MakeRespSP: Calculate Poles and Zeros of Short-Period Sensor

In TDD: Time-Domain Deconvolution of Seismometer Response

Description

Many mechanical short-period seismometers are characterized by three parameters: the natural angular frequency (omega naught), damping coefficient (h), and sensitivity. The response of these sensors to a velocity impulse has two poles and two zeros; the response is zero at the origin, increases roughly proportionately with f^2 up to a low corner, and is flat above the low corner.

The differential equation describing this, where y is the output voltage and v is the velocity of the ground, is

y” + 2*h*omega_0*y' + omega_0^2*y = Sense * v” Some short-period sensors are customizable, so it is very important to make sure you use the correct parameters for your installation here.

Usage

MakeRespSP(h, omega0, Sense, f_Sense = NULL)

Arguments

h	Damping coefficient (unitless, 1 for critical damping)
omega0	Natural angular frequency (rad/s)
Sense	Sensitivity in passband (V * s/m)
f_Sense	If given, the frequency (Hz) at which Sense is valid. If NULL (which should ordinarily be the case), Sense is assumed to be valid at frequencies much higher than the low corner.

Value

List including the following elements:

Sense	Sensitivity of instrument (V * s/m)
Knorm	Normalization constant
poles	Poles of Laplace transform of instrument impulse response (rad/s)
np	Number of poles
zeros	Zeros of Laplace transform of instrument impulse response (rad/s)
nz	Number of zeros

Author(s)

Jake Anderson

See Also

GetPZ ReadInstr

Examples

# L4C3D
omega0 = 2*pi # 1 Hz natural frequency * 2pi
h = 0.707
Sense = 171
MakeRespSP(h, omega0, Sense)

Example output

Loading required package: signal

Attaching package: 'signal'

The following objects are masked from 'package:stats':

    filter, poly

Loading required package: RSEIS
Loading required package: pracma

Attaching package: 'pracma'

The following objects are masked from 'package:RSEIS':

    detrend, hypot, logspace, peaks, trapz

The following objects are masked from 'package:signal':

    conv, ifft, interp1, pchip, polyval, roots


Attaching package: 'TDD'

The following object is masked from 'package:RSEIS':

    ReadInstr

$Sense
[1] 171

$poles
[1] -4.442212-4.443554i -4.442212+4.443554i

$np
[1] 2

$zeros
[1] 0 0

$nz
[1] 2

$Knorm
[1] 1

TDD documentation built on May 2, 2019, 4:51 a.m.