Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.

We present a 1D shear-velocity model for Los Humeros geothermal field (Mexico) obtained from three-component beamforming of ambient seismic noise, imaging for the first time the bottom of the sedimentary basement ∼5  km below the volcanic caldera, as well as the brittle-ductile transition at ∼10  km depth. Rayleigh-wave dispersion curves are extracted from ambient seismic noise measurements and inverted using a Markov chain Monte Carlo scheme. The resulting probability density function provides the shear-velocity distribution down to 15 km depth, hence, much deeper than other techniques applied in the area. In the upper 4 km, our model conforms to a profile from local seismicity analysis and matches geological structure inferred from well logs, which validates the methodology. Complementing information from well logs and outcrops at the near surface, discontinuities in the seismic profile can be linked to geological transitions allowing us to infer structural information of the deeper subsurface. By constraining the extent of rocks with brittle behavior and permeability conditions at greater depths, our results are of paramount importance for the future exploitation of the reservoir and provide a basis for the geological and thermodynamic modeling of active superhot geothermal systems, in general.

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We have evaluated an explicit relationship between the representations of internal multiples by source-receiver interferometry and an inverse-scattering series. This provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect. A downside of the existing representations is that their computational cost is extremely high, which can be a precluding factor especially in 3D applications. Using our insight from source-receiver interferometry, we have developed an alternative, computationally more efficient way to predict internal multiples. The new formula is based on crosscorrelation and convolution: two operations that are computationally cheap and routinely used in interferometric methods. We have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set.

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An automated algorithm uses recordings of acoustic energy across a spatially-distributed array to derive information about multiply scattered acoustic waves in heterogeneous media. The arrival time and scattering-order of each recorded diffracted acoustic wave, and the exact sequence of diffractors encountered by that wave, are estimated without requiring an explicit model of the medium through which the wave propagated. Individual diffractors are identified on the basis of their unique single-scattering relative travel-time curves (move-outs) across the array, and secondary (twice-scattered) waves are detected using semblance analysis along temporally offset primary move-outs. This information is sufficient to estimate travel times and scattering paths of all multiply diffracted waves of any order, and for these events to be identified in recorded data. The algorithm is applied to synthetic acoustic data sets from a variety of media, including different numbers of point-diffractors and a medium with strong heterogeneity and non-hyperbolic move-outs.

<p>We give an overview of a new toolbox for easy and fast beamforming analysis of three-component ambient seismic noise and discuss examples from different seismic arrays to solve different application challenges. From only a couple of hours of array recordings, the beamformer provides estimates of surface wave dispersion curves, surface wave azimuthal anisotropy, frequency-dependent wavefield composition including surface and body waves, and the direction of arrival for different wave types and frequencies. The beamformer can be used with three-component arrays from the lab to the field scale, provided ambient noise is available in the corresponding frequency range. Compared to standard (single-component) beamforming analysis, our approach integrates all three components recorded at every seismometer. Considering the phase shifts across the components, it identifies wave-specific particle motion and hence discriminates different wave types on account of their polarisation. The new implementation of the beamformer does not use the cross-spectral density matrix of the data explicitly (as done, for example, by the MUSIC algorithm and Capon beamformer), which reduces computation times significantly and makes it feasible to compute beam responses for a full day of data recorded on 100s of stations on a standard laptop PC. The toolbox will be available on github for both MATLAB and Python.</p> <p>In an example from Los Humeros geothermal field (Mexico) we show Rayleigh wave azimuthal anisotropy as a function of frequency, corresponding to varying fast directions as a function of depth. A good agreement between the observed anisotropy and stress data from well logs as well as geological information indicates that fast directions correlate with the orientation of major faults and dykes. Anisotropy analysis thus provides a means to assess fault properties at depth, giving information about potential secondary permeability – a vital parameter in deep geothermal plays. Beamforming analysis of noise recordings in the Groningen area (Netherlands) reveals dominant prograde motion in both fundamental and 1<sup>st</sup> higher mode Rayleigh waves. This behaviour is indicative of a large impedance contrast between the very low shear-velocities in sedimentary basins and the underlying bedrock. The resolution of particle motion as a function of frequency allows us to observe the osculation frequency where fundamental and 1<sup>st</sup> higher mode Rayleigh waves approach each other and both modes change particle motion from prograde to retrograde and vice versa. The osculation frequency can be used to estimate the depth of the major impedance contrast, that is, the depth of the sedimentary basin. While body wave observations must be interpreted with care, considering the resolution capabilities of the array with respect to the expected (larger) wavelengths, the examples show that body waves contribute to the ambient noise wavefield with varying degree as a function of frequency, challenging the assumption of surface wave dominance common in ambient noise studies. Overall, we demonstrate that our beamforming toolbox provides direct information about structural features as well as fundamental a-priori information on wavefield composition and source characteristics, valuable for further ambient noise methods.</p>

<p>Surface wave dispersion curves derived from ambient noise recordings are frequently used to invert for subsurface velocity information. Rayleigh wave ellipticities and phase velocities are exploited, and sometimes jointly inverted, for the velocity structure beneath seismic arrays. Wavelengths of surface waves become large at low frequencies and are, thus, sensitive to great depths, but provide only very smooth velocity profiles. However, sudden velocity increases in the subsurface are of particular interest to delineate the extent of reservoirs, i.e., by sub-horizontal faults or detachments, or estimate the depth of sedimentary basins.</p> <p>Here, we report a new approach to estimate sudden velocity increases in vertical velocity profiles using Rayleigh wave ellipticities and phase velocities. Using Kepler’s law of motion on elliptical orbits, we can theoretically delineate the frequency-dependent half-height and half-width of the energy ellipse described by Rayleigh waves.</p> <p>In the presence of sudden velocity increases, fundamental and first higher mode Rayleigh waves have similar phase velocities at the so-called osculation frequency. This often leads to mode misidentification that biases inversion results. We show that this osculation frequency is close to the frequency where the Rayleigh ellipticity of the fundamental mode is one, i.e., motion is circular, and the ellipticity of the first higher mode has its maximum. At this frequency, our derived relation only requires the phase velocity of the first higher mode to estimate the half-height of the ellipse, which is a very good approximation of the depth of the sudden velocity increase.</p> <p>To derive phase velocities and ellipticities of Rayleigh waves for synthetic three-component waveforms and real-world datasets from three sites (Weisweiler in Germany, FORGE in Utah, USA and Groningen, the Netherlands), we use three-component beamforming, which provides velocity and polarization parameters of recorded waves in short ambient noise time windows and thus can distinguish wave types and modes. From identified Rayleigh waves, we pick the phase velocity of the first higher mode at the osculation frequency directly in the beamformer plots and estimate the depth of sudden velocity increases using our new relation. No inversion scheme is needed for this approach.</p> <p>This approach provides more accurate depth estimates of velocity jumps than other ambient noise methods. The depth sensitivity is only limited by the inter-station distances in the array configuration and the useable frequency range. The derived depths of sudden velocity increases can be used to constrain inversion schemes for more accurate velocity models or can be used directly to map structural changes in the subsurface.</p>