Velocity analysis using AB semblance AB semblance : correlation with a trend

I derive and analyze an explicit formula for a generalized semblance attribute, which is suitable for velocity analysis of prestack seismic gathers with distinct amplitude trends. While the conventional semblance can be interpreted as squared correlation with a constant, the AB semblance is defined as a correlation with a trend. This measure is particularly attractive for analyzing class II AVO anomalies and converted waves. Analytical derivations and numerical experiments show that the resolution of the AB semblance is approximately twice lower than that of the conventional semblance. However, this does not prevent it from being an effective attribute. I use synthetic and field data examples to demonstrate the improvements in velocity analysis from AB semblance. INTRODUCTION Since its introduction by Taner and Koehler (1969), the semblance measure has been an indispensable tool for velocity analysis of seismic records. Conventional velocity analysis of seismic gathers scans different values of effective moveout velocity, computes semblance of flattened gathers and generates velocity spectra for later velocity picking (Yilmaz, 2000) . While effective in most practical situations, semblance becomes troublesome in the case of strong variation of amplitudes along seismic events (Sarkar et al., 2001). A particular example is class II AVO anomalies (Rutherford and Williams, 1989) that cause seismic amplitudes to go through a polarity reversal. To address this problem, Ratcliffe and Adler (2000) and Sarkar et al. (2001, 2002) developed algorithms for correcting the semblance measurement for amplitude variations. In this paper, I interpret the semblance attribute as a correlation with a constant and derive an explicit mathematical expression for the measure which corresponds to correlation with an amplitude trend. This measure is equivalent to AB semblance proposed by Sarkar et al. (2001, 2002). It reduces, in the case of constant amplitudes, to the conventional semblance. I analyze the statistics of the AB semblance attribute and quantify the loss of resolution associated with it. Numerical experiments with synthetic and field data demonstrate the effectiveness of the AB semblance as a robust velocity analysis attribute, which is applicable even in the presence of strong Fomel 2 Velocity analysis using AB semblance amplitude variations and polarity reversals. Moreover, the ratio of the AB and conventional semblances serves as a useful AVO indicator attribute. THEORY I start by interpreting the meaning of the conventional semblance attribute as a correlation with a constant. Next, I define AB semblance as a correlation with a trend and analyze its statistical properties. Semblance as correlation The correlation coefficient γ between two sequences of numbers a = a1, a2, . , aN and b = b1, b2, . , bN is defined as γ(a,b) = a · b |a| |b| = N ∑ i=1 ai bi √√√√ N ∑ i=1 ai √√√√ N ∑ i=1 bi (1) The correlation coefficient is analogous to the cosine of the angle between two vectors a and b. It takes values in the range from −1 to 1. Taking a correlation of a sequence a with a constant sequence c = C,C, . , C produces a measure β, defined as β(a) = γ(a, c) = N ∑ i=1 aiC √√√√ N ∑ i=1 ai √√√√ N ∑ i=1 C2 = N ∑ i=1 ai √√√N N ∑ i=1 ai (2) Squaring the correlation with a constant yields the measure equivalent to semblance β(a) = ( N ∑ i=1 ai )2