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6 changes: 3 additions & 3 deletions 1804_Conjugate_gradient_inversion/conjugate_gradient2.ipynb
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Expand Up @@ -8,7 +8,7 @@
"\n",
"An exploration of the conjugate gradient solver. Considering the problem of getting reflectivity from a seismic trace, given the wavelet.\n",
"\n",
"This was the topic of a previous tutorial which used the numpy and scipy matrix solvers. This notebook solves same problem the conjugate gradient method and compares the result to the matrix solver results.\n",
"This was the topic of a previous tutorial which used the numpy and scipy matrix solvers. This notebook solves same problem by the conjugate gradient method and compares the result to the matrix solver results.\n",
"\n",
"We'll be working on a model, so we know the correct answer from the start."
]
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"source": [
"## Estimate the model using the preconditioned conjugate gradient method\n",
"\n",
"I will use the previous unconditioned results and attempt to concentrate amplitude in the locations that already have large amplitude. The preconditioner is to scale by sqrt(previous result smoothed amplitude^2). This scalar is just the RMS of a 3 point sliding window. The effect will be to make large amplitudes larger and small ampltudes smaller in the estimated model.\n",
"I will use the previous unconditioned results and attempt to concentrate amplitude in the locations that already have large amplitude. The preconditioner is to scale by sqrt(previous result smoothed amplitude^2). This scalar is just the RMS of a 3 point sliding window. The effect will be to make large amplitudes larger and small amplitudes smaller in the estimated model.\n",
"\n",
"Compute R the right preconditioning diagonal matrix.\n",
"\n",
Expand Down Expand Up @@ -900,7 +900,7 @@
"source": [
"def mv(v):\n",
" \"\"\"\n",
" The fordward operator, convolution.\n",
" The forward operator, convolution.\n",
" \"\"\"\n",
" return np.convolve(v, wavelet, mode='same')\n",
"\n",
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