seisgo.simulation

The simulation module provides a 1-D finite-difference acoustic wave solver and a layered velocity model builder for synthetic testing and method validation.

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Function Summary

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fd1d_dx4dt4 — 1-D FD Acoustic Solver

Solves the first-order acoustic wave equation on a 1-D spatial grid using:

• Spatial accuracy: O(Δx⁴) — 4th-order staggered-grid finite differences

• Temporal accuracy: O(Δt⁴) — Adams–Bashforth multi-step time integration

Note

Based on the scheme described in:

Bohlen, T., & Wittkamp, F. (2016). Three-dimensional viscoelastic time-domain finite-difference seismic modelling using the staggered Adams-Bashforth time integrator. Geophysical Journal International, 204(3), 1781–1788.

Parameter	Default	Description
x	required	1-D spatial grid vector (m or km, consistent with vmodel).
dt	required	Time step (s). Must satisfy CFL condition: dt ≤ 0.5 · Δx_max / v_max.
tmax	required	Total simulation duration (s).
vmodel	required	1-D velocity model, same length as x.
rho	required	1-D density model, same length as x.
xsrc	required	Source grid index (integer).
xrcv	required	Receiver grid index (integer).
stf_freq	1	Source time function frequency parameter: central frequency (Hz) for Ricker; width σ (s) for Gaussian.
stf_shift	None	Source onset time (s). Default: 3 / stf_freq for Ricker.
stf_type	"ricker"	Source wavelet: "ricker" or "gaussian".
t_interval	1	Output time sub-sampling factor. 1 = full resolution.

Returns: (tout, seisout)

• tout — time vector (s) starting from 0, accounting for source shift

• seisout — pressure seismogram at the receiver

CFL check

The solver raises ValueError if the provided dt exceeds the CFL limit:

\[dt_{\max} = 0.5 \cdot \frac{\Delta x_{\max}}{v_{\max}}\]

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build_vmodel — Layered Velocity Model Builder

Constructs a fine-grid 1-D layered velocity model with linearly increasing velocity between vmin and vmax across nlayer layers.

Parameter	Default	Description
zmax	required	Maximum model depth/length.
dz	required	Fine-grid spacing.
nlayer	required	Number of velocity layers.
vmin, vmax	required	Velocity range (surface to bottom).
rhomin, rhomax	required	Density range.
zmin	0	Starting depth.
layer_dv	None	Array of fractional velocity perturbations per layer, e.g. [-0.1, 0, 0.05, …].

Returns: (z, v, rho) — depth grid, velocity, and density arrays.

from seisgo import simulation
import numpy as np

# 500-point model, 5 layers, with layer 2 perturbed -10%
layer_dv = np.zeros(5)
layer_dv[1] = -0.10

z, v, rho = simulation.build_vmodel(
    zmax=500, dz=1.0, nlayer=5,
    vmin=1500, vmax=3500,
    rhomin=1800, rhomax=2500,
    layer_dv=layer_dv,
)