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seis

Reflection Interface Methods

sim2x.seis_interface

Functions for interface reflectivity modelling.

This module contains functions for.

Zoeppritz full scattering matrix.

akirichards(thetai, vp1, vs1, rho1, vp2, vs2, rho2, method='avseth')

Aki-Richards forumlation of reflectivity functions.

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required
method Optional

Defaults to 'avseth' - avseth formulation 'ar' - original aki-richards

 'avseth'

Returns:

Type Description
(numpy.ndarray)

Rp(theta)

bortfeld(thetai, vp1, vs1, rho1, vp2, vs2, rho2)

Calculates the solution to the full Bortfeld equations (1961)

These are approximations which work well when the interval velocity is well defined.

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required

Returns:

Type Description
ndarray

Rp(thetai) P-wave reflectivity of angle theta

calcreflp(vp1, vs1, rho1, vp2, vs2, rho2)

Calculates the reflectivity parameters of an interface.

Parameters:

Name Type Description Default
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required

Returns:

Type Description
Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]

[rVp, rVs, rrho, rVsVp, dVp, dVs, drho]

shuey(thetai, vp1, vs1, rho1, vp2, vs2, rho2, mode='rtheta')

Shuey approximation to the Aki-Richards equations.

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required
mode Literal['rtheta', 'R0_G']

what to return 'rtheta' returns Rp(theta) 'R0_G' returns [R0,G] aka [A,B]

 'rtheta'

Returns:

Type Description
ndarray

if mode='rtheta' Rp(theta); if mode='R0_G' [R0, G]

snellrr(thetai, vp1, vs1, vp2, vs2)

Snell's reflection and refraction angles for a two layered half space.

Parameters:

Name Type Description Default
thetai float

downgoing p-wave angle of incidence for wavefront (radians)

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required

Returns:

Type Description
Tuple[float, numpy.ndarray, numpy.ndarray, numpy.ndarray]

returns a list of calculated angles using Snell's Law thetai = input angle of P-wave incidence and output angle P-wave reflection thetat = output angle of P-wave transmission phir = output angle of S-wave reflection phit = output angle of S-wave transmission

zoeppritz_pdpu_only(thetai, vp1, vs1, rho1, vp2, vs2, rho2)

Calculates the solution to an incident down-going P-wave ray and upgoing P-wave only.

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required

Returns:

Type Description

Rp

zoeppritz_ponly(thetai, vp1, vs1, rho1, vp2, vs2, rho2)

Calculates the solution to an incident down-going P-wave ray.

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required

Returns:

Type Description
Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]

(Rp, Rs, Tp, Ts) of amplitudes for reflected and transmitted rays

zoeppritzfull(thetai, vp1, vs1, rho1, vp2, vs2, rho2)

Full Zoeppritz scattering matrix solution

Parameters:

Name Type Description Default
thetai float

P-wave angle of incidence for wavefront in radians

 required
vp1 ndarray

p-velocity layer 1

 required
vs1 ndarray

s-velocity layer 1

 required
rho1 ndarray

density layer 1

 required
vp2 ndarray

p-velocity layer 2

 required
vs2 ndarray

s-veloicty layer 2

 required
rho2 ndarray

density layer 2

 required

Returns:

Type Description
ndarray

[Rp, Rs, Tp, Ts] of amplitudes for reflected and transmitted rays

Domain Conversion Methods

sim2x.twt_conv

calc_domain_range(domain_vol, srate=0.001)

Calculate the domain range so we convieniently land on whole numbers starting from near the limit of our data and incrementing at srate.

Parameters:

Name Type Description Default
vol

Volume mapping dims of domain_vol to target domain

 required
srate float

The sample rate in the target domain

 0.001

Returns:

Type Description

appropriate domain_stick for domain_vol to convert to

domain_convert_vol(domain_vol, ds, mapping_dims=('xline', 'iline'), interpolation_kind='linear', to_dim='twt', from_dim='depth', domain_vol_direction='forward', output_samples=None)

Convert volumes between different domains (e.g. TWT to DEPTH)

Parameters:

Name Type Description Default
domain_vol DataArray

A DataArray with the to_dim values for from_dim

 required
ds Dataset

A Dataset with the properties to depth convert. Has same dims s twt_vol

 required
mapping_dims Sequence[str]

The dimensions over which to map the funciton

 ('xline', 'iline')
interpolation_kind

As for scipy.interpolate.interp1d(kind=) or sinc. sinc uses internal algorithm

 'linear'
to_dim str

The domain dimension for the current input ds

 'twt'
from_dim str

The domain dimension to map to

 'depth'
domain_vol_direction Literal['forward', 'reverse']

If domain volume maps to_dim to from_dim use forward, otherwise `reverse.

 'forward'
output_samples Union[NoneType, Sequence[Sequence[Sequence[Sequence[Sequence[Any]]]]], numpy._array_like._SupportsArray[numpy.dtype], Sequence[numpy._array_like._SupportsArray[numpy.dtype]], Sequence[Sequence[numpy._array_like._SupportsArray[numpy.dtype]]], Sequence[Sequence[Sequence[numpy._array_like._SupportsArray[numpy.dtype]]]], Sequence[Sequence[Sequence[Sequence[numpy._array_like._SupportsArray[numpy.dtype]]]]], bool, int, float, complex, str, bytes, Sequence[Union[bool, int, float, complex, str, bytes]], Sequence[Sequence[Union[bool, int, float, complex, str, bytes]]], Sequence[Sequence[Sequence[Union[bool, int, float, complex, str, bytes]]]], Sequence[Sequence[Sequence[Sequence[Union[bool, int, float, complex, str, bytes]]]]]]

Specify the samples at which ds will be interpolated to using domain_vol. Should be a 1D array. Ignored if domain_vol_direction="reverse"

 None

Returns:

Type Description
Dataset

The properties of ds converted to domain using domain_vol

peg_time_interval(twt_vol, depth_surf, twt_surf, mapping_dims=('xline', 'iline'))

Shifts twt_vol to create such that the depth conversion of depth_surf with twt_vol matches twt_surf

Parameters:

Name Type Description Default
twt_vol DataArray

TWT volume in depth

 required
depth_surf DataArray

The depth surface at twt_surf

 required
twt_surf DataArray

The TWT surface at depth_surf

 required

time_integral(vp, depth_dim='depth')

Get the time integral from a vp Dataset with axis depth

Synthetic Seismic

sim2x.seis_synth

Functions necessary for synthetic seismic modelling (e.g. sim2seis).

convolution1d_vol(ds, reflectivity_key, wavelet_amp, mapping_dims=('xline', 'iline'))

Convolved a reflectivity array from a Dataset with a wavelet.

Wavelet must have same sample rate as seismic twt

Parameters:

Name Type Description Default
ds Dataset

A Dataset with the properties to depth convert. Has same dims s twt_vol

 required
mapping_dims Sequence[str]

The dimensions over which to map the funciton

 ('xline', 'iline')

Returns:

Type Description
Dataset

The properties of depth_ds converted to twt using twt_vol

reflectivity(theta, velp, vels, rho, method='full')

Reflectivity for theta from acoustic vectors

Parameters:

Name Type Description Default
theta float

P-wave incidence angle

 required
velp ndarray

P-wave velcoities

 required
vels ndarray

S-wave velocities

 required
rho ndarray

density values

 required
method Literal['full', 'zoep_pud', 'ar']

The modelling method to use

 'full'

Returns:

Type Description
ndarray

interface reflectivity arrays (padded 0 at front to keep same length as input)

reflectivity_vol(ds, theta, mapping_dims=('xline', 'iline'))

Convert elastic properties "vp", "vs" and "density" to reflectivity

Parameters:

Name Type Description Default
ds Dataset

A Dataset with the properties to depth convert. Has same dims s twt_vol

 required
mapping_dims Sequence[str]

The dimensions over which to map the funciton

 ('xline', 'iline')

Returns:

Type Description
Dataset

The properties of depth_ds converted to twt using twt_vol