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Monte Carlo methods are powerful approaches to solve nonlinear problems and are becoming very popular in Earth sciences. One reason being that, at first glance, no constraints or explicit regularization of model parameters are required. At second glance, one might realize that regularization is done through a prior. The choice of this prior, however, is subjective, and with its choice, unintended or undesired extra information can be injected into the problem. The principal criticism of Bayesian methods is that the prior can be “tuned” in order to get the expected solution. Consequently, detractors of the Bayesian method could easily argue that the solution is influenced by the form of the prior distribution, which choice is subjective. Hence, models obtained with Monte Carlo methods are still highly debated. Here we investigate the influence of a priori constraints (i.e., fixed crustal discontinuities) on the posterior probability distributions of estimated parameters, that is, vertical polarized shear velocity VSV and radial anisotropy ξ, in a transdimensional Bayesian inversion for continental lithospheric structure. We follow upon the work of Calò et al. (2016), who jointly inverted converted phases (P to S) without deconvolution and surface wave dispersion data, to obtain 1‐D radial anisotropic shear wave velocity profiles in the North American craton. We aim at verifying whether the strong lithospheric layering found in the stable part of the craton is robust with respect to artifacts that might be caused by the methodology used. We test the hypothesis that the observed midlithospheric discontinuities result from (1) fixed crustal discontinuities in the reference model and (2) a fixed Vp/Vs ratio. The synthetic tests on two Earth models show that a fixed Vp/Vs ratio does not introduce artificial layering, even if the assumed value is slightly wrong. This is an important finding for real data inversion where the true value is not always available or accurate. However, fixing crustal discontinuities can lead to the introduction of spurious layering, and this is not recommended. Additionally, allowing the Vp/Vs ratio to vary does not help preventing that. Applying the modified approach resulting from these tests to two stations (FRB and FCC) in the North American craton, we confirm the presence of at least one midlithospheric low‐velocity layer. We also confirm the difficulty of consistently detecting the lithosphere‐asthenosphere boundary in the craton.

SUMMARY Seismic body wave traveltime tomography and surface wave dispersion tomography have been used widely to characterize earthquakes and to study the subsurface structure of the Earth. Since these types of problem are often significantly non-linear and have non-unique solutions, Markov chain Monte Carlo methods have been used to find probabilistic solutions. Body and surface wave data are usually inverted separately to produce independent velocity models. However, body wave tomography is generally sensitive to structure around the subvolume in which earthquakes occur and produces limited resolution in the shallower Earth, whereas surface wave tomography is often sensitive to shallower structure. To better estimate subsurface properties, we therefore jointly invert for the seismic velocity structure and earthquake locations using body and surface wave data simultaneously. We apply the new joint inversion method to a mining site in the United Kingdom at which induced seismicity occurred and was recorded on a small local network of stations, and where ambient noise recordings are available from the same stations. The ambient noise is processed to obtain inter-receiver surface wave dispersion measurements which are inverted jointly with body wave arrival times from local earthquakes. The results show that by using both types of data, the earthquake source parameters and the velocity structure can be better constrained than in independent inversions. To further understand and interpret the results, we conduct synthetic tests to compare the results from body wave inversion and joint inversion. The results show that trade-offs between source parameters and velocities appear to bias results if only body wave data are used, but this issue is largely resolved by using the joint inversion method. Thus the use of ambient seismic noise and our fully non-linear inversion provides a valuable, improved method to image the subsurface velocity and seismicity.

The birefringence of core-refracted shear waves (e.g. SKS or SKKS) is often used to study seismic anisotropy in the Earth. However, depth resolution and multilayer anisotropy is generally poor for many regions on Earth. This is primarily due to SKS or SKKS phases that are not observable for different backazimuths either because of missing seismicity at the required distance range or because of a too low signal-to-noise ratio (SNR). We propose a new method called Simultaneous Inversion of Multiple Waveforms (SIMW), which allows the joint inversion of multiple core-refracted shear waves from different earthquakes within the same source region, observed by either the same seismic station or by a seismic network. The waveforms are concatenated into a combined signal, which is then inverted with the Silver & Chan method to determine the two splitting parameters: time delay δt, and fast polarization direction. We apply our method to recordings at the large aperture Norwegian NORSAR Array and the German Gräfenberg array (GRF). Our results demonstrate that SIMW allows a stable determination of splitting results for low-amplitude or noisy SKS signals. Splitting parameter uncertainties can be reduced and reliable results are obtained for both arrays. Moreover, new backazimuth directions can be explored, enabling a more accurate derivation of two-layer anisotropy models. Our new methodology is particularly helpful for temporary station deployments with limited recording times in order to utilize as many as possible signals including such with low-amplitude and small SNR.

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