index, the log of the values are taken. The data is then divided into interval of width Φ whose value is log 2. The width of the peaks are taken to be four times 1/4Φ centered on their maximum values. Bimodality indices Wang's index The bimodality index proposed by Wang et al assumes that the distribution is a sum of two normal distributions with equal variances but differing means. It is defined as follows: where μ1, μ2 are the means and σ is the common standard deviation. where p is the mixing parameter. Sturrock's index A different bimodality index has been proposed by Sturrock. This index (B) is defined as When m = 2 and γ is uniformly distributed, B is exponentially distributed. This statistic is a form of periodogram. It suffers from the usual problems of estimation and spectral leakage common to this form of statistic. de Michele and Accatino's index Another bimodality index has been proposed by de Michele and Accatino. Their index (B) is where μ is the arithmetic mean of the sample and where mi is number of data points in the ith bin, xi is the center of the ith bin and L is the number of bins. The authors suggested a cut off value of 0.1 for B to distinguish between a bimodal (B > 0.1)and unimodal (B < 0.1) distribution. No statistical justification was offered for this value. Sambrook Smith's index A further index (B) has been proposed by Sambrook Smith et al where p1 and p2 are the proportion contained in the primary (that with the greater amplitude) and secondary (that with the lesser amplitude) mode and φ1 and φ2 are the φ-sizes of the primary and secondary mode. The φ-size is defined as minus one times the log of the data size taken to the base 2. This transformation is commonly used in the study of sediments. The authors recommended a cut off value of 1.5 with B being greater than 1.5 for a bimodal distribution and less than 1.5 for a unimodal distribution. No statistical justification for this value was given. Otsu's method Otsu's method for finding a threshold for separation between two modes relies on minimizing the quantity where ni is the number of data points in the ith subpopulation, σi2 is the variance of the ith subpopulation, m is the total size of the sample and σ2 is