A B S T R A C TWell-log data are processed in order to derive subsurface physical parameters, namely rock porosity, fluid saturations and permeability. This step involves the selection and inversion of experimental constitutive equations, which are the link between the rock parameters and geophysical measurements. In this paper we investigate the rock parameter observability and the reliability of well-log data processing. We present a visual analysis of the constitutive equations and of the inverse problem conditioning, when using independently, or jointly, log data from different domains. The existence of a common set of rock properties (cross-properties) that influence different measurements, makes it possible to reduce the ambiguities of the interpretation. We select a test case in a reservoir scenario and we explore how to determine rock porosity and fluid saturation from sonic, conductivity and density logs. We propose a Bayesian joint inversion procedure, which is able to control the conditioning problems, to efficiently take into account input data and model uncertainty and to provide a confidence interval for the solution. The inversion procedure is validated on a real well-log data set.

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Seismic wave reflection amplitudes are used to detect fluids and fracture properties in reservoirs. This paper studies the characterization of a vertically fractured fluid‐filled reservoir by analyzing the reflection amplitudes of P‐waves with varying incident and azimuthal angles. The reservoir is modeled as a horizontal transversely isotropic medium embedded in an isotropic background, and the linearized P‐waves reflection coefficient are considered. The conditioning of the inverse problem is analyzed, and fracture density is found to be the best conditioned parameter. Using diffraction tomography under the Born approximation, an inversion procedure is proposed in the transformed k–ω domain to detect fracture density variations within the reservoir. Seismic data are rearranged in pairs of incident and reflected plane waves, enlightening only one spectral component of the fracture density field at a time. Only the observable spectral components are inverted. Moreover, working in the transformed domain, picking reflection amplitudes is not required. An example of the inversion applied to a synthetic data set is presented. The limitation of source and receiver numbers and the finite bandwidth of the wavelet produce a loss of resolution, but the overall fracture density variations are recovered correctly.

Many noise reduction applications are targeted at multi-tonal disturbances. Active noise control (ANC) solutions for such problems are generally based on the combination of multiple adaptive notch filters. Both the performance and the computational cost are negatively affected by an increase in the number of controlled frequencies. In this work we study a different modeling approach for the secondary path, based on the estimation of various small local models in adjacent frequency subbands, that greatly reduces the impact of reference-filtering operations in the ANC algorithm. Furthermore, in combination with a frequency-specific step size tuning method it provides a balanced attenuation performance over the whole controlled frequency range (and particularly in the high end of the range). Finally, the use of small local models is greatly beneficial for the reactivity of the online secondary path modeling algorithm when the characteristics of the acoustic channels are time-varying. Several simulations are provided to illustrate the positive features of the proposed method compared to other well-known techniques