Ambient Noise Surface Waves: Shallow Velocity

The near-surface velocities are usually difficult to measure with seismic reflection data because of the lack of coherent shallow reflectors. Refraction data has difficulties producing a detailed 3D map of the velocities because local scattering mades the waves difficult to pick. An alternative is to use surface waves (ground roll) which samples the near surface zone and is relatively insensitive to scattering.

Here we show some preliminary results for the 3D S-wave velocities in the top 800m of the Long Beach area. The technique consists of two steps. First the apparent phase velocity maps are made for each surface wave frequency. This usually involves measuring apparent velocities between various points in the grid and then using a tomographic inverse to produce a map of the lateral variations in the phase velocity for that frequency. This is then followed by an inversion for each (x,y)-point which maps phase velocity as a function of frequency into shear velocity as a function of depth. Note that the Rayleigh wave phase velocity is only weakly dependent on the P-wave velocity and density, and so they are not usually determined in the inversion.

Determining the Phase Velocity The left panel shows the travel time surface from an virutal source located at the white star. The virtual source is created by cross-correlating the trace recorded by the sensor at the location of the virtual source with all other sensors in the array. The correlation was done for 10 days of recording. The colors show the travel time contours and the lines are the 2-sec contour levels. To measure the phase velocity from this type of plot, the Eikonal relationship which says that the gradient of the travel-time surface equals the slowness function (inverse of velocity) at each point. This method was developed for regional surface waves by Lin et al (2008). This procedure is then repeated for each virtual source (of which there can be as many as the number of receivers in the array). Each virtual source potential generates a complete velocity map. These are stacked together with some weighting applied for poorly estimated regions.

The right panel shows a phase velocity map for a frequency of 0.66 Hz. Surface waves at this frequency are sensitive to S-wave veocities down to 200m.

The results of determining phase velocites are shown for 2 frequencies. The high-frequency with sensitivity down to 200m show slow velocities near the coast. The lower-frequency map with sensitivity to 600m depth shows a high-velocity zone that is along the Newport-Inglewood Fault Zone.
Inversion to depth The phase velocities a function of frequency are then inverted to get S-velocity as a function of depth. The is done indepedently for each (x,y)-point. The inversion process is described by Moschetti et al (2010).
Shallow S-wave model The results of the inversion process described above are shown. The left panel shows the horizontal slice at 600m, and shows the high velocity associated with the NIFZ, and also what appear to be an old channel (perhaps of the Los Angeles River which currently flows down the left side of the Long Beach array). The panels to the right show a sequence of N-S profiles, which show that the feature associated with the NIFZ is plunging to the east.
Simple 3D images of the S-wave velocity function. The plunging feature associated with the NIFZ can be seen in the right panel.
Vertical travel time through the model. The integrated travel time through the 3D S-wave velocity is shown. These times indicate the level of static corrections needed for the reflection survey. The time will need to be scaled to equivalent P-wave traveltimes to be directly used as static corrections.