Mondaic - Full Waveform Solutions

Cross correlation misfit without observed data.

This misfit formulation is based on that described in equation (11.25) from Fichtner, 2011 (https://doi.org/10.1007/978-3-642-15807-0). This corresponds to,

\\mathbf{f}^\\dagger = \\frac{1}{\\| \\partial_t \\varphi \\|_2^2} \\partial_t \\varphi \\, \\delta (\\mathbf{x} - \\mathbf{x}_\\mathrm{r}),

where

\\mathbf{f}^\\dagger

is the adjoint source,

\\varphi

is the synthetic waveform, and

\\delta (\\mathbf{x} - \\mathbf{x}_\\mathrm{r})

is a sampling function that extracts the waveforms at the receiver location

\\mathbf{x}_\\mathrm{r}

Note that this function is only intended for computing the adjoint source for the given synthetic waveforms. The returned misfit value is meaningless, as no quantity is computed for it.

SIGNATURE

def cross_correlation_no_observed_data(
    data_synthetic: npt.NDArray,
    sampling_rate_in_hertz: float,
    data_observed: None = None,
) -> tuple[float, npt.NDArray]: ...

ARGUMENTS

Required

data_synthetic

Type:	`npt.NDArray`
Description:	synthetic waveforms.

Required

sampling_rate_in_hertz

Type:	`float`
Description:	Sampling rate.

Optional

data_observed

Type:	`None`
Default value:	`None`
Description:	observed waveforms. Must be None!

RETURNS

Return type: tuple[float, npt.NDArray]

tuple of misfit value and adjoint source

Getting Started

First Steps

Next Steps

Models and topography

Meshing

Salvus' UnstructuredMesh

Meshing of layered models

Importing external meshes

Sources and receivers

Waveform physics

Materials and Anisotropy

Data analysis

Inversion

Full-waveform inversion

Advanced Interface

Seismology

Geotech

NDT

Real data continental-scale FWI

Near Surface

Analytic Tests

Gradient Tests

salvus.opt.misfits.cross_correlation_time_shift

Functions

cross_correlation_no_observed_data()

cross_correlation_time_shift()

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