Questions and Answers of Geology

Use your own words to define predictive deconvolution. What are the assumptions, general procedure, and solution? What is the prediction error operator?
Given a data series \(\mathbf{d}(t)=\left\{d_{0}, d_{1}, d_{2}, \ldots, d_{N}\right\}\) and its estimated wavelet \(\mathbf{w}(t)=\left\{w_{0}\right.\), \(\left.w_{1}, w_{2}, \ldots, w_{M}\right\}\),
Figure 6.5 shows the input and output data for a predictive deconvolution. Explain the origin of the extra events in the output panel. What will happen if random noise is added in the input?Figure
Why do we prefer broadband data for deconvolution? How broad does the frequency band need to be?
When applying deconvolution in the frequency domain to remove the effect of a known broadening filter, any noise that came with the filter will be greatly amplified by the division. The typically
Describe spectral extension in terms of its objectives, assumptions, procedure, and limitations.
Following the description of the quality factor \(Q\) in Section 4.5, compute the expressions of a \(20-\mathrm{Hz}\) Ricker wavelet at one-way traveltime of \(1 \mathrm{~s}, 2 \mathrm{~s}\), and \(3
In the situation of non-stationary convolution shown in Box 6.2 Figure 2, if we know the seismogram \(g(t)\), the original filter \(a(t-\tau)\), and the fact that a constant \(Q\) is a good
Comment on the similarities of the four deconvolution results with the reflectivity function \(r(t)\) in Figure 6.13. How will you quantify the similarity? How can you quantify the solution quality
The four zero-mean moments (mean, variance, skewness, and varimax) have a number of applications in data processing, geo-statistics, and attribute studies. Search geophysics literature for their
For 2D land pre-stack reflection seismic data, design processing flows to suppress noises specified below. State the type of gather, method, assumptions, and potential pitfalls or cautions.(i)
Discuss the effects of minimum phase and white noise in deconvolution. For each factor, illustrate your point using a particular deconvolution method.
Why is a deterministic processing method usually preferred over a statistical one? Are there exceptions? Please give examples to support your arguments.
Will the deconvolution method be applicable to multi-component data? How will you utilize the connection between different data components? Devise an approach and discuss its assumptions, procedure,
Make a table describing the deconvolution methods covered in this chapter. Characterize each method using the following entries: the model, the assumptions, requirements (e.g., minimum phase),
In what situations is the exploding reflector model in Figure 7.1 not applicable?Figure 7.1 Velocity = V Velocity = V/2 (a) (b)
Discuss the differences between a depth migration and a time migration followed by a time to depth conversion.
A well \(\log\) records a physical property at a constant depth increment of \(1 \mathrm{ft}\) \(\left(w_{j}=w\left(j^{*} \Delta z\right), \Delta z=1 \mathrm{ft}\right)\). A depth-to-time conversion
How can you constrain Kirchhoff migration so that it will produce a result similar to that from a NMO stacking? Discuss what is missing from NMO stacking if taking it as a seismic imaging method.
For the zero-offset section shown in Figure 7.11, apply the common-tangent method to obtain the migrated section.Figure 7.11 Time in s d 3- 6 Surface location in km 8 9 10 11 12 23 13
Figure 7.12 shows a common-shot gather over a five-layer model using a line of surface receivers and a single surface shot in the middle. Write a procedure to migrate these data and show your
Explain the use of Fourier transform in Stolt migration. What are the benefits of using FT? What is the assumption involved in the use of FT?
Read the paper by Stoffa et al. (1990) on split-step Fourier migration, and create a summary covering the procedure, assumptions, benefits, and limitations of the method.
Compare and contrast between the PSPI and split-step \(f-k\) migration methods. How does each method treat the lateral velocity variations?
Describe the assumptions and procedure of reverse time migration.
If only first arrivals can be recognized in our data, will the RTM still be applicable? What kinds of target may be imaged by such RTM? What may be the problems?
The imaging condition for the RTM described in Section 7.4.3 involves cross-correlating the forward- and backward-propagated wavefields. Can you suggest other types of imaging condition? For the
Describe the general assumptions and procedure of seismic migration. What are the specifics for Kirchhoff, Stolt, and reverse time migration methods? For seismic data in an area with nearly flat
How would you check the quality of a seismic migration method? Make a list of tests that you would conduct in order to quantify the quality.
Someone has said that smoothing the velocity model is a practical way to improve the migration result. Discuss the possible effects of smoothing velocity model on seismic migration. What are the
Using a spreadsheet to compile observed \(1 \mathrm{D}\), or \(V(z)\), profiles from the literature, make a list of entries to include location, geologic setting, wave type, frequency, depth range,
If velocity increases linearly with depth, what is the maximum depth of the raypath of a first arrival at \(10-\mathrm{km}\) offset between a source and a receiver located on the surface?
The traveltimes and raypaths of transmitted and reflected waves are dependent on velocity variation but independent of density variation. The amplitudes of transmitted and reflected waves depend on
In semblance velocity analysis we usually stack all traces with equal weight. Should we apply variable weights as a function of offset and intersection time? Devise a way to conduct such a weighted
Explain why the root-mean-square velocity is not the exact stacking velocity. Which of the two velocities is usually faster than the other and why?
Use an Excel spreadsheet to illustrate the Cheops Pyramid in imaging a point diffractor.
Some people say that a correct velocity model will result in a more focused migration image. Explain the possible reasons for this statement, and its limitations.
Explain why, even when using the correct velocity model, some reflection events on a CIG may not be flat (e.g. in Figure 8.21b).Figure 8.21b offset (m) 2000 1 0 offset (m) 2000 1 offset (m) 2000 0 1
Explain the notion that the NMO plot is a special case of the CIG plot. Compare and contrast the two plots. Can you construct a semblance graph for a CIG?
While traveltime tomography derives model updates by minimizing the traveltime misfit, are there other constraints and information that we can use to help the process? Make a list of such extra
Devise a residual velocity tomography method for common image gathers based on the Kirchhoff migration. Please provide the main formula and a list of procedures of your method.
What are the factors that we should consider in selecting the multi-scale elements in multi-scale tomography? Make a checklist for best-practice procedure in conducting multi-scale tomography.
Compile a list of the "rule of thumb" ways to \(\mathrm{QC}\) at least five types of common tomographic artifacts. Specify the tests that can be conducted to verify the artifact and quantify its
Make a computer algorithm to illustrate the de-mean artifact in traveltime tomography.
How should we deal with localized velocity anomalies, such as a small salt body, in deformable-layer tomography? Make a 2D computer algorithm to illustrate your idea.
Under what conditions may data fitting be superior to model inversion? What are the conditions for the reverse case?
How common is it in the Earth that the density is much more slowly varying than the velocity, like that shown in the first two logs in Box 9.1 Figure 1 ? Given a slowly varying function and a rapidly
In Figure 9.8 , if the velocity follows a layer-cake model, what is the value of the velocity corresponding to the \(\mathrm{AB}\) segment of the first arrivals?Figure 9.8 reduced time (t-x/6.0)
Why is the definition of length measure or norm an important issue for inverse theory? How does the issue connect with real signal and noise properties?
Discuss the benefits of expressing a function as the combination of basis functions like that shown in (9-16). What are the preferred properties of the basis functions?
An experiment yielded the following measures of a function \(v(t)\) :(a) Graph the data;(b) Write the forward system of a linear fit, and its \(\mathrm{L}_{2}\) inverse system;(c) If we want to force
If you have a least squares algorithm already, how will you use this algorithm to solve for the \(\mathrm{L}_{1}\) solution? In other words, how will you minimize the \(\mathrm{L}_{1}\) error using
When Sir Harold Jeffreys analyzed seismic traveltime residuals, he noticed that the distribution of the residuals was not quite Gaussian. He expressed it as\[ f(t)=\frac{1-\varepsilon}{\sqrt{2 \pi
Why it is difficult to derive the focal depth of earthquakes? Can we use first arrivals at three stations to determine four focal parameters \(\left(x, y, z, T_{0}\right)\) ?
Show that if \(\lambda\) is an eigenvalue of the problem \(\mathbf{A x}=\lambda \mathbf{x}\), it is also an eigenvalue of the "adjoint" problem \(\mathbf{A}^{\mathrm{T}} \mathbf{y}=\lambda
For a \(2 \times 2\) matrix \(\mathbf{A}=\left(\begin{array}{cc}10 & 2 \\ -10 & 2\end{array}\right)\)(a) Take an eigenvalue-eigenvector decomposition, i.e., find \(\mathbf{X}\) and
For a linear equation set \(\left\{\begin{array}{c}x_{1}+x_{3}=1 \\ x_{2}=2 \\ -x_{2}=1\end{array}\right.\)(a) Form the least squares inverse;(b) Compute the model parameters using the generalized
The Backus-Gilbert method has been applied to derive 3D phase or group velocity structures based on surface wave data. Describe how this is done by searching out and reading publications on this
The damping factor \(\varepsilon^{2}\) in the minimum-norm LS solution (9-54) appears again in Section 9.5.3.1 on a priori information. Explain why the damping factor is able to preferentially
A joint inversion can be regarded as a constrained inversion, and vice versa. However, not all joint inversions achieve better results than separated inversions. Make a list of criteria for choosing
Explain or refute a notion that in early days of reflection seismology people took -70 \(\mathrm{dB}\) as the noise level when there were no other references available.
Conduct a literature search to summarize the principles of ambient-noise seismology. What are the pros and cons?
There are possible errors in the phase angle of the reflectors shown in panels (b) and (d) of Figure 10.7. How will you evaluate errors in the phase angle? What are your estimates of phase angle
Make a table to summarize major attributes of three groups of multiple suppression methods. The attribute list should include assumptions, principles, main method(s), applicable situations, and
Come up with three different ways to quantify the effectiveness of the two multiple suppression methods shown in Figure 10.20, panels (b) and (c).Figure 10.20 Time (s) 3.7 3.5 3.3 (a) 21 Time (s) 3.7
Devise a way to construct a common image gather (CIG) using multiple reflections. What type of migration operator should be used? How will such a CIG differ from a CIG based on primaries?
Name several geologic settings that are suitable for HTI and VTI models, respectively. What are the impacts of HTI and VTI media on surface seismic reflection data? Comment on the effectiveness of
Use a spreadsheet to compile a list of diagnostics for distinguishing velocity anisotropy from velocity heterogeneity using seismic and other geophysical and geologic information.
Prove via theoretical derivation or numerical calculation that a raypath in a homogeneous TI medium follows a straight line.
Compile in a table the criterion and diagnostics for recognizing a converted wave. Please specify the type of data, data domain, and principles of the recognition.
Conduct a literature search and summarize the idea and procedure of median filters that were used in Figure 10.51 to enhance upgoing reflections.Figure 10.51 (a) (d) 1000 Pdown PS up 1000 down 1200
Section 8.4.2 described a simple case of tomographic inversion using first arrivals of VSP data. Prepare a data processing flowchart to build velocity model using first arrivals and traveltimes of
Discuss the sensitivity of the AVO attribute with respect to noise. List the measures that may help reduce the influences of various types of noise.
The amplitude of two time series \(\mathrm{S} 1\) and \(\mathrm{S} 2\) can be matched to a similar level by multiplying one of them by a constant \(a\). How would you determine the value of \(a\) in
Describe two ways to quantify the seismic-to-well tie level. Write computer code to quantify the "similarity" between Trace 5 and Trace 6 in Figure 10.71 this can be done in Excel. Would you apply a
Along the unit circle in the complex \(z\)-plane shown in Figure 5.10, indicate the angle of:(a) Zero frequency;(b) Nyquist frequency;(c) \(100 \mathrm{~Hz}\) if the time sampling rate is \(4
Find the \(z\)-transform formula and recursive formula of the filter whose block diagram is shown in Figure 5.11.Figure 5.11 x(z) input- N 3 Z 2 1 y(z) output
What type of filter is\[ y_{t}=\frac{1}{18} x_{t}-\frac{1}{6} x_{t-1}+\frac{1}{2} x_{t-2}+\frac{1}{2} y_{t-1}-\frac{1}{4} y_{t-2} ? \]For a signal sampled at 125 sample/second, at what frequency
For a seismic dataset sampled at \(2 \mathrm{~ms}\), design a minimum-phase and real-number filter that will suppress noise associated with \(\mathrm{AC}\) power at \(60 \mathrm{~Hz}\). What is the
For the following filter\[ f(z)=\frac{1.21+1.1 \sqrt{2} z+z^{2}}{1.44+1.2 \sqrt{2} z+z^{2}} \](a) Sketch the pole-zero locations and identify the filter type;(b) Sketch the amplitude response and
The acquisition of seismic data for petroleum exploration usually applies a low-cut filter in the field. Find the reasons for using this low-cut filter by searching the literature.
A geophone is specified by a frequency, such as \(14 \mathrm{~Hz}, 4.5 \mathrm{~Hz}\), etc. What is the meaning of the specified frequency? Is it possible for a geophone to record signals of
Explain the benefit of using tapers in applying filtering in frequency domain. Is it possible to remove the entire Gibbs artifact associated with a DFT?
Frequency-wavenumber or \(f-k\) filtering is an effective way to remove linear noise. Please research this topic and then write a short report describing \(f-k\) filtering in terms of: (1) the idea;
Explain why a smooth transition between the rejection zone and pass zone is necessary in \(f-k\) filtering.
Explain or refute the following statement: For broad band input, the cross-correlation function of the input and output of a system is the impulse response of the system.
For a single seismic trace \(y(t)\) as the input, write a computer program (or a flowchart of descriptions) of the first five iterations of the inverse filtering method using the Levinson recursion.
The auto-covariance of a length-3 trace data trace \(y(z)\) is \((6,35,62,35,6)\).(a) Find the filter \(F(z)\) using the root method;(b) Form the Toeplitz normal equations;(c) Find the inverse filter
In the deconvolution example shown in Figure 5.29, the predicted signal shown in panel \((\mathrm{C})\) is much longer than the airgun signal in panel (B). Explain the origin of the long tails of the
How would you estimate the fold, the number of the source-to-receiver midpoints in each CMP bin, from a survey map like that shown in Figure 1.6? Describe your procedure and assumptions.Figure 1.6
As shown in Figure 1.7, the shapes of reflection raypaths tend to resemble the letter “U” rather than the letter “V”. Explain the reason behind this phenomenon.Figure 1.7 -h. V3 M < -h R >M <
Update the processing flow shown in Figure 1.8 by finding and reading at least two papers published within the past 10 years. What happened to those processing steps in Figure 1.8 that are missing
A given seismic trace is sampled at 4 milliseconds. If the signal frequency is known to be up to 60 Hz, find a way to reduce the total number of sampling points without losing the signal.
In Figure 1.9 try to identify as many of the seismic events as you can. What are the main primary reflection events? What are the factors affecting the amplitudes of seismic events in this
In your own words, define the following terms: signal, time series, z-transform, processing artifact, and spatial aliasing.
Find an example of AGC in seismic data processing from the literature. What was the gain function used and what was the reason for it?
In Figure 1.14 why do the panels with lower central frequencies have smoother radiation patterns? What was the likely orientation of the airgun array and why?Figure 1.14 80 60 40 40 80 Frequency: 10
Search the literature to find the basic physical principles for the use of AVO to detect fluid properties in subsurface. Why is AGC not allowed in AVO studies?
When a time series is reversed, what happens to its phase properties? Demonstrate your point using the time series (1, 2, 3, 4).
How can the phase of a seismic trace be advanced by 30°? How can it be advanced by any degree?

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