COLORED INVERSION HAMPSON RUSSELL CODE
COLORED INVERSION HAMPSON RUSSELL WINDOWS

We will focus on an area of interest of about 300 ms in thickness between two horizons Figure 6 presents the resulting relative impedance section scaled (0вЂ“1) in this area.ДЇigure 7. Since the relative impedance result contains no low frequencies, it does not inform us about trends, so it makes more sense to look at the result in a single formation. NumPy's apply_along_axis() applies any function to all columns of an array, so we can pass it the convolution:Дef convolve(t): return np.convolve(t, operator, mode='same')Д¬i = np.apply_along_axis(convolve, axis=0, arr=seis) Once the operator is calculated a simple trace-by-trace convolution with the reflectivity data is needed to perform CI. Gap = spec_log_model - spec_seismic_model Finally, we rotate the phase by taking the quadrature of the signal, represented by the imaginary component and shown in Figure 5. We move back to the time domain with an inverse Fourier transform, then shift zero time to the center of the time window. Now, continuing with Lancaster and Whitcombe's methodology, we can derive an inversion operator. It is important to note that our end result will be influenced greatly by this choice, and care should be applied at this stage.ДЇigure 5.

COLORED INVERSION HAMPSON RUSSELL WINDOWS

In this example, taper windows of 0вЂ“5 Hz and 100вЂ“120 Hz have been defined. Figure 4 shows the resulting modeled spectrum. Then we take seismic traces at the well location, average them, and repeat the procedure we did on the well to get the spectrum. We define a simple function to generate a 50-points Hanning-shaped taper at both ends of the spectrum the result is shown in Figure 4. This is a critical part that will have great influence on the end result. We first define some boundaries to our modeled spectrum in the frequency domain. The next major step of the workflow is to compute an operator that is representative of the difference between the log spectrum and the seismic spectrum. Now we have a continuous function that mathematically approximates the well-log spectrum. F02-1 well spectrum approximated by a linear function in log space.

Prior to running the workflow on your data, noise attenuation should be performed to ensure that the inversion process recovers frequencies associated only with the earth.ДЇigure 3. This tutorial focuses on presenting the whole workflow in the simplest fashion rather than trying to optimize parameters to recover interpretable features.

COLORED INVERSION HAMPSON RUSSELL CODE

You can read and run the code for yourself from the repository at /seg/tutorials-2017. The idea of this tutorial is to achieve a CI without any external software, just Python code with the NumPy and SciPy libraries.

As a quality control (QC) step, check the residuals by comparing log and AI section spectrums.

Convolve the operator with the stacked seismic.

Convert the difference spectrum to an operator.

Get a difference spectrum by substracting the seismic spectrum.

In this tutorial, we follow the steps presented by Lancaster and Whitcombe in their 2000 expanded abstract to achieve the so-called вЂњfast-track colored inversion.вЂќ Using open-source algorithms, we describe all the steps to go from reflectivity data to inverted cubes: What's more, since CI is directly linked to seismic data, the relative impedance it produces can be used as a base for comparison with other inversion to see what kind of information is introduced by numerical constraints or the low-frequency model. Like other inversions, CI can help remove the smearing effects of the seismic wavelet and enhance features such as thin beds and discontinuities. Recognizing that the popular sparse-spike inversion process could be approximated by a single operator, yielding relative impedance via simple convolution with the reflectivity data, the authors showed that this operator can be derived from well logs. Lancaster and Whitcombe (2000) published a fast method for band-limited inversion of seismic data known as colored inversion (CI) that generated widespread interest among interpreters. This is crucial because, while reflectivity informs us about boundaries, impedance can be converted to useful earth properties such as porosity and fluid content via known petrophysical relationships. Broadly, inversion converts reflectivity data to physical properties of the earth, such as acoustic impedance (AI), the product of seismic velocity and bulk density.

Whether it is deterministic, band-limited, or stochastic, seismic inversion can bear many names depending on the algorithm used to produce it.

Colored inversion hampson russell