This API reference is not for the latest stable Salvus version.

`salvus.opt.misfits.time_frequency_phase_misfit`

Time-frequency phase misfit and adjoint sources.

Functions

`time_frequency_phase_misfit_and_adjoint_source()`

def time_frequency_phase_misfit_and_adjoint_source(
    data_synthetic: numpy.ndarray,
    data_observed: numpy.ndarray,
    sampling_rate_in_hertz: float,
    segment_length_in_seconds: Union[
        int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64
    ],
    segment_overlap_fraction: Union[
        int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64
    ] = 0.75,
    frequency_limits: Sequence[
        Union[
            int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64
        ]
    ],
    absolute_value_threshold: Union[
        int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64
    ] = 0.001,
    taper_type: str = "hanning",
    stft_window: Union[str, Tuple[Union[str, float], ...]] = "hann",
    plot: bool = False,
) -> Tuple[float, numpy.ndarray]:
    ...

Compute a phase difference misfit in the time frequency domain together with an associated adjoint source.

Parameters

data_synthetic numpy.ndarray — Synthetic data.
data_observed numpy.ndarray — Observed data.
sampling_rate_in_hertz float — Sampling rate in Hertz.
segment_length_in_seconds Union[int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64] — Length of each segment for which an FFT will be computed. Should be at least as long and probably longer than the largest period of interest to be able to estimate their frequency domain representation. Longer windows create better frequency domain phase estimates but a worse temporal resolution. The algorithm will automatically select the next larger length that the FFT implementation can efficiently compute so no need to play any tricks here. It is always at a most a few samples more.
segment_overlap_fraction Union[int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64] — The overlap between two successive windows as a fraction of the segment length. More overlap causes a better temporal resolution but comes with a higher computational cost.
frequency_limits Sequence[Union[int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64]] — Either (f1, f2, f3, f4) or (f2, f3). In the latter case it will set f1 = 0.5 * f2 and f4 = 2 * f3. These are frequency limits for a Fourier domain bandpass filter. Every frequency smaller than f1 and larger than f4 will be completely filtered out, frequencies between f2 and f3 will be fully retained with them being tapered for f1 < f < f2 and f3 < f < f4.
absolute_value_threshold Union[int, numpy.int32, numpy.int64, float, numpy.float32, numpy.float64] — Only perform the phase difference measurement for frequencies whose absolute value is at least this fraction of the maximum absolute value of all frequencies. This is important because phase measurements for frequencies with little energy would otherwise distort the result and could potentially even dominate it. Frequencies with absolute values smaller than 0.5 * absolute_value_threshold * max_abs_value will be fully muted, those in between both bounds will be tapered.
taper_type str — Tapering function to use for the frequency and thresholding tapers. Currently supported are "hanning", "tanh", and "linear".
stft_window Union[str, Tuple[Union[str, float], ...]] — Desired window to use for the short term fourier transform used to compute the signals’ time frequency representations. Passed to scipy.signal.get_window() so please refer to it for all available choices. This can have quite an impact on the resulting adjoint sources so make to have a look at them before using this in production.
plot bool — Optionally plot some details about the computation. Useful for debugging and tuning.

Returns Tuple[float, numpy.ndarray] — Tuple of misfit value and adjoint source.