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.