Source code for bruges.attribute.discontinuity

"""
Various methods to compute seismic discontinuity. 

:copyright: 2015 Joe Kington, SEG Tutorial https://library.seg.org/doi/pdf/10.1190/tle34121510.1
:license: Apache 2.0
"""
import numpy as np
from scipy.ndimage import generic_filter
from scipy.ndimage import gaussian_filter1d


[docs]def moving_window(traces, func, window): """ Helper function for multi-trace attribute generation. This function applies a 3D function func to process a region of shape `window` over a dataset `data`. """ wrapped = lambda x: func(x.reshape(window)) return generic_filter(traces, wrapped, window)
[docs]def marfurt(traces): """ Marfurt, K., V. Sudhaker, A. Gersztenkorn, K. D. Crawford, and S. E. Nissen, 1999, Coherency calculations in the presence of structural dip: GEOPHYSICS, 64, 104-111. doi:10.1190/1.1444508 """ i, x, t = traces.shape traces = traces.reshape(-1, t) square_sums = np.sum(traces, axis=0)**2 sum_squares = np.sum(traces**2, axis=0) c = square_sums.sum() / (sum_squares.sum() + 1e-12) return c / (i * x)
[docs]def gersztenkorn(traces): """ Gersztenkorn, A., and K. J. Marfurt, 1999, Eigenstructure‚Äźbased coherence computations as an aid to 3-D structural and stratigraphic mapping: GEOPHYSICS, 64, 1468-1479. doi:10.1190/1.1444651 """ # Stack traces in 3D traces into 2D array. traces = traces.reshape(-1, traces.shape[-1]) # Calculate eigenvalues of covariance matrix. cov = traces.dot(traces.T) vals = np.linalg.eigvalsh(cov) return vals.max() / (vals.sum() + 1e-12)
[docs]def gradients(traces, sigma): grads = [] for axis in range(3): grad = gaussian_filter1d(traces, sigma, axis=axis, order=1) grads.append(grad[..., np.newaxis]) return np.concatenate(grads, axis=3)
[docs]def moving_window4d(grad, window, func): """Applies the given function *func* over a moving *window*, reducing the input *grad* array from 4D to 3D.""" # Pad in the spatial dimensions, but leave the gradient dimension unpadded. half_window = [(x // 2, x // 2) for x in window] + [(0, 0)] padded = np.pad(grad, half_window, mode='reflect') out = np.empty(grad.shape[:3], dtype=float) for i, j, k in np.ndindex(out.shape): region = padded[i:i+window[0], j:j+window[1], k:k+window[2], :] out[i,j,k] = func(region) return out
[docs]def gst_calc(region): region = region.reshape(-1, 3) gst = region.T.dot(region) eigs = np.sort(np.linalg.eigvalsh(gst))[::-1] return (eigs[0]-eigs[1]) / (eigs[0]+eigs[1])
[docs]def gst_discontinuity(seismic, window, sigma=1): """ Gradient structure tensor discontinuity. Randen, T., E. Monsen, C. Singe, A. Abrahamsen, J. Hansen, T. Saeter, and J. Schlaf, 2000, Three-dimensional texture attributes for seismic data analysis, 70th Annual International Meeting, SEG, Expanded Abstracts, 668-671. """ grad = gradients(seismic, sigma) return moving_window4d(grad, window, gst_calc)
[docs]def discontinuity(traces, duration, dt, step_out=1, kind='gst', sigma=1): """ Compute discontinuity for a seismic section using one of various methods. Expects time or depth to be in the last axis of a 2D or 3D input. :param traces: A 2D or 3D NumPy array arranged as (cdp, twt) or (iline, xline, twt). :param duration: The length in seconds of the window trace kernel used to calculate the discontinuity. :keyword dt (default=1): The sample interval of the traces in sec. (eg. 0.001, 0.002, ...). Will default to one, allowing duration to be given in samples. :keyword step_out (default=1): The number of adjacent traces to the kernel to compute discontinuity over. :keyword kind (default='gst'): The method to use for the computation. Can be "marfurt", "gersztenkorn" or "gst" (gradient structure tensor). :keyword sigma (default=1): The width of the Gaussian function used to compute gradients. """ if traces.ndim == 2: traces = traces[:, None, :] window = 2*step_out+1, 1, int(duration / dt) elif traces.ndim == 3: window = 2*step_out+1, int(duration / dt), 2*step_out+1 else: raise NotImplementedError("Expected 2D or 3D seismic data.") methods = { "marfurt": moving_window(traces, marfurt, window), "gersztenkorn": moving_window(traces, gersztenkorn, window), "gst": gst_discontinuity(traces, window, sigma) } return np.squeeze(methods[kind])
similarity = discontinuity