### Abstract

We consider a model of a floodplain evolving with channel avulsion, deposition, and erosion. Avulsion is modeled as a random process in space and time. Sediment transport is modeled by the diffusion equation (Culling's model). The power spectrum of variations in the topographic profiles predicted by the model S(k) is proportional to k^{-2} (where k is the wavenumber). This is the Brown noise often observed in topography. The power spectrum of variations in fhe local elevation in time is proportional to f^{-3/2} (where f is the frequency). The model prediction of Brown noise floodplain topography is roughly consistent with spectal analyses of microtopography measured with laser altimetry. We inferred Brown noise paleotopography by comparing the pair correlation function of showing wells in the Denver and Powder River basins with a synthetic oil field based on a caprock with Brown noise topography. Topographic control of variations in the grain size of deposited sediment suggests that porosity variations may exhibit the scale invariance predicted for the topographic profile. To illustrate vertical scale invariance in porosity variations, we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the Gulf of Mexico. At spatial scales above 3 m we find an average power spectral exponent of -1.4, close to our model prediction of -1.5.

Original language | English (US) |
---|---|

Pages (from-to) | 28165-28175 |

Number of pages | 11 |

Journal | Journal of Geophysical Research: Space Physics |

Volume | 101 |

Issue number | 12 |

State | Published - Dec 10 1996 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Earth and Planetary Sciences (miscellaneous)
- Atmospheric Science
- Geochemistry and Petrology
- Geophysics
- Oceanography
- Space and Planetary Science
- Astronomy and Astrophysics
- Earth and Planetary Sciences(all)
- Environmental Science(all)

### Cite this

*Journal of Geophysical Research: Space Physics*,

*101*(12), 28165-28175.

**Scale-invariant topography and porosity variations in fluvial sedimentary basins.** / Pelletier, Jon; Turcotte, D. L.

Research output: Contribution to journal › Article

*Journal of Geophysical Research: Space Physics*, vol. 101, no. 12, pp. 28165-28175.

}

TY - JOUR

T1 - Scale-invariant topography and porosity variations in fluvial sedimentary basins

AU - Pelletier, Jon

AU - Turcotte, D. L.

PY - 1996/12/10

Y1 - 1996/12/10

N2 - We consider a model of a floodplain evolving with channel avulsion, deposition, and erosion. Avulsion is modeled as a random process in space and time. Sediment transport is modeled by the diffusion equation (Culling's model). The power spectrum of variations in the topographic profiles predicted by the model S(k) is proportional to k-2 (where k is the wavenumber). This is the Brown noise often observed in topography. The power spectrum of variations in fhe local elevation in time is proportional to f-3/2 (where f is the frequency). The model prediction of Brown noise floodplain topography is roughly consistent with spectal analyses of microtopography measured with laser altimetry. We inferred Brown noise paleotopography by comparing the pair correlation function of showing wells in the Denver and Powder River basins with a synthetic oil field based on a caprock with Brown noise topography. Topographic control of variations in the grain size of deposited sediment suggests that porosity variations may exhibit the scale invariance predicted for the topographic profile. To illustrate vertical scale invariance in porosity variations, we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the Gulf of Mexico. At spatial scales above 3 m we find an average power spectral exponent of -1.4, close to our model prediction of -1.5.

AB - We consider a model of a floodplain evolving with channel avulsion, deposition, and erosion. Avulsion is modeled as a random process in space and time. Sediment transport is modeled by the diffusion equation (Culling's model). The power spectrum of variations in the topographic profiles predicted by the model S(k) is proportional to k-2 (where k is the wavenumber). This is the Brown noise often observed in topography. The power spectrum of variations in fhe local elevation in time is proportional to f-3/2 (where f is the frequency). The model prediction of Brown noise floodplain topography is roughly consistent with spectal analyses of microtopography measured with laser altimetry. We inferred Brown noise paleotopography by comparing the pair correlation function of showing wells in the Denver and Powder River basins with a synthetic oil field based on a caprock with Brown noise topography. Topographic control of variations in the grain size of deposited sediment suggests that porosity variations may exhibit the scale invariance predicted for the topographic profile. To illustrate vertical scale invariance in porosity variations, we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the Gulf of Mexico. At spatial scales above 3 m we find an average power spectral exponent of -1.4, close to our model prediction of -1.5.

UR - http://www.scopus.com/inward/record.url?scp=0030432857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030432857&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030432857

VL - 101

SP - 28165

EP - 28175

JO - Journal of Geophysical Research: Space Physics

JF - Journal of Geophysical Research: Space Physics

SN - 2169-9380

IS - 12

ER -