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...

International audienceIn seismic applications, the bulk modulus of porous media saturated with liquid and gas phases is often estimated using Gassmann's fluid substitution formula, in which the effective bulk modulus of the two-phase fluid is the Reuss average of the gas and liquid bulk moduli. This averaging procedure, referred to as Wood's approximation, holds if the liquid and gas phases are homogeneously distributed within the pore space down to sizes well below the seismic wavelength and if the phase transfer processes between liquid and gas domains induced by the pressure variations of the seismic wave are negligible over the timescale of the wave period. Using existing theoretical results and low-frequency acoustic measurements in bubbly liquids, we argue that the latter assumption of "frozen" phases, valid for large enough frequencies, is likely to fail in the seismic frequency range where lower effective bulk modulus and velocity, together with dispersion and attenuation effects, are expected. We provide a simple method, which extends to reservoir fluids a classical result by Landau and Lifshitz valid for pure fluids, to compute the effective bulk modulus of thermodynamically equilibrated liquid and gas phases. For low gas saturation, this modulus is significantly lower than its Wood's counterpart, especially at the crossing of bubble point conditions. A seismic reflector associated to a phase transition between a monophasic and a two-phase fluid thus will appear. We discuss the consequences of these results for various seismic applications including fizz water discrimination and hydrocarbon reservoir depletion and CO2 geological storage monitoring

A linearized elastic migration/inversion (M/I) technique is applied to multicomponent offset VSP data collected in the North Sea. High‐resolution elastic images of the target zone (P- and S-wave velocities and density) are obtained from upgoing P-P and P-S wave fields. These M/I images are an approximate representation of rapid variations of subsurface parameters. Three image confidence criteria provide a measure of uncertainty in the interpretation. VSP-CDP transform maps assisted in the definition of the confidence region in M/I images. M/I was helpful in delineating the Brent reservoir, and detecting a twofault system. Preliminary interpretation indicates an increase in Poisson’s ratio at the top of the reservoir. Surface data were not able to image this target due to strong multiples at the Cretaceous base. This is the first time elastic depth images have been obtained from M/I of offset VSP field data. Generally, image artifacts depend on the following conditions: (1) good quality data with satisfactory coverage of the target zone; (2) accurate, amplitude‐preserving data preprocessing techniques for filtering out “unwanted” waves; and (3) an elastic background model which adequately represents the main subsurface features. Our M/I approach is flexible, since it can be used with single or multicomponent prestack data P-P, P-S, S-P, and S-S scattered waves simultaneously, an arbitrary acquisition geometry, and a two‐dimensional heterogeneous background model. Computational efficiency results from concentrating the inversion on a target zone and using the paraxial ray method to compute ray‐approximate Green’s functions.

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