Source code for bruges.transform.nmo

# -*- coding: utf-8 -*-
Normal moveout.

© 2017 Leo Uieda, licensed BSD 3-clause license.
import numpy as np
from scipy.interpolate import CubicSpline

[docs]def reflection_time(t0, x, vnmo): """ Calculate the travel-time of a reflected wave. Doesn't consider refractions or changes in velocity. The units must be consistent. E.g., if t0 is seconds and x is metres, vnmo must be m/s. Args: t0 (float): The 0-offset (normal incidence) travel-time. x (float): The offset of the receiver. vnmo (float): The NMO velocity. Returns: t (float): The reflection travel-time. """ t = np.sqrt(t0**2 + x**2/vnmo**2) return t
[docs]def sample_trace(trace, time, dt): """ Sample an amplitude at a given time using interpolation. Args: trace (1D array): Array containing the amplitudes of a single trace. time (float): The time at which I want to sample the amplitude. dt (float): The sampling interval. Returns: amplitude (float or None): The interpolated amplitude. Will be None if *time* is beyond the end of the trace or if there are fewer than two points between *time* and the end. """ # Use floor to get the index that is right before our desired time. before = int(np.floor(time/dt)) N = trace.size # Use the 4 samples around time to interpolate samples = np.arange(before - 1, before + 3) if any(samples < 0) or any(samples >= N): amplitude = None else: times = dt * samples amps = trace[samples] interpolator = CubicSpline(times, amps) amplitude = interpolator(time) return amplitude
[docs]def nmo_correction(cmp, dt, offsets, velocities): """ Performs NMO correction on the given CMP. The units must be consistent. E.g., if dt is seconds and offsets is meters, velocities must be m/s. Args: cmp (ndarray): The 2D array CMP gather that we want to correct. dt (float): The sampling interval. offsets (ndarray): A 1D array with the offset of each trace in the CMP. velocities (ndarray): A 1D array with the NMO velocity for each time. Should have the same number of elements as the CMP has samples. Returns: ndrray: The NMO corrected gather. """ nmo = np.zeros_like(cmp) nsamples = cmp.shape[0] times = np.arange(0, nsamples*dt, dt) for i, t0 in enumerate(times): for j, x in enumerate(offsets): t = reflection_time(t0, x, velocities[i]) amplitude = sample_trace(cmp[:, j], t, dt) # If the time t is outside of the CMP time range, # amplitude will be None. if amplitude is not None: nmo[i, j] = amplitude return nmo