How to Plot a Ricker Curve Using SciPy - Python?

Python is one of the most popular and versatile programming languages. It is a dynamically-typed, high level language. It offers support for multiple libraries and tools for various scientific and mathematical research. It is hence widely used in data analysis and research.

SciPy is a widely used python library, which provides a collection of functions and abilities for scientific computing. In this article, we will learn and understand how to plot a Ricker curve using SciPy in Python. The Ricker curve, which is also popular as the Mexican Hat wavelet, is commonly used in signal processing, seismic exploration, etc. By the end of this article you will be able to generate and visualize this distinguishing wavelet.

Prerequisites

Definitely, you need a working computer with python installed before we learn to plot the Ricker curve. Python can be installed on your operating system from the official website.

Install the latest one as per your system specification(Prefer 3.XX or higher).

You can install SciPy or any library using the pip package manager available in python. Use the simple command in your terminal or command prompt window:

pip install scipy
pip install library_name

Understanding the Ricker Curve

The Ricker curve is a part of a wave or waveform with a symmetric shape that looks like a hat or bell. These curves or waves are used in seismic explorations and geophysics to analyze relative data and extract information about subsurface structures.

This curve is the second derivative of the Gaussian function to a given frequency. It is distinguished by a central high or peak followed by oscillations that narrow off on both sides.

Plotting the Ricker Curve

Now, let's see how you can practically implement the curve using the SciPy library. Open any or your favorite Python integrated development environment (IDE) or a plain text editor to begin. An IDE is an environment with programming capabilities compiled together, that helps us code, test, debug and run.

Step 1: Importing the Required Libraries

We will start by importing the necessary libraries: NumPy and SciPy. NumPy is another fundamental package for scientific calculations in Python, providing support for a collection of mathematical functions and large, multi-dimensional arrays. NumPy can be installed using pip manager.

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt

Step 2: Defining Parameters

Now, we have to define the parameters for the Ricker curve. Frequency is a key parameter, often denoted as "f" or "f0," which determines the central frequency of the curve. Additionally, denote the total duration of the curve, as "t" or "duration", and the number of data points to generate for the curve can be defined as “num_points”. These parameters stored in variables will be used ahead to generate our curve.

frequency = 10  # Central frequency of the Ricker curve
duration = 1  # Total duration of the curve (in seconds)
num_points = 1000  # Number of data points to generate

Step 3: Generating the Ricker Curve

Use the defined parameters above and generate the Ricker curve. The signal.ricker function in SciPy library is used. This function will take the number of data points and the frequency as input. It processes the data and returns an array containing the Ricker wavelet. The time axis can be defined as shown.

time = np.linspace(-duration / 2, duration / 2, num_points)  # Time axis
ricker_wavelet = signal.ricker(num_points, frequency)

Remember the “ricker_wavelet” is just an array with data of the Ricker Curve Waveform. To generate it visually we need another powerful library to help us.

Step 4: Plotting the Ricker Curve

The generated Ricker curve data can now be plotted graphically using the Matplotlib library in python. Matplotlib provides a collective set of plotting functions for creating high-quality visual plots. Install matplotlib library with the help of pip manager as earlier.

plt.plot(time, ricker_wavelet)
plt.title("Ricker Curve")
plt.xlabel("Time (s)")
plt.ylabel("Amplitude")
plt.grid(True)
plt.show()

Example

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
frequency = 10  # Central frequency of the Ricker curve
duration = 1  # Total duration of the curve (in seconds)
num_points = 1000  # Number of data points to generate
time = np.linspace(-duration / 2, duration / 2, num_points)  # Time axis
ricker_wavelet = signal.ricker(num_points, frequency)
plt.plot(time, ricker_wavelet)
plt.title("Ricker Curve")
plt.xlabel("Time (s)")
plt.ylabel("Amplitude")
plt.grid(True)
plt.show()

Output

Applications of Ricker Curve

• Seismic Exploration: It is extensively used in seismic data analysis to identify subsurface structures, such as reflectors, faults, and reservoirs. The Ricker wavelet helps in characterizing and interpreting seismic data.

• Signal Processing: The Ricker wavelet is valuable in tasks like wavelet analysis, time-frequency analysis, and feature extraction. Its shape and characteristics make it suitable for detecting and analyzing transient phenomena or events with localized energy in signals. It finds applications in seismic signal processing, image processing, speech recognition, and event detection in time series data.

• Geophysics: The Ricker wavelet is employed in geophysical studies to model and analyze seismic data and other geophysical phenomena. It aids in subsurface imaging, estimating rock properties, assessing hydrocarbon reservoirs, and understanding the propagation of seismic waves. It is also used in synthetic seismic modeling and inversion techniques.

• Biomedical Imaging: In medical imaging, the Ricker wavelet serves as a basis function in certain image reconstruction algorithms. It helps in tasks such as image denoising, feature extraction, edge detection, and image enhancement. The Ricker wavelet's ability to capture localized features and sharp transitions makes it valuable in biomedical imaging applications.

Other applications also include Pattern Recognition, Wavelet Transformation, Data Compression etc.

Conclusion

With this we come to the end of this article, we have seen the power of small lines of codes to generate and plot Ricker graphs. Python gives us the libraries and functions available to generate or recreate visual plots and graphs accordingly in simple lines of code.

Ricker graphs are widely used in seismic data study and subsurface structural analysis and python gives us easy access to libraries that help us to visualize and also use the data in detail. The SciPy and Matplotlib libraries make way for the calculations and graphical plot respectively.