mydocs.pd

# Info

## EAS 4803/8803: Exploration Seismology

### Instructor

[Felix J. Herrmann](mailto:felix.herrmann@gatech.edu)
Phone: +1 (404) 385-7069
Cherry Amerson, room 203

### General Information

Time and Location Monday/Wednesday 3:00 pm - 4:15 pm, ES&T to be announced

Office Hours: Tuesday/Thursday 13:30 pm - 14:30 pm (or by appointment)

#### Course Description


*This course contains a comprehensive review of reflection seismology and its application to oil and gas exploration industry. It includes key aspects of basic seismic data acquisition & processing and wave-equation based imaging and inversion.*

#### Required Textbook

None required

##### Recommended texts

- [Sheriff, R. E., and L. P. Geldart (1995), Exploration Seismology (second edition), Cambridge University Express.](https://www.amazon.com/Exploration-Seismology-R-E-Sheriff/dp/0521468264)

- [Yilmaz, O. (2001), Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data, Society of Exploration Geophysicists.](https://library.seg.org/doi/book/10.1190/1.9781560801580)

- [Yilmaz, O., SEG wiki page on Seismic Data Analysis](https://wiki.seg.org/wiki/Seismic_Data_Analysis)

- [Zhou, H. (2014), Practical Seismic Data Analysis, Cambridge University Press.](https://www.amazon.com/Practical-Seismic-Data-Analysis-Hua-Wei/dp/0521199107)

- [Heiner Igel, Computational Seismology---A Practical Introduction](https://www.amazon.com/Computational-Seismology-Introduction-Heiner-Igel/dp/0198717415)

- [Fichtner, Andreas, Full Seismic Waveform Modelling and Inversion](https://www.amazon.com/Modelling-Inversion-Geophysical-Environmental-Mathematics/dp/3642158064)


Additional material will be made available on the course [website].

[website]:

***

### Course Outline

See Outline tab

- [General introduction](outline.md#General introduction)

- [Seismic data acquisition](outline.md#Seismic data acquisition)

- [From processing to inversion](outline.md#From processing to inversion)

- [Compressive sensing](outline.md#Compressive sensing)

- [Linearized inversion](outline.md#Linearized inversion)

- [RTM & FWI](outline.md#RTM & FWI)

***

### Evaluation

- Homework assignments (35%)

- Midterm exam (25%)

- Course project (15%)

- Final exam (25%)

***

### Homework

There will be homework exercises, which will mostly involve geophysics-related programs, computer simulations, and data analysis. These assignments is designed for each student to work by him/herself. This homework will count as 35% of your overall course grade.

***

### Project

You are required to write a term paper on any topic related to geophysics. This can be a literature review of a selected topic, or research project involving calculations, data analysis, or theoretical results done in consultation with the instructor. The topic needed to be approved by the instructor before the midterm. Your paper should be written up in a journal form with length, figures and referencing in a format suitable for submission to journals like Geophysical Research Letters (GRL). Preliminary version of the final paper should be shown to the instructor for approval at least two weeks before the final due date. You will present your term paper in a 15 minute AGU-style talk; a 12 minute presentation with 3 minutes of questions. The project will count as 15% of your overall course grade. Grading for your project will be based on the 12% of the quality of the research and the written paper, and 3% of your presentation.

***

### Exams

There will be a midterm (25%) and a final exam (25%). Both of them are closed book. Reference to texts or other documents such as previous semester course materials during exams is strictly forbidden. Using these materials will be considered a direct violation of academic policy and will be dealt with according to the GT Academic Honor Code. The use of electronic devices (e.g. cellular phones, computers etc.) other than non-programmable calculators during exams and quizzes is not allowed.

***

### Academic Honesty

It is expected that all students are aware of their individual responsibilities under the Georgia Tech Academic Honor Code, which will be strictly adhered to in this class. The complete text of the Georgia Tech Academic Honor Code is at [http://www.honor.gatech.edu/](http://www.honor.gatech.edu/).

***


# Outline

## General introduction

#### Basic seismic data processing

- Explanation of the seismic method
- Seismic acquisition, different gathers, basics land and marine acquisition
- Post-stack seismic-data processing flow to create a seismic image:
   - Common-midpoint sorting
   - Normal-moveout correction
   - Stack
   - Zero-offset migration
- Time-to-depth conversion
- Time or depth migration
- Drawbacks of post-stack processing
- Intro pre-stack migration and velocity analysis

#### Wavefield extrapolation, pre-stack migration, and velocity analysis

- Wavefield extrapolation via Rayleigh II
- Wavefield extrapolation via the f-k domain
- $V(z)$ migration
- Shot record migration
- Recursive extrapolation in varying media
- Pre-stack shot migration
- One-way wave-equation migration
- Reverse-time migration
- Velocity-model estimation
   - Traveltime tomography
   - migration-velocity analysis

#### Filtering

- ``f-k`` filtering
- Radon filtering
   - Linear Radon
   - Multiple-removal via parabolic Radon transform
   - Parabolic versus hyperbolic Radon
- Deconvolution

***


## Seismic data acquisition

- Marine acquisition
- Challenges of 3D acquisition
- Wide-azimuth marine acquisition
- Coil sampling

***

## From processing to inversion

- Forward and inverse problems
- Over and underdermined problems
- Pseudo/generalized inverses
- Least-squares and damped least-squares inversion
- Convolution/correlation, Radon, and NMO in tems of linear operators (matrices)
- Forward and adjoint operations and the 'dot test’ a la Jon Claerbout
- Pseudo inverse and regularization
- Deconvolution as an inversion problem ('matrix inverse’)
- Forward operator for NMO and least-squares NMO
- Removing multiples by high-resolution Radon transform

***

## Compressive sensing

- Nyquist sampling and aliasing
- Exploiting structure is seismic data by transform-domain sparsity promotion
- Basics of Compressive Sensing
- Design principles of Compressive Sensing
- Application of Compressive Sensing to Exploration Seismology
- Jittered sampling of shots
- Simultaneous 'land’ acquisition by summing randomly weighted shots
- Simultaneous 'marine’ acquisition with time-dithered sources

***

## Linearized inversion

- Introduction linearized amplitude versus offset/angle inversion
- Linearization of the reflection and transmission coefficients w.r.t. contrasts in density, compressional, and shear wavespeeds.
- Convolutional model for seismic reflectivity
- Relation between amplitudes of seismic data in the Radon domain and the linearized reflection coefficient.
- Practical workflow for linearized inversion of amplitude-versus-offset data.

***

## RTM & FWI

- Basics of reverse-time migration (RTM) and full-waveform inversion (FWI) via the adjoint state method from physical and mathematical perspectives
- Derivation of expressions for the Jabobian and its adjoint
- Migration as the gradient of FWI
- Least-squares migration as the Gauss-Newton Hessian of FWI
- FWI with gradient descents
- FWI with Gauss-Newton
- Latest developments

# Goals

## General introduction

#### Basic seismic data processing

- Give a description of a surface-seismic experiment
- Describe the basic steps of the post-stack seismic data flow and why they are important
- Explain why we need seismic exploration
- Name seismic transducers and setup for land and marine acquition
- Describe different seismic gathers
- What are the assumptions underlying NMO
- What is the role of the “fold” of the acquisition and why is it important
- Describe the mathematical relation between midpoint/offset and source-receiver coordinates
- Why is the sampling rate different for common-shot and common midpoint gathers
- Describe the principle of velocity estimation with NMO
- What does migration try to accomplish
- Give a geometric description of the process of zero-offset migration.
- Describe the different terms in the Rayleigh II integral
- Decribe the extrapolation “work flow”
- Flowshart for shot extrapolation in the f-k domain
- What is the expression for the wavefield extrapolation operator in the ``f-k`` domain.
- What change do you need to make to do inverse extrapolation
- Describe in pictures forward wavefield extrapolation for a shot record with two events
- Describe recursive inverse wavefield extrapolation of a shot record with a single reflection event by a number of plots
- What is the main assumption on the behavior of the velocity in f-k based recursive extrapolation and what happens to the extrapolation operator compared to the lateral invariant case
- Name the five steps of prestack migration
- What are the underlying assumptions regarding the use of a particular migration scheme in relation to the complexity of the subsurface.
- Draw a schematic of the “impulse” response of the migration operator and the linearized scattering operator.
- Describe the different steps of pre-stack shot migration
- What is the difference between pre- and post-stack migration?
- What is the effect of summing the images of the different shot gathers
- In what situation is pre-stack time migration a viable option and when not
- What migration scheme would you use in case of complex velocities and complex structure

#### Wavefield extrapolation, pre-stack migration, and velocity analysis

- Wavefield extrapolation via Rayleigh II
- Wavefield extrapolation via the f-k domain
- $V(z)$ migration
- Shot record migration
- Recursive extrapolation in varying media
- Pre-stack shot migration
- One-way wave-equation migration
- Reverse-time migration
- Velocity-model estimation
   - Traveltime tomography
   - migration-velocity analysis
- What are the two prevailing methods to estimate the velocity model and what information do they need
- Describe the main principles of travel-time tomography
- Describe the main principles of migration velocity analyses
- What are the differences between these two methods of velocity model estimation

#### Filtering

- Describe the principle and assumptions behind f-k filtering
- Write down the Radon transform in the physical and Fourier domain
- Describe Radon filtering sequence of operations to remove multiples
- Describe what the process of seismic deconvolution tries to accomplish

***


## Seismic data acquisition

- Give the Nyquist sampling critrion for the sampling of spatio-temporal wavefields
- Describe aliasing in 1-D and 2- D (``f-k`` domain).
- What is an airgun
- What is the ghost?
- What is the effect of the ghost on the amplitude spectrum?
- Describe azimuth and name at least three disadvantages of near azimuth acquisition.
- What does a rose diagram plot?
- Mention two different configurations to improve azimuthal coverage. Include sketches of the arrays and sources.
- Describe rich azimuth acquisition and include drawing.
- What is the main driver behind WAZ acquisition?
- Name at least four improvemens related to wide-azimuth acquisition?
- What is fold and why is it important?
- What are the main challenges in marine acquisition?
- What are the challenges of 3D acquisition?
- Name some recent developments.
- Describe coil sampling
- Give the main reasons why large offsets are required?

***

## From processing to inversion

- Describe what the forward and inverse models signify.
- What property do unitaty matrices have?
- What type of solution method should be used when the data synthetic data does not fit observed data exactly?
- Describe how one arrives at the least-squares solution ``m_{LS}=(A^TA)^{-1})A^Td``?
- In what situation, is the least-squares solution used? Is the matrix to be inverted tall, square, or fat?
- Describe the minmum norm solution and when is its use appropriate?
- Describe in words what the expression ``min_x|x|_2 subject to Ax=b`` expresses.
- Explain the difference between processing (applying the adjoint) and inversion
- How are convolution and correlation related related to linear operations
- Describe the 'dot test’ and what does it accomplish
- Mention and describe at least three forward-adjoint pairs relevant to exploration seismology
- Write stacking, zero padding, and sampling as a matrix
- Proof that matrices that represent convolution and correlation are adjoints.
- What kind of matrix is the convolution in the Fourier domain.
- Sketch a column of the Parabolic Radon 'reverse’ transform (``L^H``).
- Explain why it is important to 'invert the 'reverse’ Radon transform’ for multiple removal?
- What is the underlying assumption of minimizing the energy (``\ell_2``-norm) on the model parameters?
- What does high-resolution try to accomplish and what is the underlying assumption on the model and the data?

***

## Compressive sensing

- How is sampling related to a linear system.
- When is the linear system underdetermined.
- How do the concepts of over- and underdetermined systems relate to sampling?
- Give the key ideas of Compressive Sensing.
- Give two examples of transforms that exploit the signal's structure by sparsity.
- Which interferences/artifacts are worse. Coherent aliases due to periodic sampling or incoherent noise due to randomized samping and why?
- Give at least two examples of randomized sampling and describe the impact on the sampling artifacts compared to conventional deterministic acquisition.
- Give an example of measurement (M) and sampling (R) matrices with low and hight coherence
- Which of the following acquisition scenarios creates favorable recovery conditions?
- Explain the role of sparsifying transforms and sparsity-promoting recovery.
- Describe what happens with the recovery SNR as (i) the subsampling ratio decreases, (ii) the sparsity-level increases, (iii) the noiselevel increases, and (iv) the decay rate of the sorted transform-domain coefficients increases.
- List a number of pitfalls/challenges related to applying compressive sensing to seismic acquisition in the field.

***

## Linearized inversion

- Describe three factors that influence the amplitudes of seismic waves
- Describe when the linearized refflection coefficients is a good approximation
- Give two different expressions for the linearized reflection coefficient in the acoustic case
- Mention “non-ray” amplitude effects
- Describe linearized inversion. What are the two key factors expressing the relationship between the amplitudes of the reflection events and the acoustic medium properties. Introduce the corresponding matrices.
- What are the boundary conditions for the elastic wave equation at an interface?
- Describe the different reflection and transmission coefficients for the elastic case.
- Describe the linear convolutional model for the seismic reflection response. What are the underlying assupmtions of this model?
- What does the background velocity model describe and what properties should it have?
- List the different reflection and transmission coefficients for an interface between two elastic layers. What are these coefficients a function of and w.r.t. to which medium properties can these expressions be linearized? For non-zero and pre-critical angles, what are the orders in deltall 1 for these different reflection and transmission coefficients?
- Describe the “work flow” of AVP inversion.
- Describe how the amplitudes of the plane-wave decomposition (via the linear Radon transform) are related to contrasts in the density, compressional, and shear wavespeeds.
- Describe the damped least-squares procedure to estimate the medium perturbations/contrasts. Is the system under or over determined? Why is damping needed?
- Describe issues with the spectral gap.

***

## RTM & FWI

- Describe in words what the adjoint state method corresponds to physically
- What is the geophysical interpretation of the gradient?
- Describe the equations for the computation of the gradient. What is their physical meaning?
- Draw the impulse response of a the linear Born scattering operator and its adjoint for a constant velocity model.
- What is the relationship between least-squares migration and Gauss-Newton?
- How is the action of the Jacobian evaluated? How many PDE solves does it take?
- List at least two difference between linearized inversion (least-squares migration and full-waveform inversion).
- Describe for what purpose full-waveform inversion is used in the context of migration and why.
- Describe a method to make imaging and inversion more efficient
- Describe a cross-well experiment
- Describe a surface-seismic experiment
- How does the sensitivity of these two methods compare?
- What sort of waves does full-waveform inversion rely on and why.
- List at least two requirements of full-waveform inversion on the acquisition.
- What does non-uniquness in full-waveform inversion refer to?
- List at least one strategy people use to avoid getting stuck in a local minimum? What does this imply w.r.t. the wavelength and the propagation distance.

# Reading

## General introduction

##### Reading material

- John Scales: [Theory of Seismic Imaging](https://www.slim.eos.ubc.ca/~felix/Teaching/EOSC454/2014/reading/imaging.pdf) Chapters 1, 2, 10.3
- Guy Drijkoningen: Seismic Data Processing - TG001 / TA3600 Chapters 1,2,3, 4.6, 4.7. and Introduction to Reflection Seismology TA3520 Chapter 5.
- Yilmaz's “bible”

##### Material presented in class

- Slides for basics of seismic data processing
- Slides for wavefield extrapolation, prestack migration, and velocity analysis
- Slides for f-k filtering, Radon filtering, and deconvolution

***

## Seismic data acquisition

##### Material presented in class

- Practical aspects of seismic acquisition

***

## From processing to inversion

##### Reading material

- Jon Claerbout: IMAGE ESTIMATION BY EXAMPLE: Geophysical Soundings Image Construction Chapter 1.
- John A. Scales, Martin L. Smith and Sven Treitel Introductory Geophysical Inverse Theory Chapter 4
- Richard Baraniuk: More Is Less: Signal Processing and the Data Deluge
- Felix J. Herrmann, Michael P.Friedlander, Ozgur Yilmaz: Fighting the curse of dimensionality: compressive sensing in exploration seismology
- Felix J. Herrmann: Randomized sampling and sparsity: getting more information from fewer samples. Geophysics 75, WB173 (2010); doi:10.1190/1.350614

##### Material presented in class

- From Processing to Inversion

***

## Compressive sensing

##### Reading material

- IEEE Signal Processing Magazine Richard Baraniuk: Compressive sensing and More Is Less: Signal Processing and the Data Deluge
- Emmanuel Candes and Michael Wakin: An introduction to Compressive Sensing
- Justin Romberg: Imaging via compressive sampling
- Felix J. Herrmann: Randomized sampling and sparsity: getting more information from fewer samples. Geophysics 75, WB173 (2010); doi:10.1190/1.350614
- Felix J. Herrmann, Michael P. Friedlander, Ozgur Yilmaz: Fighting the curse of dimensionality: compressive sensing in exploration seismology

##### Material presented in class

- Basics of Compressive sensing

***

## Linearized inversion

##### Reading material

- A. Gisolf. On the shortcomings of linear AVP( AVO/AVA) inversion.

#####Material presented in class

- Linearized inversion of amplitude-versus-offset data

***

## RTM & FWI


##### Reading material

- Gerhard Pratt: Gauss-Newton and full Newton methods in frequency domain seismic waveform inversion. Geophysical Journal International, 133, 341-362.
- Andreas Fichtner: Full Seismic Waveform Modelling and Inversion chapter 10 and 11

##### Material presented in class

- Full-waveform inversion


# Homework

### Exercises

During the course you will work on the following excercises

1. A first look at seismic data.

1. NMO correction and velocity analysis

1. Wavefield extrapolation and migration.

1. Fourier, Radon and filtering.

1. From processing to inversion I.

1. From processing to inversion II.

1. Introduction to Compressive Sensing

1. Full Waveform inversion

These exercises will introduce you to the [Julia programming language](https://julialang.org), [Devito](https://www.devitoproject.org)-a Domain-specific Language (DSL) for automatic code generation for highly optimized finite differences, and [Judi](https://github.com/slimgroup/JUDI.jl)-a framework for large-scale seismic modeling and inversion and designed to enable rapid translations of algorithms to fast and efficient code that scales to industry-size problems.

#### Hand in

Please turn in your assignments as pdf files. The assignments should be send to [Felix J. Herrmann](mailto:felix.herrmann@gatech.edu). Late hand ins are not accepted.

Unless stated otherwise the labs are due one week after the lab.

#### Feedback

We will give you feedback on the marking of the exercises.