Surface waves are of increasing interest in seismic prospecting. Traveltime tomography based on dispersion measurements is often used to process surface-wave data, but it has limitations due to the a priori information it requires. The surface-wave eikonal tomography proposed here does not require such a priori information. In complex scattering environments, picking arrivals is difficult because the waveforms are complicated. Working in narrow frequency bands makes it even more difficult as it spreads arrivals in time and introduces overlap. We present here a neighborhood-based cross-correlation picking method that overcomes this difficulty, which then allows for reliable calculation of 2D phase-velocity variation through the eikonal equation.


Surface-waves are of increasing interest in seismic prospecting, as they provide information about shallow structures (e.g., Campman and Riyanti, 2007; Socco and Boiero, 2008). They are usually processed using linearized (asymptotic) traveltime tomography, to obtain per-frequency phase- or group-velocity maps first, which are then inverted into a S- and P-wave velocity model at shallow depth. Linearized traveltime tomography requires a priori information, that is, a starting model, which will be updated in the tomography process. Moreover, it requires a ray tracer to compute traveltimes in the chosen model, which implies some approximations about how waves propagate in the medium. As we will see in the following, eikonal tomography does not need such a priori information, nor does it require ray tracing, which makes it a powerful method in complex media where lack of accurate a priori information may prevent meaningful linearization. Surface-wave phase (or group) velocity tomography also requires the fundamental mode of the Rayleigh wave (or Love wave, if using the horizontal transverse component) to be isolated from other arrivals, as its arrival needs to be picked as an input for the method. When dealing with complex shallow subsurface structure, the surface-wave waveforms are composed of multiple arrivals that can be close in time, or overlap. It is then difficult to recognize specific phases or modes, especially in a narrow frequency band, because the arrivals are spread in time and modes may interfere.

Eikonal tomography

Traveltime tomography consists of estimating spatial variations in the propagation speed of seismic waves, from a set of measured phase arrival times between known source and receiver locations.

Traveltime measurements

Because taking the gradient is a numerically unstable operation, measuring the phase arrival times must be done with great care. In a medium with strong scattering, waveforms can be complex, making it difficult to pick phase arrivals with classical methods. We used a neighborhood-based cross-correlation method to measure traveltime differences between close-by receivers.

The network

For our study we use data from a high-resolution survey of a 1 km×1 km carbonate (karst) area in Northern Oman conducted by Petroleum Development Oman (PDO). Seismic vibrator trucks were used as the source on each node of the source grid. Records are 4 s long and the sampling frequency is 125 Hz.

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