N045 Seismic Inversion and Applications to Stochastic Reservoir Modelling

Course Facts

Course Code:
4 days
3.2 Continuing Education Units
32 Professional Development Hours
Certificate Issued Upon Completion


This practical course explains the principles of inversion from seismic data to rock properties, emphasising the analogies with geostatistics. It demonstrates that seismic inversion must be considered as a stochastic process/exercise and, by extensive use of examples, provides a non-mathematical basis for understanding the concepts.

Duration and Training Method

A four-day classroom course, comprising short lectures and classroom exercises.

Participants will learn to:

  1. Assess the quality of the  key well-tie process, fundamental to seismic interpretation projects.
  2. Perform fluid replacement analysis and Backus upscale modelling on the wavelet in the well-tie process.
  3. Design a simple seismic modelling strategy to examine tuning and fluid effects using wedge models.
  4. Evaluate how a wavelet may be constructed that most closely resembles the base seismic, and the pitfalls such an estimation may encounter.
  5. Appraise the various methods of seismic inversion and their value to interpretation, including model-based methods, structural deconvolution and Relative Acoustic Impedance.
  6. Compare inversion methodologies and results with the wider family of seismic attributes.
  7. Assess the principles of geostatistics in its role as spatial correlation estimator and relation to simpler averaging and correlation strategies.
  8. Compare kriging and best estimation seismic inversion approaches and the role of stochastic simulation in removing bias in best estimate inversion calculations.
  9. Evaluate how inversion results can be integrated with well data, using various strategies, such as kriging with external drift and co-kriging.
  10. Rate the latest inversion technologies and role of stochastic methods in their development.
  11. Assess the potential pitfalls of inversion.

The course covers well-tie and zero-phasing issues, wavelet estimation, Acoustic Impedance Inversion, pitfalls in inversion, upscaling of well logs (Backus upscaling), attribute analysis and stochastic inversion methods. Extensive use is made of examples and exercises.

1. To Tie a Well
The key difference between a development geophysics study and exploration geophysics is the attention to detail required. This is nowhere more important than in the well-to-seismic tie.

The section will begin by reviewing the common ways used to refer to wavelet phase (zero phase and linear phase, minimum phase, maximum and mixed phase) and attempt to bring a little precision to the usage of these terms. The abuse and poor understanding of phase common amongst geophysicists will be addressed by describing the effect of zero phasing as various simple steps in forming a zero phase deconvolution operator. The steps are described in the form of a matching filter, built from a time shift (linear phase term), an intercept (average rotation) and full phase solution.

The common wavelet types, including Ricker, Butterworth, Ormsby and Klauder will be described, along with their theoretical and practical applications.

Checkshot Calibration
The first practical session will to be perform a check shot calibration of a sonic log in an Excel spreadsheet. The various styles of shift will be described and applied. In addition, the problem of knowing the start time of the sonic log, and the importance of this in tying wells, determining wavelets and phase will be emphasised.

Fluid Replacement Modelling
A short discussion of the use of fluid replacement to model in situ conditions and to try alternative scenarios will be included. A Java applet implementing the Xu & White model will be used for practical interaction.

Backus Upscaling
Backus upscaling will be described and demonstrated using the excellent published example by Marion. The importance of understanding whether Ray Theory or Effective Medium Theory is most appropriate will be highlighted. A practical example will be given, demonstrating the effect of upscaling on a well log and improving the well to seismic tie in a thin, alternating shale environment. The effect of upscaling on increasing the apparent bandwidth of the extracted wavelet will be demonstrated with a model example.

Synthetic Modelling
Some simple seismic modelling will demonstrate the use of wedge models to describe tuning and fluid effects. A simple atlas of models will illustrate some of the effects of tuning at fluid contacts, brightening or dimming of amplitudes due to gas or oil, and the appearance of dip in seismic expression of fluid contacts. A reminder on the importance of offset dependence in amplitudes will be made and the complementary nature of AVO and inversion studies described.

The models will be used later to understand the response of inversion to properties of interest such as porosity, net:gross and saturation.

2. Wavelet Estimation
The section will begin with a review of the claims made by a number of methods to determine wavelets directly from seismic without any external reference such as a well log or VSP. The difficulty of estimating just the amplitude spectrum, never mind the phase spectrum, in the absence of additional information will be demonstrated.

Several strategies will be described, including Kurtosis, amplitude envelope and cross-correlation. The merits of each will be discussed.

Next phase in VSP data sets will be considered, and the importance of downgoing wavefield deconvolution (deterministic deconvolution) in zero phasing VSP upgoing wavefields.
The emphasis will then be on the various approaches to wavelet estimation using well logs, including statistical extraction, full extraction and the Roy White method. Wavelet estimation will involve a practical session to try out the various methods and understand the consequence of effects such as time shifts on the extracted wavelet. Inversion will be described as zero phase deconvolution, followed by integration (inversion itself) and scaling to absolute values (the model component).

3. Acoustic Impedance Inversion
A spreadsheet and simple examples will be used to demonstrate the various methods of inversion, including the model based methods, structural deconvolution as used in VSP and Relative Acoustic Impedance Inversion (RAI). The L1 and L2 norms will be discussed in the context of minimisation strategies. The status of inversion results as a seismic attribute will provide a link to the latter part of the following section on geostatistics, where the integration of well and seismic data is considered. Inversion as a well/seismic integration method with many similarities to kriging will be emphasised, and the consequence of this comparison will be reinforced in the geostatistics section.

4. Geostatistics Primer
A condensed primer on statistics and geostatistics will include the importance of the average or mean in estimation, the concept of expectation, or probability weighted outcome. There will be a discussion of correlation and correlation coefficient and confidence intervals. A spurious correlation Java Applet will be demonstrated. Finally the concept of the mean or average will be developed into estimation using spatial correlation in the form of kriging. The comparison between kriging and best estimation in acoustic impedance inversion will be made. Finally, the problem of bias under best estimate computations will be demonstrated and its solution using stochastic simulation described. This is particularly important for understanding the use of inversion results for purposes such as porosity or net:gross prediction.

The role of geostatistics in integrating inversion results with well data will be demonstrated and various strategies described, including kriging with external drift, co-kriging and collocated co-kriging with Markov-Bayes.

5. Pitfalls in Inversion
Various pitfalls in inversion will be demonstrated, including:

  • Over-zealous stretch and squeeze in wavelet estimation
  • Artefacts in model-based inversion
  • Non-uniqueness
  • Trace scaling and normalisation
  • Skew in cumulative distribution function.
  • Estimator shrinkage (the similarity with kriging will be illustrated).

6. Inversion Practicals
A full sized field data set comprising 2D seismic data and well logs will be used for a full practical investigation, including time picking, model building, wavelet estimation, and interpretation of results. The data will a genuine D&P example of which the presenter has intimate knowledge, including well location decisions.

Examples of 3D seismic inversion, particularly model building, will be illustrated using the Stratton data set.

7. Stochastic Inversion Methods
The latest inversion techniques using stochastic methods will be described. The necessity of developing stochastic approaches will be emphasised, and in particular the link with geostatistics will be made. The various strategies for stochastic inversion will be shown, including the Elf method.

The problems associated with stochastic methods, such as the speed and enormous quantities of output data produced will be highlighted, along with the future of these methods.

Who should attend

Geophysicists and geologists. An understanding of basic mathematics and physics is required. Although presenting advanced geophysical techniques this should not deter people without an in-depth knowledge of geophysics from attending.

Prerequisites and linking courses

There are no prerequisites other than mentioned above, but course N092 (Fundamentals of  Reservoir Geophysics) provides, among other topics, an introduction to this subject.

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Ashley Francis

Very informative. The instructor was fantastic.