We present a theory for the decay of sedimentary organic matter made of a spectrum (a continuous distribution of an infinite number) of reactive types which can be characterized by a variable function of the decay constant, k. A fundamental property of the continuum theory is that it can generate an apparent order of reaction for the decay of the total mixture greater than one. The apparent order is related to the predominance of the more refractory components of the continuum relative to the more reactive. A Gamma distribution of reactivities is a particularly valuable model for the initial distribution, g(k, 0). The Gamma distribution, g(k, 0) = g0K(nu-1)e-ak/GAMMA(nu), is characterized by two free parameters, "a" and nu where "a" measures the average life-time of the more reactive components of the mixture and nu is a nondimensional parameter solely related to the shape of the distribution near k = 0 (and GAMMA() is the Gamma function). Analysis of the experimental data reported in Westrich and Berner (1984) illustrates that the continuum model, based on the Gamma distribution, requires half as many parameters as the traditional multi-exponential model. This analysis indicates that the decay reaction is characterized by nu = 0.125 (equivalent to an apparant 9th order reaction). A similar treatment of nine organic C profiles from the historical zone of various shallow and deep-water sediments shows that these cores can be divided into two groups. The larger group of five profiles displays nu values that range primarily from 0.1 to 0.2 (6th-11th order). A second group of three cores is characterized by nu congruent-to 1.0 (apparent 2nd order reactions), but two of these cores may contain data from the mixed zone or may not be at steady state. The apparent order of the experimental data agrees with that of the first group of profiles and suggests that there may be an important similarity to such data over broad spatial/time scales. In addition, we also examined the decay of Westrich's (1983) hypothetical 8-component organic matter and found that it can be represented with nu = 0.1 (11th order). If this similarity in nu values is substantiated by further studies, it would be a valuable tool in theoretical studies. Though the data set is small, the analysis also suggests that the parameter "a" varies systematically with the sedimentation rate. In the mixed zone of marine sediments, the continuum model generates rather complicated integrals for the organic matter concentration profiles. In general, these integrals are amenable to numerical methods only. They will, however, reduce to analytically manageable forms, if the mixed zone can be assumed to extend to infinity and advective transport ignored. The theory of reactive continuums suggests, in general, that a standard Arrhenius plot of log(e) (rate) versus T-1 (T = absolute temperature) will curve upward with falling T-1. However, we have found that because of the restricted temperature range normal to sedimentary environments, this plot will exhibit little deviation from linearity. Therefore, a single apparent activation energy, E(eff), for the decay of the total mass can be calculated from the slope of such a plot.
