Matched Field Processing for complex Earth structure

Matched Field Processing (MFP) is a technique to locate the source of a recorded wave field. It is the generalization of beamforming, allowing for curved wavefronts. In the standard approach to MFP, simple analytical Green's functions are used as synthetic wave fields that the recorded wave fields are matched against. We introduce an advancement of MFP by utilizing Green's functions computed numerically for real Earth structure as synthetic wave fields. This allows in principle to incorporate the full complexity of elastic wave propagation, and through that provide more precise estimates of the recorded wave field's origin. This approach also further emphasizes the deep connection between MFP and the recently introduced interferometry-based source localisation strategy for the ambient seismic field. We explore this connection further by demonstrating that both approaches are based on the same idea: both are measuring the (mis-)match of correlation wave fields. To demonstrate the applicability and potential of our approach, we present two real data examples, one for an earthquake in Southern California, and one for secondary microseism activity in the Northeastern Atlantic and Mediterranean Sea. Tutorial code is provided to make MFP more approachable for the broader seismological community.

Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves

In this paper, we study the mean and variance of the Eulerian and Lagrangian fluid velocities as a function of depth below the surface of directionally spread irregular wave fields given by JONSWAP spectra in deep water. We focus on the behaviour of these quantities in the bulk of the water, and using second-order potential flow theory we derive new simple asymptotic approximations for their decay in the limit of large depth below the surface. Specifically, we show that when the depth is greater than about 1.5 peak wavelengths, the variance of the Eulerian velocity decays in proportion to exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) , and the mean Lagrangian velocity decays in proportion to 1 ( − k p z ) 1 / 6 exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) . Here, k p is the peak wave number and z is the vertical coordinate measured positively upwards from the still water level. We test the accuracy of the second-order formulation against new fully nonlinear simulations of both short crested and long crested irregular wave fields and find a good match, even when the simulations are known to be affected substantially by third-order effects. To our knowledge, this marks the first fully nonlinear investigation of the Eulerian and Lagrangian velocities below the surface in irregular wave fields.

Multiwave Total Focusing Method for Full-Matrix Imaging Using Ultrasonic Phased Array

The imaging range of the traditional total focusing method (TFM) is usually limited by the directivity of excitation of a single wave pattern. In this paper, a multiwave TFM technique is proposed, which uses both compression and shear vertical (SV) waves for detection and imaging simultaneously. Based on this technique, a special ultrasonic transducer for multiwave detection is designed that can balance the excitation amplitude of compression and SV waves. Multiwave TFM uses the compression and SV wave fields generated by the same excitation, and the signals reflected by the two sound fields passing through the discontinuity are received. The signals are respectively processed by TFM according to the compression and SV wave velocities. The two processed signals are shifted and aligned according to the time difference between the compression wave with SV wave propagation, and then added together. Finally, the detection image of the block is obtained. Through simulation and experiments, it is shown that the special transducer can optimize the imaging range and effect of multiwave TFM, and multiwave TFM can effectively detect discontinuities and reduce the rate of missed detection at higher steering angles. The detection results show that the maximum amplitude gain of multiwave TFM relative to TFM can be increased about 6 dB.

Imaging seismic wave-fields with AlpArray and neighboring European networks

The AlpArray experiment and the deployment of Swath-D together with the dense permanent network in Italy allow for detailed imaging of the spatio-temporal imaging complexity of seismic wave-fields within the greater Alpine region. The distance of any point within the area to the nearest station is less than 30 km, resulting in an average inter-station distance of about 45 km. With a much denser deployment in a smaller region of the Alps (320 km in length and 140 km wide), the Swath-D network possesses an average inter-station distance of about 15 km. We show that seismogram sections with a spatial sampling of less than 5 km can be obtained using recordings of these regional arrays for just a single event. Multiply reflected body waves can be observed for up to 2 h after source time. In addition, we provide and describe animations of long-period seismic wave-fields using recordings of about 1300–1600 broadband stations for six representative earthquakes. These illustrate the considerable spatio-temporal variability of the wave-field’s properties at a high lateral resolution. Within denser station distributions like those provided by Swath-D, even shorter period body and surface wave features can be recovered. The decrease of the horizontal wavelength from to to surface waves, deviations from spherically symmetric wavefronts, and the capability to detect multi-orbit arrivals are demonstrated qualitatively by the presented wave-field animations, which are a valuable tool for educational, quality control, and research purposes. We note that the information content of the acquired datasets can only be adequately explored by application of appropriate quantitative methods accounting for the considerable complexity of the seismic wave-fields as revealed by the now available station configuration.