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GY 402: Sedimentary Petrology

UNIVERSITY OF SOUTH ALABAMA. GY 402: Sedimentary Petrology. Lecture 9: Walther’s Law. Instructor: Dr. Douglas W. Haywick. Today’s Agenda. Walther’s Law Sequence stratigraphy Markov Chain Analysis. Walther’s Law. Walther’s Law.

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GY 402: Sedimentary Petrology

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  1. UNIVERSITY OF SOUTH ALABAMA GY 402: Sedimentary Petrology Lecture 9: Walther’s Law Instructor: Dr. Douglas W. Haywick

  2. Today’s Agenda Walther’s Law Sequence stratigraphy Markov Chain Analysis

  3. Walther’s Law

  4. Walther’s Law Named after Johannes Walther (1860-1937), a German geologist, who in 1894, noted a fundamental relationship between the vertical and lateral distribution of facies.

  5. Walther’s Law Sedimentary environments that started out side-by-side will end up overlapping one another over time due to transgressions and regressions.

  6. Walther’s Law Sedimentary environments that started out side-by-side will end up overlapping one another over time due to transgressions and regressions. The result is a vertical sequence of beds. The vertical sequence of facies mirrors the original lateral distribution of sedimentary environments.

  7. Walther’s Law Sedimentary environments that started out side-by-side will end up overlapping one another over time due to transgressions and regressions.

  8. Walther’s Law But… • Walther's Law can only apply to sections without unconformities. Tan and white layers of Mesozoic Era Period Pio Nono Formationin Georgia's Coastal Plain Province. http://itc.gsw.edu/faculty/daskren/fallline.htm

  9. Walther’s Law And… • Walther's Law can only apply to a section without subdividing diachronous boundaries [e.g., transgressive surfaces (TS), maximum flooding surfaces (mfs) etc.]

  10. Sequence Stratigraphy First utilized by the petroleum industry to interpret depositional surfaces on seismic sections. Now used by all geologists to explain vertical and lateral changes in sediment rock distribution. http://strata.geol.sc.edu/exerices/seismic/07SeqNo_LST_TST_HST.jpg

  11. Sequence Stratigraphy First utilized by the petroleum industry to interpret depositional surfaces on seismic sections. Now used by all geologists to explain vertical and lateral changes in sediment rock distribution. The 3 controls are: 1) sea level position, 2) sediment input, 3) accommodation space. http://strata.geol.sc.edu/exerices/seismic/07SeqNo_LST_TST_HST.jpg

  12. Sequence Stratigraphy Changes in sea level and sediment supply produce changes in the “stacking of sedimentary packages”. Here sediment supply keeps up with sea level changes

  13. Sequence Stratigraphy Here sediment supply exceeds sea level change.

  14. Sequence Stratigraphy Here sea level changes exceeds sediment supply.

  15. Sequence Stratigraphy Ultimately, sedimentary “packages” are bounded by specific surfaces (reflectors in the seismic lines), and this is where/when Walther’s Law breaks down

  16. Walther’s Law But even with these limitations, Walther’s Law offers powerful predictive capabilities, especially for basic facies modeling. Consider the adjacent sequence…

  17. Walther’s Law SS: Scoured contact

  18. Walther’s Law SS: Scoured contact A: laminated red shale

  19. Walther’s Law SS: Scoured contact B: rippled siltstone A: laminated red shale

  20. Walther’s Law C: Cross-stratified c-quartz arenite SS: Scoured contact B: rippled siltstone A: laminated red shale

  21. Walther’s Law D: Parallel laminated f-quartz arenite C: Cross-stratified c-quartz arenite SS: Scoured contact B: rippled siltstone A: laminated red shale

  22. Walther’s Law E: Trough cross bedded vc-quartz arenite D: Parallel laminated f-quartz arenite C: Cross-stratified c-quartz arenite SS: Scoured contact B: rippled siltstone A: laminated red shale

  23. Walther’s Law F: massive c-quartz arenite E: Trough cross bedded vc-quartz arenite D: Parallel laminated f-quartz arenite C: Cross-stratified c-quartz arenite SS: Scoured contact B: rippled siltstone A: laminated red shale

  24. Walther’s Law G: rippled c to vc-quartz arenite F: massive c-quartz arenite E: Trough cross bedded vc-quartz arenite D: Parallel laminated f-quartz arenite C: Cross-stratified c-quartz arenite SS: Scoured contact B: rippled siltstone A: laminated red shale

  25. Walther’s Law Recall that facies repeat in a sedimentary sequence. If you determine the number and variety of transitions, you can start to understand the means by which facies shifted during deposition.

  26. Walther’s Law Below are the observed facies transitions for the outcrop(s) in question. The problem is that you really don’t know which are random. All data in these slides from Walker (1979)

  27. Walther’s Law Enter statistics (Markov Chain Analysis). Determine the number of transitions from each facies to every other facies and put in a 9 x 9 matrix (one row/column per facies)

  28. Walther’s Law Determine the number of transitions from each facies to every other facies

  29. Walther’s Law Then calculate the observed transition probabilities (each row =1.00).

  30. nj Rij = N-ni Walther’s Law Next calculate transition probabilities for a random sequence Where Rij is the random probability of transition from facies i to j, ni and nj are the number of occurences of facies i and j and N is the total number of occurrences of all facies

  31. Walther’s Law Now it’s a matter of simple math. Observed – random transitions

  32. Walther’s Law Positive transitions occur in nature, high positive transitions dominate.

  33. Walther’s Law

  34. Walther’s Law

  35. GY 402: Sedimentary Petrology Lecture 9: Walther’s Law Instructor: Dr. Doug Haywick dhaywick@southalabama.edu This is a free open access lecture, but not for commercial purposes. For personal use only.

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