Seismic inversion (poststacking vs prestacking)
Seismic inversion, most of the time used in oil and gas industry, is the process used to reconstruct earth properties. It combines seismic and well data to predict rock properties (lithology, fluid content, porosity) across a survey. These rock properties can be used to identify hydrocarbon and reservoir.
Description
Importance of impedance attribute
Many of these rocks properties can be identified by using well log data (gamma ray, water saturation, shale volume) or seismic data (more difficult to obtain). However, with seismic inversion we can obtain other rocks properties such as impedance and its attributes (Pimpedance, Simpedance, Poisson’s Ratio, V_{p}/V_{s}, Lambda*Rho, Mu*Rho). Those properties are linked to fluid content, porosity, lithology. For example, for a given lithology, if we know the Pimpedance, we can predict its porosity. From this relationship, by combining impedance at the well and the impedance calculated from seismic data, we can predict hydrocarbon across the survey.
How to calculate impedance
Pimpedance= density *Pvelocity
Simpedance= density*Svelocity
Note that all other attributes can be calculated from the impedance.
From well log data we used density and velocity data to get the impedance and the Poisson’s ratio. From Seismic data, we obtain impedance by using seismic inversion which converts seismic from a boundary property to a layer property. Indeed, well data show us properties of the rock’s layer and seismic data show us information about the boundary between rock layers. In seismic inversion, the seismic data is changed into impedance.
How seismic inversion works?
Seismic Inversion removes the imprints of the wavelet in the seismic data by deconvolution and then by converting the result into impedance.
Poststacking inversion
Seismic inversion can be divided into two techniques which are poststacking and prestacking inversion.
The first technique, PostStacking inversion is the most common approach used for inversion. This technique transforms a single seismic information volume into an acoustic impedance volume by using seismic data, well data, and basics knowledge in stratigraphy for interpretation. By removing the wavelet from seismic data, we assist at the creation of a high resolution image of the subsurface.
The poststacking methods are colored inversion, modelbased inversion, sparse spike inversion and Bandlimited impedance inversion.
Colored Inversion
Colored Inversion (CI) is a process to approximately match or convolve the amplitude spectrum of a seismic with the acoustic impedance spectra issued from well data. It calculates its own inverted operator based on the frequency of seismic and well data. This method is very easy to use, fast, and strong even if there is noise. It can also be applied with or without well data and background model. The inconvenient is that the seismic input must be at zerophase and it considers the reflectivity data of one well as the data of all the region.
Modelbased inversion
In this method, the seismic trace (initial model) is convoluted with a wavelet to get a synthetic seismic trace. Then the impedance is confronted to many iterations until the difference between the inverted trace and the initial trace is reduced to a limit value.
Seismic trace = (wavelet*Reflectivity) +noise
[[File:Mbi.pngthumbcenterModelbased inversion example. It starts with an initial model and ends with a residual model. The initial model is process by iteration. Credit: Veeken ^{[3]}
Sparse Spike Inversion
Sparse spike inversion assumes the seismic trace models the subsurface reflectivity by using small number of acoustic impedance interface. It presents two techniques: linear programming and maximum likelihood. Note that it final purpose is to obtain high resolution impedance.
Linear programming
It is an algorithm which extracts an estimate of the reflectivity by using frequency domain constraints to recover the high frequencies of the seismic spectrum. This reflectivity is by the end incorporated under the initial model, where the sparse reflectivity is created. This method is to restore the impedance by minimizing error between the modeled and the initial trace.^{[4]}
Maximum Likelihood
The particularity of this algorithm is to disturb the reflectivity from the seismic trace. Assuming the wavelet is known, its job will be to add reflections coefficients until a best match is found.^{[4]}
BandLimited Impedance inversion
Bandlimited impedance inversion (BLI) changes post stack seismic data into impedance, density and Pwave velocity. This method is defined by the relationship between the seismic trace and seismic impedance.^{[4]}
Prestacking inversion
To obtain multiple impedance attributes we do prestacking. Prestacking inversion changes seismic into Pimpedance, Simpedance, and density by integrating well and seismic data.
The two techniques used on prestacking are: simultaneous and elastic inversion. Note that those technics required global wavelets and background model.
Simultaneous inversion
Simultaneous prestacking inversion is defined by ^{[4]}:
Elastic inversion
Recall:
AkiRichards equation ^{[4]}
Elastic Impedance ^{[4]}
Elastic inversion model:
Differences and Similarities
Similarities 
Differences 


References
 ↑ Farfour, M., Yoon, W. and Kim, J. (2015). Seismic attributes and acoustic impedance inversion in interpretation of complex hydrocarbon reservoirs. Journal of Applied Geophysics, 114, pp.6880.
 ↑ Petrologic.dmt.de. (2018). PostStack Inversion: Petrologic Geophysical Services GmbH. [online] Available at: http://petrologic.dmt.de/services/poststackinversion.html [Accessed 24 Apr. 2018].
 ↑ ^{3.0} ^{3.1} Veeken, P. C. H., and Da Silva, M., 2004, Seismic inversion methods and some of their constraints: First Break, 22, 4770, accessed October 28, 2017; https://www.researchgate.net/publication/277392423_Seismic_Inversion_Methods_and_some_of_their_constraints
 ↑ ^{4.0} ^{4.1} ^{4.2} ^{4.3} ^{4.4} ^{4.5} Maurya, S.P., and Sarkar, P., 2016, Comparison of Post stack Seismic Inversion Methods:A case study from Blackfoot Field, Canada: International Journal of Scientific & Engineering Research, 7, 10911101, accessed October 28, 2017; https://www.ijser.org/onlineResearchPaperViewer.aspx?ComparisonofPoststackSeismicInversionMethodsAcasestudyfromBlackfootField,Canada.pdf
 ↑ Petrologic.dmt.de. (2018). PreStack Inversion: Petrologic Geophysical Services GmbH. [online] Available at: http://petrologic.dmt.de/services/prestackinversion.html [Accessed 24 Apr. 2018].
External link
 Doyen, P. M. (1988). Porosity from seismic data: A geostatistical approach. Geophysics, 53(10):12631275. https://library.seg.org/doi/pdf/10.1190/1.1442404
 Dufour, J., Squires, J., Goodway, W. N., Edmunds, A., and Shook, I. (2002). Integrated geological and geophysical interpretation case study, and lame rock parameter extractions using avo analysis on the blackfoot 3c3d seismic data, southern alberta, canada. Geophysics, 67(1):2737.https://library.seg.org/doi/pdf/10.1190/1.1451319
 Li, Q., 2002, Sparse Spike Inversion and the Resolution Limit: CSEG, accessed October 28, 2017; https://cseg.ca/assets/files/resources/abstracts/2002/Li_Q_Sparse_Spike_Inversion_MOD1.pdf
 Russell, Brian H., 1988, Introduction to Seismic Inversion Methods: Society of Exploration Geophysicists, accessed October 28, 2017; https://library.seg.org/doi/book/10.1190/1.9781560802303