Linear approximation of Beer-Lambert law is no longer accepted under high optic depth, so that the popular 2nd harmonic detection in wavelength modulation spectroscopy(WMS) becomes invalid. Logarithmic spectroscopy in WMS is compared with the second-to-first harmonic ratio method. The relationship between harmonic signal and optical depth as well the resolution of both is studied theoretically. WMS optical fiber methane sensor at 1650 nm are described. The Foureier coefficients of amplitude modulation of laser in logarithmic spectroscopy are achieved, and the factors affecting the resolution of both methods are studied. The results show that signal-to-noise ratio（SNR) with the logarithmic method is 2～3 order larger than that of ratio method.