Abstract
In sedimentology, stratigraphic sequences and cycles are ordered by time spans and physical scales, such as thickness, and bounded by discontinuities, including unconformities or flooding surfaces. Spectral analysis based on wavelet transform (WT) maxima is proposed and used as a quantitative tool to identify multi-order stratigraphic boundaries and cycles in well log data. The proposed spectral analysis is based on quantitative analysis on the center frequencies and resolutions of Gaussian wavelets in time and frequency, and uses a combination of the WT maxima based on both the first order Gaussian wavelet having a high time resolution and the seventh order Gaussian wavelet having a high frequency resolution. WT maxima spectra, which can characterize the evolution of WT maxima across scales and periods along WT maxima lines concerned with sequence boundaries, are used to detect dominant spectral peaks corresponding to the time-period domain WT maxima and to determine WT maxima spectral slopes. The WT maxima spectral slopes are helpful for discriminating sequence boundaries from intrasequence cyclic variations in well log data, and the time-period domain WT maxima are used to relate the detected boundaries to relevant cycles. The interval WT maxima spectra and the stationary index, related to the WT maxima spectra, are introduced as indicators that can be used for the hierarchical ordering of the boundaries and cycles. Application of the proposed method to well log data shows that the suggested method is efficient in identifying multi-order sequences that relate well to the Milankovitch cycles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Addison PS (2002) The illustrated wavelet transform handbook: introduction theory and applications in science, engineering, medicine and finance. Institute of Physics Publishing, London, pp 10–351
Bailey RJ, Smith DG (2008) Quantitative tests for stratigraphic cyclicity. Geol J 43:431–446
Benitez R, Bolos VJ, Ramirez ME (2010) A wavelet-based tool for studying non-periodicity. Comput Math Appl 60:634–641
Berman Z, Baras JS (1993) Properties of the multiscale maxima and zero-crossings representations. IEEE Trans Signal Process 41(12):3216–3231
Chandrasekhar E, Rao VE (2012) Wavelet analysis of geophysical well-log data of Bombay offshore basin, India. Math Geosci 44:901–928
Davis AC, Christensen NB (2013) Derivative analysis for layer selection of geophysical borehole logs. Comput Geosci 60:34–40
Fedi M (2003) Global and local multiscale analysis of magnetic susceptibility data. Pure Appl Geophys 160:2399–2417
Henriques MVC, Leite FEA, Andrade RFS, Andrade JS Jr, Lucena LS, Lucena Neto M (2015) Improving the analysis of well-logs by wavelet cross-correlation. Physica A 417:130–140
Herrmann JF (2001) Singularity characterization by monoscale analysis: application to seismic imaging. Appl Comput Harmon Anal 11:64–88
Hruška M, Corea W, Seeburger D, Schweller W, Crane WH (2009) Automated segmentation of resistivity image logs using wavelet transform. Math Geosci 41:703–716
Karacan CÖ, Olea RA (2014) Inference of strata separation and gas emission paths in longwall overburden using continuous wavelet transform of well logs and geostatistical simulation. J Appl Geophys 105:147–158
Li XH, Guo Y (2013) Application of activity and wavelet analysis on well logging sedimentary cycle division. Open J Geol 3:62–65
Li X, Fan YR, Deng SG, Wang TS (2009) Automatic demarcation of sequence stratigraphy using the method of well logging multiscale data fusion. Petrol Exp Dev 36(2):221–227
Mallat S (2000) A wavelet tour of signal processing, 2nd edn. Academic Press, New York, pp 163–219
Mallat S, Zhong S (1992) Characterization of signals from multiscale edges. IEEE Trans Pattern Anal Mach Intell 14(7):710–732
Miall AD (2010) The geology of stratigraphic sequences. Springer, Berlin, pp 103–352
Misiti M, Misiti Y, Oppenheim G, Poggi JM (2000) Wavelet toolbox: for use with MATLAB. The MathWorks Inc, NewYork, pp 12–941
Mohammad H, Abdolrahim J (2013) Wavelet analysis in determination of reservoir fluid contacts. Comput Geosci 52:60–67
Morales EC, Jarillo GR, Enriquez JOC (2010) Multi-scale analysis of well-logging data in petrophysical and stratigraphic correlation. Geofísica Int 49(2):55–67
Olsen PE (1990) Tectonic, climatic, and biotic modulation of lacustrine ecosystems—examples from Newark Supergroup of eastern North America. In: Katz BJ (ed) Lacustrine basin exploration: case studies and modern analogs, vol 50. American Association of Petroleum Geologists Memoir, NewYork, pp 209–222
Pan SY, Hsieh BZ, Lu MT, Lin ZS (2008) Identification of stratigraphic formation interfaces using wavelet and Fourier transforms. Comput Geosci 34:77–92
Paulissen WE, Luthi SM (2011) High-frequency cyclicity in a Miocene sequence of the Vienna Basin established from high-resolution logs and robust chronostratigraphic tuning. Palaeogeogr Palaeoclimatol Palaeoecol 307:313–323
Pelletier JD, Turcotte DL (1996) Scale-invariant topography and porosity variations in fluvial sedimentary basins. J Geophys Res 101(12):165–175
Prokoph A, Agterberg FP (2000) Wavelet analysis of well-logging data from oil source rock, Egret member, offshore eastern Canada. Bull Am Assoc Petrol Geol 84(10):1617–1632
Prokoph A, Barthelemes F (1996) Detection of nonstationarities in geological time series: wavelet transform of chaotic and cyclic sequences. Comput Geosci 22:1097–1108
Prokoph A, Bilali HE (2008) Cross-wavelet analysis: a tool for detection of relationships between paleoclimate proxy records. Math Geosci 40:575–586
Rampino MR, Prokoph A, Adler A (2000) Tempo of the end-Permian event: high-resolution cyclostratigraphy at the Permian-Triassic boundary. Geology 28(7):643–646
Rivera NA, Ray S, Jensen JL, Chan AK, Ayers WB (2004) Detection of cyclic patterns using wavelets: an example study in the Ormskirk sandstone, Irish Sea. Math Geol 36(5):529–542
Schulza M, Mudelsee M (2002) REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series. Comput Geosci 28:421–426
Song MH, Li GH, Kim SN (2018) Evaluation of periodicities and fractal characteristics by wavelet analysis of well log data. Comput Geosci 117:29–38
Tochmechi B, Memarian H, Rasouli V, Noubari HA, Moshiri B (2009) Fracture detection from water saturation log data using a Fourier–wavelet approach. J Petrol Sci Eng 69:129–138
Vermeer PL, Alkemade JAH (1992) Multiscale segmentation of well logs. Math Geol 24(1):27–43
Weedon GP (2003) Time-series analysis and cyclo-stratigraphy: examining stratigraphic records of environmental cycles. Cambridge University Press, Cambridge, pp 12–259
Yuan XX, Guo YH, Yu JF, Shen YL, Shao YB (2013) Correlation and analysis of well-log sequence with Milankovitch cycles as rulers: a case study of coal-bearing strata of late Permian in western Guizhou. Int J Min Sci Technol 23:563–568
Acknowledgements
Dr. Pauline Le Bouteiller and an anonymous reviewer are thanked for their suggestions and comments helpful for improving the paper. Prof. Roussos Dimitrakopoulos is also thanked for his support for this work.
Funding
This work was not supported by anyone.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
There are no conflicts of interest.
Rights and permissions
About this article
Cite this article
Song, M.H., Won, C.D., Chae, C.H. et al. Spectral Analysis based on Wavelet Transform Maxima: Identification of Multi-order Stratigraphic Boundaries and Cycles. Math Geosci 53, 969–997 (2021). https://doi.org/10.1007/s11004-020-09879-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-020-09879-w