{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The frequency of a Ricker wavelet\n", "\n", "We often use Ricker wavelets to model seismic, for example when making a synthetic seismogram with which to help tie a well. One simple way to guesstimate the peak or central frequency of the wavelet that will model a particlar seismic section is to count the peaks per unit time in the seismic. But this tends to overestimate the actual frequency because the maximum [frequency](http://www.subsurfwiki.org/wiki/Frequency) of [a Ricker wavelet](http://subsurfwiki.org/wiki/Ricker_wavelet) is more than the peak frequency. The question is, how much more?\n", "\n", "To investigate, let's make a Ricker wavelet and see what it looks like in the time and frequency domains." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "T, dt, f = 0.256, 0.001, 25\n", "\n", "import bruges\n", "w, t = bruges.filters.ricker(T, dt, f, return_t=True)\n", "\n", "import scipy.signal\n", "f_W, W = scipy.signal.welch(w, fs=1/dt, nperseg=256)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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fJ2koW4OYGMPliT61QyGiFDGRI1KQ1LVyqSty0h45jiAgIlo8qdFJvnWsnK6B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\nZia/+tWvHMtNJhMnT54kJSWF8ePHExoaCsCdd97J9u3bW3zf5ORkvv3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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(figsize=(15,5), ncols=2)\n", "axs[0].plot(t, w)\n", "axs[0].set_xlabel(\"Time [s]\")\n", "axs[1].plot(f_W[:25], W[:25], c=\"C1\")\n", "axs[1].set_xlabel(\"Frequency [Hz]\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "When we count the peaks in a section, the assumption is that this apparent frequency — that is, the reciprocal of apparent period or distance between the extrema — tells us the dominant or peak frequency.\n", "\n", "To help see why this assumption is wrong, let's compare the Ricker with a signal whose apparent frequency does match its peak frequency: a pure cosine:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "c = np.cos(2*25*np.pi*t)\n", "\n", "f_C, C = scipy.signal.welch(c, fs=1/dt, nperseg=256)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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U6hEMUkuLWR7CxwtQPZuFoao1WbsAc8zyY2PQS0rV1gneqJOTEKNRiE3Vu+rM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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(figsize=(15,5), ncols=2)\n", "axs[0].plot(t, c, c=\"C2\")\n", "axs[0].set_xlabel(\"Time [s]\")\n", "axs[1].plot(f_C[:25], C[:25], c=\"C1\")\n", "axs[1].set_xlabel(\"Frequency [Hz]\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Notice that the signal is much narrower in bandwidth. If we allowed more oscillations, it would be even narrower. If it lasted forever, it would be a spike in the frequency domain.\n", "\n", "Let's overlay the signals to get a picture of the difference in the relative periods:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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ArjrH3vmBa5j8v6F45pTjPierbeTzSp89i55O0XPj9Q35vKf37Gbhtdfp8Oqo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\n90AuUePv9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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15, 5))\n", "plt.plot(t, c, c='C2')\n", "plt.plot(t, w)\n", "plt.xlabel(\"Time [s]\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "The practical consequence of this is that if we estimate the peak frequency to be $f\\ \\mathrm{Hz}$, then we need to reduce $f$ by some factor if we want to design a wavelet to match the data. To get this factor, we need to know the apparent period of the Ricker function, as given by the time difference between the two minima.\n", "\n", "Let's look at a couple of different ways to find those minima: numerically and analytically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find minima numerically" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll use [`scipy.optimize.minimize`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize) to find a numerical solution. In order to use it, we'll need a slightly different expression for the Ricker function — casting it in terms of a time basis `t`. We'll also keep `f` as a variable, rather than hard-coding it in the expression, to give us the flexibility of computing the minima for different values of `f`. \n", "\n", "Here's the equation we're implementing:\n", "\n", "$$w(t, f) = (1 - 2\\pi^2 f^2 t^2)\\ e^{-\\pi^2 f^2 t^2}$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def ricker(t, f):\n", " return (1 - 2*(np.pi*f*t)**2) * np.exp(-(np.pi*f*t)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that the wavelet looks like it did before, by comparing the output of this function when `f` is 25 with the wavelet `w` we were using before:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = 25\n", "np.allclose(w, ricker(t, f=25))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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GthXvQBAARQE8ztuq2l9razdePLIQAOC2m6raFxERNS9OrSQiooYWCA5DEHLlaMYCo8FY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\ntCo2JrHRaurDDz/U8uXLVVhYqMLCQlVXVwePlZe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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15, 5))\n", "plt.plot(w, lw=3)\n", "plt.plot(ricker(t, f), '--', c='C4', lw=3)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we call SciPy's `minimize` function on our `ricker` function. It itertively searches for a minimum solution, then gives us the `x` (which is really `t` in our case) at that minimum:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: -0.4462603202963996\n", " hess_inv: array([[1]])\n", " jac: array([-2.19792128e-07])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 30\n", " nit: 1\n", " njev: 10\n", " status: 0\n", " success: True\n", " x: array([0.01559393])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.optimize\n", "\n", "f = 25\n", "\n", "scipy.optimize.minimize(ricker, x0=0, args=(f))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So the minimum amplitude, given by `fun`, is $-0.44626$ and it occurs at an `x` (time) of $\\pm 0.01559\\ \\mathrm{s}$. \n", "\n", "In comparison, the minima of the cosine function occur at a time of $\\pm 0.02\\ \\mathrm{s}$. In other words, the period appears to be $0.02 - 0.01559 = 0.00441\\ \\mathrm{s}$ shorter than the pure waveform, which is..." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.22050000000000003" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(0.02 - 0.01559) / 0.02" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...about 22% shorter. This means that if we naively estimate frequency by counting peaks or zero crossings, we'll tend to overestimate the peak frequency of the wavelet by about 22% — assuming it is approximately Ricker-like; if it isn't we can use the same method to estimate the error for other functions.\n", "\n", "This is good to know, but it would be interesting to know if this parameter depends on frequency, and also to have a more precise way to describe it than a decimal. To get at these questions, we need an analytic solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find minima analytically\n", "\n", "Python's [SymPy package](http://sympy.org/) is a bit like Maple — it understands math symbolically. We'll use [`sympy.solve`](http://docs.sympy.org/latest/modules/solvers/solvers.html) to find an analytic solution. It turns out that it needs the Ricker function writing in yet another way, using SymPy symbols and expressions for $\\mathrm{e}$ and $\\pi$. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import sympy as sp\n", "\n", "t = sp.Symbol('t')\n", "f = sp.Symbol('f')\n", "\n", "r = (1 - 2*(sp.pi*f*t)**2) * sp.exp(-(sp.pi*f*t)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can easily find the solutions to the Ricker equation, that is, the times at which the function is equal to zero:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-sqrt(2)/(2*pi*f), sqrt(2)/(2*pi*f)]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.solvers.solve(r, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But this is not quite what we want. We need the minima, not the zero-crossings.\n", "\n", "Maybe there's a better way to do this, but here's one way. Note that the gradient (slope or derivative) of the Ricker function is zero at the minima, so let's just solve the first time derivative of the Ricker function. That will give us the three times at which the function has a gradient of zero." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0, -sqrt(6)/(2*pi*f), sqrt(6)/(2*pi*f)]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dwdt = sp.diff(r, t)\n", "sp.solvers.solve(dwdt, t)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "In other words, the non-zero minima of the Ricker function are at:\n", "\n", "$$\\pm \\frac{\\sqrt{6}}{2\\pi f}$$\n", "\n", "Let's just check that this evaluates to the same answer we got from `scipy.optimize`, which was 0.01559." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.015593936024673521" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(6) / (2 * np.pi * 25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solutions agree.\n", "\n", "While we're looking at this, we can also compute the analytic solution to the amplitude of the minima, which SciPy calculated as -0.446. We just substitute one of the expressions for the minimum time into the expression for `r`:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2*exp(-3/2)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r.subs({t: sp.sqrt(6)/(2*sp.pi*f)})" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Apparent frequency\n", "\n", "So what's the result of all this? What's the correction we need to make?\n", "\n", "The minima of the Ricker wavelet are $\\sqrt{6}\\ /\\ \\pi f_\\mathrm{actual}\\ \\mathrm{s}$ apart — this is the apparent period. If we're assuming a pure tone, this period corresponds to an apparent frequency of $\\pi f_\\mathrm{actual}\\ /\\ \\sqrt{6}\\ \\mathrm{Hz}$. For $f = 25\\ \\mathrm{Hz}$, this apparent frequency is:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "32.06374575404661" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(np.pi * 25) / np.sqrt(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we were to try to model the data with a Ricker of 32 Hz, the frequency will be too high. We need to multiply the frequency by a factor of $\\sqrt{6} / \\pi$, like so:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "25.00019823475659" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "32.064 * np.sqrt(6) / (np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives the correct frequency of 25 Hz.\n", "\n", "To sum up, rearranging the expression above:\n", "\n", "$$f_\\mathrm{actual} = f_\\mathrm{apparent} \\frac{\\sqrt{6}}{\\pi}$$\n", "\n", "Expressed as a decimal, the factor we were seeking is therefore $\\sqrt{6}\\ /\\ \\pi$:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.779696801233676" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(6) / np.pi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is, the reduction factor is 22%." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "Curious coincidence: in [the recent Pi Day post](https://agilescientific.com/blog/2018/3/14/happy-pi-day-einstein), I mentioned the Riemann zeta function of 2 as a way to compute pi. It evaluates to $(\\pi / \\sqrt{6})^2$. Is there a connection between the Ricker wavelet and the Riemann hypothesis?\n", "\n", "I doubt it." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }