moment_tensor
¶
This module provides various moment tensor related utility functions.
It can be used to convert between strike-dip-rake and moment tensor representations and provides different options to produce random moment tensors.
Moment tensors are represented by MomentTensor
instances. The
internal representation uses a north-east-down (NED) coordinate system, but it
can convert from/to the conventions used by the Global CMT catalog
(up-south-east, USE).
If not otherwise noted, scalar moment is interpreted as the Frobenius norm
based scalar moment (see MomentTensor.scalar_moment()
. The scalar
moment according to the “standard decomposition” can be found in the
output of MomentTensor.standard_decomposition()
.
- random_axis(rstate=None)[source]¶
Get randomly oriented unit vector.
- Parameters:
rstate –
numpy.random.RandomState
object, can be used to create reproducible pseudo-random sequences
- rotation_from_angle_and_axis(angle, axis)[source]¶
Build rotation matrix based on axis and angle.
- Parameters:
angle – rotation angle [degrees]
axis – orientation of rotation axis, either in spherical coordinates
(theta, phi)
[degrees], or as a unit vector(ux, uy, uz)
.
- random_rotation(x=None)[source]¶
Get random rotation matrix.
A random rotation matrix, drawn from a uniform distrubution in the space of rotations is returned, after Avro 1992 - “Fast random rotation matrices”.
- Parameters:
x – three (uniform random) numbers in the range [0, 1[ used as input to the distribution tranformation. If
None
, random numbers are used. Can be used to create grids of random rotations with uniform density in rotation space.
- random_strike_dip_rake(strikemin=0.0, strikemax=360.0, dipmin=0.0, dipmax=90.0, rakemin=-180.0, rakemax=180.0)[source]¶
Get random strike, dip, rake triplet.
Note
Might not produce a homogeneous distribution of mechanisms. Better use
MomentTensor.random_dc()
which is based onrandom_rotation()
.
- to6(m)[source]¶
Get non-redundant components from symmetric 3x3 matrix.
- Returns:
1D NumPy array with entries ordered like
(a_xx, a_yy, a_zz, a_xy, a_xz, a_yz)
- symmat6(a_xx, a_yy, a_zz, a_xy, a_xz, a_yz)[source]¶
Create symmetric 3x3 matrix from its 6 non-redundant values.
- values_to_matrix(values)[source]¶
Convert anything to moment tensor represented as a NumPy array.
Transforms
MomentTensor
objects, tuples, lists and NumPy arrays with 3x3 or 3, 4, 6, or 7 elements into NumPy 3x3 array objects.The
values
argument is interpreted depending on shape and type as follows:(strike, dip, rake)
(strike, dip, rake, magnitude)
(mnn, mee, mdd, mne, mnd, med)
(mnn, mee, mdd, mne, mnd, med, magnitude)
((mnn, mne, mnd), (mne, mee, med), (mnd, med, mdd))
- moment_to_magnitude(moment)[source]¶
Convert scalar moment to moment magnitude Mw.
- Parameters:
moment – scalar moment [Nm]
- Returns:
moment magnitude Mw
Moment magnitude is defined as
where is the scalar moment given in [Nm].
Note
Global CMT uses 10.7333333 instead of 10.7, based on [Kanamori 1977], 10.7 is from [Hanks and Kanamori 1979].
- magnitude_to_moment(magnitude)[source]¶
Convert moment magnitude Mw to scalar moment.
- Parameters:
magnitude – moment magnitude
- Returns:
scalar moment [Nm]
- euler_to_matrix(alpha, beta, gamma)[source]¶
Given euler angle triplet, create rotation matrix
Given coordinate system (x,y,z) and rotated system (xs,ys,zs) the line of nodes is the intersection between the x,y and the xs,ys planes.
- Parameters:
alpha – is the angle between the z-axis and the zs-axis [rad]
beta – is the angle between the x-axis and the line of nodes [rad]
gamma – is the angle between the line of nodes and the xs-axis [rad]
Usage for moment tensors:
m_unrot = numpy.array([[0,0,-1],[0,0,0],[-1,0,0]]) euler_to_matrix(dip,strike,-rake, rotmat) m = num.dot(rotmat.T, num.dot(m_unrot, rotmat))
- unique_euler(alpha, beta, gamma)[source]¶
Uniquify eulerian angle triplet.
Put eulerian angle triplet into ranges compatible with
(dip, strike, -rake)
conventions in seismology:alpha (dip) : [0, pi/2] beta (strike) : [0, 2*pi) gamma (-rake) : [-pi, pi)
If
alpha1
is near to zero,beta
is replaced bybeta+gamma
andgamma
is set to zero, to prevent this additional ambiguity.If
alpha
is near topi/2
,beta
is put into the range[0,pi)
.
- as_mt(mt)[source]¶
Convenience function to convert various objects to moment tensor object.
Like
MomentTensor.from_values()
, but does not create a newMomentTensor
object whenmt
already is one.
- class MomentTensor(m=None, m_up_south_east=None, m_east_north_up=None, strike=0.0, dip=0.0, rake=0.0, scalar_moment=1.0, mnn=None, mee=None, mdd=None, mne=None, mnd=None, med=None, strike1=None, dip1=None, rake1=None, strike2=None, dip2=None, rake2=None, p_axis=None, t_axis=None, magnitude=None, moment=None)[source]¶
Moment tensor object
- Parameters:
m – NumPy array in north-east-down convention
m_up_south_east – NumPy array in up-south-east convention
m_east_north_up – NumPy array in east-north-up convention
strike,dip,rake – fault plane angles in [degrees]
p_axis,t_axis – initialize double-couple from p and t axes
scalar_moment – scalar moment in [Nm]
magnitude – moment magnitude Mw
Global CMT catalog moment tensors use the up-south-east (USE) coordinate system convention with (up), (south), and (east).
- ♦ mnn¶
float
, default:0.0
- ♦ mee¶
float
, default:0.0
- ♦ mdd¶
float
, default:0.0
- ♦ mne¶
float
, default:0.0
- ♦ mnd¶
float
, default:-1.0
- ♦ med¶
float
, default:0.0
- ♦ strike1¶
float
, optional
- ♦ dip1¶
float
, optional
- ♦ rake1¶
float
, optional
- ♦ strike2¶
float
, optional
- ♦ dip2¶
float
, optional
- ♦ rake2¶
float
, optional
- ♦ moment¶
float
, optional
- ♦ magnitude¶
float
, optional
- classmethod random_dc(x=None, scalar_moment=1.0, magnitude=None)[source]¶
Create random oriented double-couple moment tensor
The rotations used are uniformly distributed in the space of rotations.
- classmethod random_mt(x=None, scalar_moment=1.0, magnitude=None)[source]¶
Create random moment tensor
Moment tensors produced by this function appear uniformly distributed when shown in a Hudson’s diagram. The rotations used are unifomly distributed in the space of rotations.
- classmethod from_values(values)[source]¶
Alternative constructor for moment tensor objects
This constructor takes a
MomentTensor
object, a tuple, list or NumPy array with 3x3 or 3, 4, 6, or 7 elements to build a Moment tensor object.The
values
argument is interpreted depending on shape and type as follows:(strike, dip, rake)
(strike, dip, rake, magnitude)
(mnn, mee, mdd, mne, mnd, med)
(mnn, mee, mdd, mne, mnd, med, magnitude)
((mnn, mne, mnd), (mne, mee, med), (mnd, med, mdd))
MomentTensor
object
- eigenvals()[source]¶
Get the eigenvalues of the moment tensor in accending order.
- Returns:
(ep, en, et)
- eigensystem()[source]¶
Get the eigenvalues and eigenvectors of the moment tensor.
- Returns:
(ep, en, et, vp, vn, vt)
- m6_up_south_east()[source]¶
Get moment tensor in up-south-east convention as a six-element array.
- Returns:
(muu, mss, mee, mus, mue, mse)
- m6_east_north_up()[source]¶
Get moment tensor in east-north-up convention as a six-element array.
- Returns:
(mee, mnn, muu, men, meu, mnu)
- scalar_moment()[source]¶
Get the scalar moment of the moment tensor (Frobenius norm based)
The scalar moment is calculated based on the Euclidean (Frobenius) norm (Silver and Jordan, 1982). The scalar moment returned by this function differs from the standard decomposition based definition of the scalar moment for non-double-couple moment tensors.
- deviatoric()[source]¶
Get deviatoric part of moment tensor.
Returns a new moment tensor object with zero trace.
- standard_decomposition()[source]¶
Decompose moment tensor into isotropic, DC and CLVD components.
Standard decomposition according to e.g. Jost and Herrmann 1989 is returned as:
[ (moment_iso, ratio_iso, m_iso), (moment_dc, ratio_dc, m_dc), (moment_clvd, ratio_clvd, m_clvd), (moment_devi, ratio_devi, m_devi), (moment, 1.0, m) ]
- rotated(rot)[source]¶
Get rotated moment tensor.
- Parameters:
rot – ratation matrix, coordinate system is NED
- Returns:
new
MomentTensor
object
- random_rotated(angle_std=None, angle=None, rstate=None)[source]¶
Get distorted MT by rotation around random axis and angle.
- Parameters:
angle_std – angles are drawn from a normal distribution with zero mean and given standard deviation [degrees]
angle – set angle [degrees], only axis will be random
rstate –
numpy.random.RandomState
object, can be used to create reproducible pseudo-random sequences
- Returns:
new
MomentTensor
object
- other_plane(strike, dip, rake)[source]¶
Get the respectively other plane in the double-couple ambiguity.
- order_like(sdrs, sdrs_ref)[source]¶
Order strike-dip-rake pair post closely to a given reference pair.
- Parameters:
sdrs – tuple,
((strike1, dip1, rake1), (strike2, dip2, rake2))
sdrs_ref – as above but with reference pair
- kagan_angle(mt1, mt2)[source]¶
Given two moment tensors, return the Kagan angle in degrees.
After Kagan (1991) and Tape & Tape (2012).