12

This is a very good question, not just important to seismic inversion, but also modeling in general. Lets set this problem up differently. Lets say point's A and D are nodes. Each node represents a system of equations, and these equations are only calculated on these points. Therefore, the model can only exist on the points in which they are calculated. ...


10

Because those frequencies are not present in the seismic data. Here's an example with some typical numbers: Seismic sample interval: 4 ms Therefore Nyquist is 0.5 $\times$ 1/0.004 = 125 Hz Usually there is a filter on the recorder at 0.8 $\times$ Nyquist = 100 Hz So the seismic does not contain frequencies beyond 100 Hz The maximum frequency $f_\text{max}$...


9

Colored inversion is designed to approximately match the average spectrum of inverted seismic data with the average spectrum observed impedance (Lancaster and Whitcombe, 2000). The earth’s reflectivity can be considered fractal, and the resulting amplitude spectrum favors high frequencies (spectral blueing). If there was no preferred frequency, then you ...


9

Two-way time to depth calibration is a vertical problem. How you handle deviated wells probably depends a bit on how you are tying the wells. Here are two things to watch out for: You should be tying to true vertical depth (TVD) anyway — make sure you're not using measured depth somehow. I expect you are using TVD — so the deviated section will be ...


8

It depends on the implementation, but bare-bones reverse time migration is usually not amplitude friendly. The problem is that the ideal imaging condition — deconvolution — is difficult to apply or unstable in the time domain. So cross-correlation is used instead, and this loses the relative amplitude information... so amplitudes are no longer necessarily ...


7

Seismic, but... There are lots of ways of estimating wavelets. None of them rely on well logs alone, because they don't contain any information about the wavelet. Some methods are purely statistical, some use the seismic data, and some of them use seismic and well logs. Background I recommend reading what you can about wavelet extraction. Especially these ...


6

My preferred way of doing this (I've been working in seismic data processing and analysis for over 20 years now) is: Start with theoretical (or notional) source wavelet. Shape the source wavelet to zero phase (or minimum phase, depending on your application). Design a cross-equalization filter that takes the input from step 1 as the source and step 2 as ...


5

The answer by @aretxabaleta is dealing specifically with seismic data (which was your question). I only want to add that the colour of noise is a general term to describe frequency spectra, that comes from electronics/physics and is used in many other fields (e.g. in colour of environmental variability in ecology). White, blue, brown/red and pink are all ...


5

It depends.† Some factors to consider: The sample interval of your seismic data. there's not a lot of point in being smaller than that. For most legacy data it's 4 ms; these days it's often 2 ms. This is a lower bound; you can increase from here if your data have limited bandwidth; there's no point using less than 8 ms for data that's just noise past ...


5

The best reference on this is: J.A. Hudson and J.R. Heritage, 1981, The use of the Born approximation in seismic scattering problems, Geophys. J. R. Astr. Soc., v.66, 221-240. Basically, the Born approximation is a governing principle of the standard imaging condition that treats seismic wavefields from a single point scatterer. This is the justification ...


5

Here is a link to a colored inversion operator design code written and provided by Peter Zahuczki. This code requires that you provide a P-impedance log amplitude spectrum; he uses the open-source interpretation software OpendTect to compute this spectrum. Peter has a easy to follow tutorial on how to use his code with OpendTect. Good luck!


4

The propagation of seismic waves is described by the wave equation: $$\mathrm{\nabla \cdot \sigma = \frac{\partial ^2 u}{\partial t^2}}$$ Where $\sigma$ is the stress and $u$ is the displacement. Geometric ray theory is an approximation to the full wave equation where the length scale of variation in seismic wavespeed is much larger than the seismic ...


4

One common issue is that sonic logs in deviated wells are affected by rock anisotropy (e.g. TVI in shales), and thus yield quite different velocities than are measured in vertical wells. This may affect your correlations as well as things mentioned above.


3

I too have found this nomenclature rather confusing. I am pretty sure that trace-based inversion is merely where each seismic trace is inverted independently of surrounding traces. This would take into account most deterministic/probabilistic inversion types (e.g. model, coloured, sparse, etc). In contrast, geostatistical inversion would not strictly be ...


3

You may want to investigate the Delivery package available from http://www-old.dpr.csiro.au/StochasticSeismicInversion/ 'Delivery is an open-source, trace-based Bayesian seismic inversion code for use in oil reservoir characterisation at the early development and appraisal stage. See the Computers and Geosciences paper for most of the details, and the ...


3

There is a good discussion of the anisotropy issue by Hornby, Howie and Ince, 2003, Anisotropy correction for deviated-well sonic logs: Application to seismic well tie, Geophysics, 68(2):464-471, doi 10.1190/1.1567212. If you have an estimate of the anisotropy parameters it is possible to correct your sonic logs for the anisotropic effect. Note that well ...


2

It depends on what your starting information about your seismic data is. For example, if you know that your data contains an impulsive (minimum phase) source wavelet (i.e. the acquisition source was dynamite or a big ol' hammer, or some other impulsive source, and has not been modified) then you can apply the workflow of txpaulm or use spiking deconvolution. ...


2

Inverse problems deal with creating theories based on observed data, as opposed to making predictions about the real world based on existing theoretical models, so the "results of the measurement of observable parameter" is a confusing way of saying "the real measurements being used as data". Parameter simply refers to the value being measured. An example ...


2

Here is the figure in question: "Traveltime inversion" is a very broad category that includes any inverse problem where the input data is a time-delay from a seismic source impulse to when it is received at a seismometer. This includes refraction tomography, reflection tomography, and most implementations of full-waveform inversion (i.e. using diving waves)....


1

Both situations are possible. Normally, the atmosphere gets colder and more rarefied with height, and cold air holds less moisture than warm air. Inversion layers trap the lower air mass closer to the ground, so there is a reversal of what you might normally expect: temperature and humidity rises as you get higher, rather than the normal decrease. Inversion ...


1

I assume that the sentence in the book mainly refers to subsidence as an adiabatic process. This sinking motion has a maximum which is at a height well above the surface, simply for the reason that air flow can not penetrate the earth's surface. Therefore maximum adiabatic heating rates occur well above the surface as well. The precise height where this ...


1

The impedance inversion problem asks: "Recover acoustic impedance from seismic reflection waveforms". The forward modeling procedure from acoustic impedance to seismic reflection waveforms involves calculating reflection coefficients and then convolving these with a wavelet. Let's assume, for now, that you have perfect seismic resolution and therefore your ...


1

You can think of this amplitude term as being part of the wavelet term such that your definition of the wavelet is: "the necessary filter/operator to convert true reflectivity into the arbitrarily scaled seismic data". This scalar depends on the data itself and therefore must be obtained empirically. In fact, it is very likely that the scalar is frequency ...


1

When performing "imaging" we are generally attempting to recover the reflectivity of the earth. At zero offset the reflectivity is the difference in Acoustic Impedance (AI) normalized by the sum. When performing colored inversion we are seeking to recover a layered representation of the band limited AI and not the reflectivity. As we go from an AI log to a ...


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