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Monitoring changes of seismic properties at depth can provide a first‐order insight into Earth's dynamic evolution. Coda wave interferometry is the primary tool for this purpose. This technique exploits small changes of waveforms in the seismic coda and relates them to temporal variations of attenuation or velocity at depth. While most existing studies assume statistically homogeneous scattering strength in the lithosphere, geological observations suggest that this hypothesis may not be fulfilled in active tectonic or volcanic areas. In a numerical study we explore the impact of a non‐uniform distribution of scattering strength on the spatio‐temporal sensitivity of coda waves. Based on Monte Carlo simulation of the radiative transfer process, we calculate sensitivity kernels for three different observables, namely travel‐time, decorrelation, and intensity. Our results demonstrate that laterally varying scattering properties can have a profound impact on the sensitivities of coda waves. Furthermore, we demonstrate that the knowledge of the mean intensity, specific intensity, and energy flux, governed by spatial variation of scattering strength, is key to understanding the decorrelation, travel‐time, and scattering kernels, respectively. A number of previous works on coda wave sensitivity kernels neglect the directivity of energy fluxes by employing formulas extrapolated from the diffusion approximation. In this work, we demonstrate and visually illustrate the importance of the use of specific intensity for the travel‐time and scattering kernels, in the context of volcanic and fault zone setting models. Our results let us foresee new applications of coda wave monitoring in environments of high scattering contrast. Plain Language Summary: To monitor the evolution of the dynamic Earth, seismologists use a part of the seismic record called "coda," which is composed of waves that have bounced multiple times off heterogeneities of the crust. The coda is extremely sensitive to weak perturbations of propagation properties induced by Earth's tectonic and volcanic activity. The correct physical modeling of coda waves is therefore key to unravel the rich information encoded in their waveforms. A limitation of current seismological monitoring techniques is the neglect of strong lateral variations of coda waves propagation properties documented by geological observations. Our work focuses specifically on this aspect. We provide a complete theoretical and numerical framework to model and understand the spatial and temporal sensitivity of coda waves to medium perturbations in complex geological settings. Using simple but realistic models of a fault zone and a volcano, we illustrate the profound impact of non‐uniform scattering properties on the coda wave sensitivity, which in turn determines the ability of seismologists to correctly retrieve the magnitude and location of physical changes in the crust. Our results let us foresee new applications of coda wave monitoring in environments of high scattering contrast, such as volcanic and fault zone settings. Key Points: A non‐uniform distribution of scattering strength can have a profound impact on the spatio‐temporal sensitivity of coda wavesWe illustrate this using Monte Carlo simulations for models with either a volcanic, fault zone, or two half‐spaces settingThe mean intensity, specific intensity, and energy flux, is key to understanding the decorrelation, travel‐time, and scattering kernels, respectively [ABSTRACT FROM AUTHOR]

Constraining the possible patterns of iron fabrics in the Earth's Uppermost Inner Core (UIC) is key to unravel the mechanisms controlling its growth and dynamics. In the framework of crystalline micro-structures composed of ellipsoidal, aligned grains, we discuss possible textural models of UIC compatible with observations of P -wave attenuation and velocity dispersion. Using recent results from multiple scattering theory in textured heterogeneous materials, we compute the P -wave phase velocity and scattering attenuation as a function of grain volume, shape, and orientation wrt to the propagation direction of seismic P -waves. Assuming no variations of the grain volume between the Eastern and Western hemisphere, we show that two families of texture are compatible with the degree-one structure of the inner core as revealed by the positive correlation between seismic velocity and attenuation. (1) Strong flattening of grains parallel to the Inner Core Boundary in the Western hemisphere and weak anisometry in the Eastern hemisphere. (2) Strong radial elongation of grains in the Western hemisphere and again weak anisometry in the Eastern hemisphere. Both textures can quantitatively explain the seismic data in a limited range of grain volumes. Furthermore, the velocity and attenuation anisotropy locally observed under Africa demands that the grains be locally elongated in the direction of Earth's meridians. Our study demonstrates that the hemispherical seismic structure of UIC can be entirely explained by changes in the shape and orientation of grains, thereby offering an alternative to changes in grain volumes. In the future, our theoretical toolbox could be used to systematically test the compatibility of textures predicted by geodynamical models with seismic observations. [ABSTRACT FROM AUTHOR]

We investigate the impact of spatial variations of absorption and scattering properties on the energy envelopes of coda waves. To model the spatiotemporal distribution of seismic energy, we employ a scalar version of the radiative transfer equation with spatially dependent absorption and scattering quality factor. The scattering pattern which describes the angular distribution of energy upon scattering is assumed to be statistically isotropic, independent of position, but otherwise arbitrary. Further assuming that the spatial variations of the governing parameters are sufficiently weak, we employ perturbation theory to derive linearized relations between the absorption/scattering properties of the medium and the intensity detected in the coda. These relations take the form of weighted integrals where so-called scattering/absorption sensitivity kernels play the role of weighting function. The kernels depend on the type of perturbation (scattering or absorption), the lapse-time in the coda, and require the knowledge of the complete angular dependence of the specific intensity describing the flow of energy in a given direction at a given location. In the long lapse-time limit, we establish simplified formulae which depend on the first two angular moments of the specific intensity only. As an illustration of the theory, we calculate the absorption and scattering sensitivity kernels in a 2-D isotropically scattering medium at different lapse-times in the coda, and discuss their singularities in detail. The sensitivity kernels are then employed to calculate the relative intensity variations of the coda caused by a localized Gaussian absorption/scattering anomaly. We find that the dominant effect of absorption anomalies is to modify the decay rate of the coda, while scattering anomalies have a more complex signature, causing either positive or negative deflection of the energy envelope, depending on their location and the lapse-time. Our results suggest the possibility to locate and discriminate between scattering and absorption anomalies from the energy envelope of coda waves. [ABSTRACT FROM PUBLISHER]

Microtremors are produced by multiple random sources close to the surface of the Earth. They may include the effects of multiple scattering, which suggests that their intensities could be well described by diffusion-like equations. Within this theoretical framework, the average autocorrelation of the motions at a given receiver, in the frequency domain, measures average energy density and is proportional to the imaginary part of the Green's function (GF) when both source and receiver are the same. Assuming the seismic field is diffuse we compute the H/ V ratio for a surface receiver on a horizontally layered medium in terms of the imaginary part of the GF at the source. This theory links average energy densities with the GF in 3-D and considers the H/ V ratio as an intrinsic property of the medium. Therefore, our approach naturally allows for the inversion of H/ V, the well-known Nakamura's ratio including the contributions of Rayleigh, Love and body waves. Broad-band noise records at Texcoco, a soft soil site near Mexico City, are studied and interpreted using this theory. [ABSTRACT FROM AUTHOR]