Near-surface velocity estimation by weighted early-arrival waveform inversion

Introduction

Near-surface velocity is important for imaging deeper targets. Complex near-surface velocity can cause serious problems for imaging deeper targets if it is not accurately estimated. Conventionally, people use ray-based methods (White, 1989; Hampson and Russell, 1984; Olson, 1984) to derive the large-scale structure of near-surface velocity. Such smooth velocity structure may be adequate for areas with simple near-surface velocity. However, in geologically complex areas, smooth velocity is not accurate enough for imaging deeper reflectors (Marsden, 1993; Bevc, 1995; Hindriks and Verschuur, 2001). In such cases, waveform inversion (Tarantola, 1984; Pratt et al., 1998; Mora, 1987) tends to give more accurate results (Sheng et al., 2006; Ravaut et al., 2004; Sirgue et al., 2009) by using finite-frequency seismic wave propagation.

Yet there are several important factors for practical application of waveform inversion. Among these are the quality of the starting velocity model, the accuracy of the source wavelet estimation, and the complexity of physics in the recorded data and the inversion engine. In addition to the P-wave velocity, the density, S-wave velocity, anisotropy parameters, attenuation and other factors all affect the recorded data. When compared with data modeled from the constant-density acoustic wave equation, these extra parameters will not only change the amplitude and phase of existing events, but they also may add extra events, such as converted waves. However, there are several problems associated with inverting these parameters. First, they are much less well constrained than the P-wave velocity, so it is much more difficult to invert all these parameters than just P-wave velocity. Second, it is more computationally expensive to incorporate all these parameters into the wave-equation engine used in inversion; for example, modeling using the elastic wave equation is at least an order of magnitude more expensive than using the acoustic wave equation. Thus the acoustic wave equation is still the most practical waveform inversion engine so far. With this choice, however, the objective function of conventional waveform inversion is inadequate to bridge the gap between the physics of the data and the physics of the inversion engine.

It is known that traveltime/phase information is less sensitive to the presence of different physics in the recorded data and also carries the information about velocity field (Shin and Min, 2006; Luo and Schuster, 1990). In conventional waveform inversion, both phase and amplitude information of the modeled data are compared with recorded data. I modify the objective function of waveform inversion, giving added weight to the match of phase information in the modeled and the recorded data for each iteration of the inversion. I do not match the recorded and modeled data by subtracting their phases, thus avoiding the ambiguity caused by phase wrapping (Shin and Min, 2006).

Near-surface velocity estimation by weighted early-arrival waveform inversion