Advanced Geophysical and Image Processing Calculations in Kalpa MineX+#
In this section, we introduce complex equations commonly used in geophysical signal processing or image processing that you can implement directly in Kalpa’s Vector Calculator. These calculations help you derive meaningful attributes from your geospatial datasets, particularly for machine learning, geophysical modeling, or data visualization.
Advanced Calculation Examples#
1. Hilbert Transform (Instantaneous Amplitude) The Hilbert Transform is widely used in signal processing to compute the instantaneous amplitude of a signal.
Condition (Python Expression):
np.sqrt(row['signal']**2 + np.imag(np.fft.hilbert(row['signal']))**2)
Example Use Case: Analyzing the envelope of seismic signals or any oscillatory data.
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2. Gradient Magnitude Calculation Compute the gradient magnitude from spatial derivatives in the X and Y directions.
Condition (Python Expression):
np.sqrt(row['gradient_x']**2 + row['gradient_y']**2)
Example Use Case: Calculate the spatial rate of change, essential for edge detection in image processing or identifying geophysical anomalies (e.g., gravity, magnetic fields).
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3. Laplacian Filter Used to detect regions of rapid intensity change, often for image and signal processing.
Condition (Python Expression):
row['d2_dx2'] + row['d2_dy2']
Example Use Case: Identify high-curvature zones in geophysical maps, such as subsurface density contrasts.
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4. Bandpass Filtering Apply a simple bandpass filter to retain features within a specific frequency range.
Condition (Python Expression):
low_cutoff <= row['frequency'] <= high_cutoff
Example Use Case: Filter seismic or geophysical signals to focus on features of interest, e.g., specific wave types or geological layers.
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5. Normalized Difference Index (NDI) A normalized ratio of two variables, commonly used in remote sensing (e.g., NDVI).
Condition (Python Expression):
(row['variable1'] - row['variable2']) / (row['variable1'] + row['variable2'])
Example Use Case: Analyze vegetation indices, detect water bodies, or other normalized geophysical relationships.
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6. Fourier Transform Coefficient Extraction Extract the real part of the first Fourier Transform coefficient for frequency-domain analysis.
Condition (Python Expression):
np.fft.fft(row['signal'])[0].real
Example Use Case: Identify dominant frequency components in geophysical signals.
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7. Directional Slope Calculation Compute the slope in a specific direction (e.g., northward).
Condition (Python Expression):
(row['z_north'] - row['z_center']) / row['distance_north']
Example Use Case: Analyze topographic or bathymetric gradients for hydrological modeling or structural geology.
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8. Gaussian Smoothing Apply Gaussian smoothing to a signal for noise reduction.
Condition (Python Expression):
np.exp(-0.5 * ((row['x'] - row['mean_x']) / row['std_dev_x'])**2)
Example Use Case: Smooth noisy geophysical data or enhance visualization of spatial datasets.
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9. Signal-to-Noise Ratio (SNR) Compute the SNR of a signal.
Condition (Python Expression):
10 * np.log10(row['signal_power'] / row['noise_power'])
Example Use Case: Evaluate the quality of geophysical signals for better interpretation.
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10. Structural Similarity Index (SSIM) Calculate SSIM for image quality assessment in two columns (e.g., predicted vs. observed).
Condition (Python Expression):
(2 * row['mean_x'] * row['mean_y'] + C1) * (2 * row['covariance'] + C2) / ((row['mean_x']**2 + row['mean_y']**2 + C1) * (row['var_x'] + row['var_y'] + C2))
Example Use Case: Compare geophysical or remote sensing images to identify changes or validate models.
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Tips for Writing Complex Equations#
Use Mathematical Libraries Leverage NumPy for mathematical operations and SciPy for advanced signal processing when supported.
Validate Columns Ensure that all referenced columns exist in the dataset to avoid runtime errors.
Break Down Complex Calculations For readability and reusability, create intermediate columns for parts of the computation. This makes debugging and documentation easier.
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