of the cavity. The results of this numerical study suggest acquiring the three components during field seismic surveys and integrating the three components simultaneously during the analysis procedure for better efficiency

Borehole seismic methods in high permeability sandstone

In this research complex field borehole seismic measurements are made at a range of frequencies in weakly-consolidated, high-permeability sandstones. New 3D visualisation of phase velocity dispersion derived from multifrequency full waveforms reveals overlapping wave-modes in both open drill holes and sand-screened wells which appear to be sensitive to hydraulic permeability. Multidisciplinary studies of virtual source tomography, vertical seismic profiling and full waveform sonic provide credible information for understanding heterogeneous aquifers with complex sedimentary structures