Source-structure trade-offs in ambient noise correlations

We analyse the physics and geometry of trade-offs between Earth structure and noise sources in interstation noise correlations. Our approach is based on the computation of off-diagonal Hessian elements that describe the extent to which variations in noise sources can compensate for variations in Earth structure without changing the misfit beyond the measurement uncertainty. Despite the fact that all ambient noise inverse problems are special in terms of their receiver configuration and data, some general statements concerning source-structure trade-offs can be made: (i) While source-structure trade-offs may be reduced to some extent by clever measurement design, there are inherent trade-offs that can generally not be avoided. These inherent trade-offs may lead to a mispositioning of structural heterogeneities when the noise source distribution is unknown. (ii) When attenuation is weak, source-structure trade-offs in ambient noise correlations are a global phenomenon, meaning that there is no noise source perturbation that does not trade-off with some Earth structure, and vice versa. (iii) The most significant source-structure trade-offs occur within two elliptically shaped regions connecting a potential noise source perturbation to each one of the receivers. (iv) Far from these elliptical regions, only small-scale structure can trade off against changes in the noise source. (v) While source-structure trade-offs mostly decay with increasing attenuation, they are nearly unaffected by attenuation when the noise source perturbation is located near the receiver-receiver line. This work is intended to contribute to the development of joint source-structure inversions of ambient noise correlations, and in particular to an understanding of the extent to which source-structure trade-offs may be reduced. It furthermore establishes the foundation of future resolution analyses that properly quantify trade-offs between noise sources and Earth structur

Source and processing effects on noise correlations

We quantify the effects of spatially heterogeneous noise sources and seismic processing on noise correlation measurements and their sensitivity to Earth structure. Using numerical wavefield simulations and adjoint techniques, we calculate interstation correlations and sensitivity kernels for arbitrarily distributed noise sources where—as in the real Earth—different frequencies are generated in different locations. While both heterogeneous noise sources and processing can have profound effects on noise correlation waveforms, narrow-band traveltime measurements are less affected, in accord with previous analytical studies. Sensitivities to Earth structure depend strongly on the source distribution and the processing scheme, and they reveal exotic frequency dependencies that go beyond the well-known frequency scaling of the Fresnel zone width. Our results indicate that modern full waveform inversion applied to noise correlations is not possible unless one of the following measures is taken: (1) properly account for noise source distribution and processing, or (2) limit measurements to phase or time shifts in narrow frequency bands. Failure to do so can lead to erroneous misfits, tomographic artefacts, and reduced resolutio

The western Mediterranean subduction system - Insight from full-waveform inversion

We present a new 3D model of anisotropic S- and P-velocity from the surface to 1,300 km depth beneath the western Mediterranean region. The construction of our model is based on the combination of spectral-element simulations of anisotropic, visco-elastic wave propagation with adjoint techniques. Spectral-element simulations provide highly accurate synthetic seismograms for nearly arbitrarily heterogeneous media, thereby reducing artefacts related to simpli- fications of the forward model. Adjoint techniques allow us to compute sensitivity kernels efficiently, which is essential for iterative gradient-based optimisation. Our model of the western Mediterranean is embedded in a larger Eurasian model. While we model and invert waves at periods from 30 to 200 s within Eurasia, we use a broader band from 12 to 200 s for the smaller western Mediterranean submodel. This multi-scale strategy allows us to simultaneously invert for crustal and mantle structure. Benefits of this approach include the absence of crustal corrections, and more reliably imaged anisotropy. The majority of seismic data used in our full-waveform inversion were recorded by IberArray and other temporary networks, as well as permanent regional networks, thus providing excellent coverage of the Iberian Peninsula, northernmost Africa, and the western Mediterranean basin. For the inversion we use those parts of the seismograms where observed and synthetic waveforms are sufficiently similar to allow for the meaningful measurement of time- and frequency-dependent phase differences. In our final model we quantify resolution with the help of second-order adjoints that can be used to com- pute direction- and position-dependent resolution lengths, as well as inter-parameter tradeoffs. The model reveals a complex system of high-velocity anomalies that may be interpreted as signatures of subducted Tethyan slabs. While subducting slabs beneath the eastern Mediterranean region may penetrate into the lower mantle, western Mediterranean slabs appear to stagnate around 660 km depth.Peer Reviewe

Models and Fréchet kernels for frequency-(in)dependent Q

We present a new method for the modelling of frequency-dependent and frequency-independent Q in time-domain seismic wave propagation. Unlike previous approaches, attenuation models are constructed such that Q as a function of position in the Earth appears explicitly as a parameter in the equations of motion. This feature facilitates the derivation of Fréchet kernels for Q using adjoint techniques. Being simple products of the forward strain field and the adjoint memory variables, these kernels can be computed with no additional cost, compared to Fréchet kernels for elastic properties. The same holds for Fréchet kernels for the power-law exponent of frequency-dependent Q, that we derive as well. To illustrate our developments, we present examples from regional- and global-scale time-domain wave propagatio

Cross-correlation imaging of ambient noise sources

We develop and apply a novel technique to image ambient seismic noise sources. It is based on measurements of cross-correlation asymmetry defined as the logarithmic energy ratio of the causal and anticausal branches of the cross-correlation function. A possible application of this technique is to account for the distribution of noise sources, a problem which currently poses obstacles to noise-based surface wave dispersion analysis and waveform inversion. The particular asymmetry measurement used is independent of absolute noise correlation amplitudes. It is shown how it can be forward-modelled and related to the noise source power-spectral density using adjoint methods. Simplified sensitivity kernels allow us to rapidly image variations in the power-spectral density of noise sources. This imaging method correctly accounts for viscoelastic attenuation and is to first order insensitive to unmodelled Earth structure. Furthermore, it operates directly on noise correlation data sets. No additional processing is required, which makes the method fast and computationally inexpensive.We apply the method to three vertical-component cross-correlation data sets of different spatial and temporal scales. Processing is deliberately minimal so as to keep observations consistent with the imaging concept. In accord with previous studies, we image seasonally changing sources of the Earth's hum in the Atlantic, Pacific and the Southern Ocean. The sources of noise in the microseismic band recorded at stations in Switzerland are predominantly located in the Atlantic and show a clear dependence on both season and frequency. Our developments are intended as a step towards full 3-D inversions for the sources of ambient noise in various frequency bands, which may ultimately lead to improvements of noise-based structural imaging.This research was supported by the Swiss National Supercomputing Center (CSCS) in the form of the GeoScale and CH1 projects, by the Swiss National Science Foundation (SNF) under grant 200021 149143 and by the Netherlands Organisation for Scientific Research (VIDI grant 864.11.008). Iber-Array data are a contribution of the Team Consolider-Ingenio 2010 TOPO-IBERIA (CSD2006-00041).Peer reviewe

Optimal observables for multiparameter seismic tomography

We propose a method for the design of seismic observables with maximum sensitivity to a target model parameter class, and minimum sensitivity to all remaining parameter classes. The resulting optimal observables thereby minimize interparameter trade-offs in multiparameter inverse problems. Our method is based on the linear combination of fundamental observables that can be any scalar measurement extracted from seismic waveforms. Optimal weights of the fundamental observables are determined with an efficient global search algorithm. While most optimal design methods assume variable source and/or receiver positions, our method has the flexibility to operate with a fixed source-receiver geometry, making it particularly attractive in studies where the mobility of sources and receivers is limited. In a series of examples we illustrate the construction of optimal observables, and assess the potentials and limitations of the method. The combination of Rayleigh-wave traveltimes in four frequency bands yields an observable with strongly enhanced sensitivity to 3-D density structure. Simultaneously, sensitivity to S velocity is reduced, and sensitivity to P velocity is eliminated. The original three-parameter problem thereby collapses into a simpler two-parameter problem with one dominant parameter. By defining parameter classes to equal earth model properties within specific regions, our approach mimics the Backus-Gilbert method where data are combined to focus sensitivity in a target region. This concept is illustrated using rotational ground motion measurements as fundamental observables. Forcing dominant sensitivity in the near-receiver region produces an observable that is insensitive to the Earth structure at more than a few wavelengths' distance from the receiver. This observable may be used for local tomography with teleseismic data. While our test examples use a small number of well-understood fundamental observables, few parameter classes and a radially symmetric earth model, the method itself does not impose such restrictions. It can easily be applied to large numbers of fundamental observables and parameters classes, as well as to 3-D heterogeneous earth model

The imprint of crustal density heterogeneities on regional seismic wave propagation

Density heterogeneities are the source of mass transport in the Earth. However, the 3-D density structure remains poorly constrained because travel times of seismic waves are only weakly sensitive to density. Inspired by recent developments in seismic waveform tomography, we investigate whether the visibility of 3-D density heterogeneities may be improved by inverting not only travel times of specific seismic phases but complete seismograms. As a first step in this direction, we perform numerical experiments to estimate the effect of 3-D crustal density heterogeneities on regional seismic wave propagation. While a finite number of numerical experiments may not capture the full range of possible scenarios, our results still indicate that realistic crustal density variations may lead to travel-time shifts of up to  ∼ 1 s and amplitude variations of several tens of percent over propagation distances of  ∼ 1000 km. Both amplitude and travel-time variations increase with increasing epicentral distance and increasing medium complexity, i.e. decreasing correlation length of the heterogeneities. They are practically negligible when the correlation length of the heterogeneities is much larger than the wavelength. However, when the correlation length approaches the wavelength, density-induced waveform perturbations become prominent. Recent regional-scale full-waveform inversions that resolve structure at the scale of a wavelength already reach this regime. Our numerical experiments suggest that waveform perturbations induced by realistic crustal density variations can be observed in high-quality regional seismic data. While density-induced travel-time differences will often be small, amplitude variations exceeding ±10 % are comparable to those induced by 3-D velocity structure and attenuation. While these results certainly encourage more research on the development of 3-D density tomography, they also suggest that current full-waveform inversions that use amplitude information may be biased due to the neglect of 3-D variations in density