The authors present a practical guide for studying nonstationary data on human motor behavior in a time-frequency representation. They explain the limits of classical methods founded exclusively on the time or frequency basis and then answer those limits with the windowed Fourier transform and the wavelet transform (WT) methods, both of which are founded on time-frequency bases. The authors stress an interest in the WT method because it permits access to the whole complexity of a signal (in terms of time, frequency, amplitude, and phase). They then show that the WT method is well suited for the analysis of the interaction between two signals, particularly in human movement studies. Finally, to demonstrate its practical applications, the authors apply the method to real data.

This article sheds light on a quantitative method allowing psychologists and behavioral scientists to take into account the specific characteristics emerging from the interaction between two sets of data in general and two individuals in particular. The current article outlines the practical elements of the cross-wavelet transform (CWT) method, highlighting WHY such a method is important in the analysis of time-series in psychology. The idea is (1) to bridge the gap between physical measurements classically used in physiology – neuroscience and psychology; (2) and demonstrates how the CWT method can be applied in psychology. One of the aims is to answer three important questions WHO could use this method in psychology, WHEN it is appropriate to use it (suitable type of time-series) and HOW to use it. Throughout these explanations, an example with simulated data is used. Finally, data from real life application are analyzed. This data corresponds to a rating task where the participants had to rate in real time the emotional expression of a person. The objectives of this practical example are (i) to point out how to manipulate the properties of the CWT method on real data, (ii) to show how to extract meaningful information from the results, and (iii) to provide a new way to analyze psychological attributes.

S U M M A R YIn the present paper, we present a generalization of the wavelet transform, known as chirplet transform, specially designed to quantify the morphological attributes of individual seismic sections (packets) constituting the seismic waveforms. The proposed transform relies on an atomic decomposition of individual seismograms based on local multiscale chirps (swept frequency wave packets) of various shape and duration. We developed an algorithm that provides an optimal representation of the waveform packets in terms of (i) arrival time, (ii) central frequency, (iii) modulus, (iv) phase, (v) duration, (vi) envelope shape and (vii) frequency modulation compacting the information contained in each seismogram into a reduced set of parameters particularly well suited to describe seismic waveforms. In the present work, we focus on the ability of atomic decomposition to classify seismic events. We illustrate the developed methodology and resulting hierarchical classification scheme (agglomerative clustering displayed as a dendrogram) to seismograms of the induced seismicity recorded in the Lacq gas field between 1989 and 1997 by a local seismic network. For the present case-study, the resulting classification reveals different levels of similarity between seismic events of a same swarm. Accurate analysis of the subsequences of seismic events associated to an injection well shows temporal changes in the morphological attributes of the recorded seismic waveforms. These changes are highly correlated with water over-pressure records of the reservoir demonstrating the capability of the method to guide investigation of the underlying processes (properties of propagation media, source, rupture processes), and in a general manner the physical properties of the reservoir. Two major difficulties in earthquake studies are the lack of (1) controlled direct and near-field observations (essential for the validation of models and concepts) and (2) signal processing tools and analysis methods closely connected to the physics of wave propagation in a heterogeneous and dispersive medium (scattering). In this way, seismologists attempt to bridge the gap between laboratory experiments and tectonic earthquakes in the crust by investigating intermediate-scale systems where the cause of seismicity is more or less understood, as it is controlled by anthropogenic activities or by visible volcano activities (Ruiz et al. 1998). Providing that seismologists are able to relate the cause of seismicity to the observed seismic activity, systems associated to subsidence caused by fossil fuel extraction, local pressure changes over large water reservoirs, alteration of the local stress field of significant volume of rock around mining area, extraction of geothermal energy, or volcano activity can be seen as natural laboratories useful for investigating seismogenic processes.The physics of earthquakes (i.e. including nucleation and rupture initiation, rupture propagation) is complex and its understanding requires to efficiently monitor small pe...

A B S T R A C TThe knowledge of the velocity model in microseismic jobs is critical to achieving statistically reliable microseismic event locations. The design of microseismic networks and the limited sources for calibration do not allow for a full tomographic inversion. We propose optimizing a priori velocity models using a few active shots and a nonlinear inversion, suitable to poorly constrained systems. The considered models can be described by several layers with different P-and S-wave velocities. The velocities may be constant or have 3D gradients; the layer interfaces may be simple dipping planes or more complex 3D surfaces. In this process the P-and S-wave arrival times and polarizations measured on the seismograms constitute the observed data set. They are used to estimate two misfit functions: i) one based on the measurement residuals and ii) one based on the inaccuracy of the source relocation. These two functions are minimized thanks to a simulated annealing scheme, which decreases the risk of converging to a local solution within the velocity model.The case study used to illustrate this methodology highlights the ability of this technique to constrain a velocity model with dipping layers. This was performed by jointly using sixteen perforation shots recorded during a multi-stage fracturing operation from a single string of 3C-receivers. This decreased the location inaccuracies and the residuals by a factor of six. In addition, the retrieved layer dip was consistent with the pseudo-horizontal trajectories of the wells and the background information provided by the customer. Finally, the theoretical position of each calibration shot was contained in the uncertainty domain of the relocation of each shot. In contrast, single-stage inversions provided different velocity models that were neither consistent between each other nor with the well trajectories. This example showed that it is essential to perform a multi-stage inversion to derive a better updated velocity model.

S U M M A R YThe goal of this paper is to propose a model of deformation pattern for the Lacq gas field (southwest of France), considering the temporal and spatial evolution of the observed induced seismicity. This model of deformation has been determined from an updating of the earthquake locations and considering theoretical and analogue models usually accepted for hydrocarbon field deformation. The Lacq seismicity is clearly not linked to the natural seismicity of the Pyrenean range recorded 30 km farther to the south since the first event was felt in 1969, after the beginning of the hydrocarbon recovery. From 1974 to 1997, more than 2000 local events (M L < 4.2) have been recorded by two permanent local seismic networks. Unlike previously published results focusing on limited time lapse studies, our analysis relies on the data from 1974 to 1997. Greater accuracy of the absolute locations have been obtained using a well adapted algorithm of 3-D location, after improvement of the 3-D P-wave velocity model and determination of specific station corrections for different clusters of events. This updated catalogue of seismicity has been interpreted taking into account the structural context of the gas field. The Lacq gas field is an anticlinal reservoir where 3-D seismic and borehole data reveal a pattern of high density of fracturing, mainly oriented WNW-ESE. Seismicity map and vertical cross-sections show that majority of the seismic events (70 per cent) occurred above the gas reservoir. Correlation is also observed between the orientation of the pre-existent faults and the location of the seismic activity. Strong and organized seismicity occurred where fault orientation is consistent with the poroelastic stress perturbation due to the gas recovery. On the contrary, the seismicity is quiescient where isobaths of the reservoir roof are closed to be perpendicular to the faults. These quiescient areas as well as the central seismic part are characterized by a surface subsidence determined by repeated levelling profiles. Moreover, the temporal evolution of the distribution of the seismicity clearly exhibits a spatial migration from the centre to the boundaries of the reservoir. We conclude that the entire field is strained but this deformation is seismically expressed only where faults are parallel to the isobaths of the reservoir roof and where these faults plunge towards outside the field according to one of the two theoretical deformation models considered in our study. Then we propose a temporal scenario of deformation along the principal axis of seismic deformation.