How to Plot a Ricker Curve Using SciPy - Python?

The Ricker curve, also known as the Mexican Hat wavelet, is a symmetric bell-shaped waveform widely used in signal processing and seismic exploration. SciPy provides built-in functions to generate and plot this important wavelet for analyzing subsurface structures and signal characteristics.

What is the Ricker Curve?

The Ricker curve is the second derivative of a Gaussian function, characterized by a central peak followed by oscillations that decay on both sides. This distinctive shape makes it ideal for detecting transient phenomena in signals and modeling seismic waves in geophysical applications.

Prerequisites

Before plotting the Ricker curve, ensure you have the required libraries installed:

pip install scipy matplotlib numpy

Importing Required Libraries

Start by importing the necessary libraries for signal processing and visualization:

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

Generating the Ricker Curve

Define the parameters and generate the Ricker wavelet using SciPy's signal.ricker() function:

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

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

# Generate time axis and Ricker wavelet
time = np.linspace(-duration / 2, duration / 2, num_points)
ricker_wavelet = signal.ricker(num_points, frequency)

# Plot the Ricker curve
plt.figure(figsize=(10, 6))
plt.plot(time, ricker_wavelet, 'b-', linewidth=2)
plt.title("Ricker Curve (Mexican Hat Wavelet)", fontsize=14)
plt.xlabel("Time (seconds)", fontsize=12)
plt.ylabel("Amplitude", fontsize=12)
plt.grid(True, alpha=0.3)
plt.axhline(y=0, color='k', linestyle='-', alpha=0.3)
plt.show()

Customizing Ricker Curves

You can create multiple Ricker curves with different frequencies to compare their characteristics:

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

# Parameters
duration = 1
num_points = 1000
frequencies = [5, 10, 20, 30]

# Generate time axis
time = np.linspace(-duration / 2, duration / 2, num_points)

# Plot multiple Ricker curves
plt.figure(figsize=(12, 8))
for freq in frequencies:
    ricker_wavelet = signal.ricker(num_points, freq)
    plt.plot(time, ricker_wavelet, label=f'Frequency = {freq} Hz', linewidth=2)

plt.title("Ricker Curves with Different Frequencies", fontsize=14)
plt.xlabel("Time (seconds)", fontsize=12)
plt.ylabel("Amplitude", fontsize=12)
plt.legend()
plt.grid(True, alpha=0.3)
plt.axhline(y=0, color='k', linestyle='-', alpha=0.3)
plt.show()

Key Parameters

Applications

• Seismic Exploration: Analyzing subsurface structures and identifying geological features like reflectors and faults.

• Signal Processing: Wavelet analysis, time-frequency analysis, and feature extraction in various signal types.

• Geophysics: Modeling seismic waves and understanding wave propagation through different media.

• Biomedical Imaging: Image reconstruction, denoising, and edge detection in medical imaging applications.

Conclusion

The Ricker curve is easily generated using SciPy's signal.ricker() function and visualized with Matplotlib. This powerful wavelet is essential for seismic analysis, signal processing, and various geophysical applications where detecting localized features is crucial.