Scale-invariant topography and porosity variations in fluvial sedimentary basins

We consider a model of • floodplain evolving with channel •vulsion, deposition, •nd erosion. Avulsion is modeled as • r•ndom process in sp•ce and time. Sediment ransport is modeled by the diffusion equation (Culling's model). The power spectrum of v•ri•tions in the topographic profiles predicted by the model S(k) is proportional to k -2 (where k is the w•venumber). This is the Brown noise often observed in topography. The power spectrum of wristions in the local elevation i time is proportional to f-s/: (where f is the frequency). The model prediction of Brown noise floodplain topography is roughly consistent with spectral •n•lyses of microtopography measured with l•ser •ltimetry. We inferred Brown noise p•leotopogr•phy by comparing the p•ir correlation function of showing wells in the Denver •nd Powder River basins with a synthetic oil field b•sed on • caprock with Brown noise topography. Topographic control of variations in the grain size of deposited sediment suggests that porosity v•ri•tions m•y exhibit the scale inv•ri•nce predicted for the topographic profile. To illustrate vertical scale invariance in porosity v•ri•tions, we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the Gulf of Mexico. At spatial scales •bove 3 m we find an •ver•ge power spectral exponent of-1.4, close to our model prediction of -1.5.