The Optical Seismometer:

A New Technology for Seismographic Observations

Mark ZumbergeJonathan Berger

Presentation to CTBTO S&T 2011

The Earthquake Spectrum

• Resolve Noise Model:

• 10-12 m /√Hz at 10 Hz

• 10-11 ms-2/octave at 200 seconds

• Several mm maximum displacement

From Prospects for Low frequency Seismometry, 2005

• K is the spring stiffness (N/m)

• γ Viscous friction (Ns/m)

• X(t) time dependent ground motion

• Y(t) absolute mass motion

• Z(t) mass to frame (ground) displacement

• z(t) = y(t) - x(t)

As seismologists, we are interested in x(t), the actual ground motion!

The Seismometer Equation

Response of Seismometer Suspension

Force-Balance Seismometer

New Vertical Component Optical Seismometer

Mechanical geometry by Wielandt - leaf spring design

Optical system by Zumberge

Michelson InterferometerDisplacement Transducer

Ellipse Pattern

Fringe:- 3 x 10-7 m

Desired Resolution:- 10-6 fringe

Ellipse Fitting Algorithm• X(t) = X0 + A*Sin(p(t) + p0); Y = Y0 + B*Cos p(t)

• Sample X and Y at ~105 sps

• Represent ellipse in nonparametric form by eliminating pfrom these equations.

• Use linear least squares to find the 5 ellipse coefficients over a ~ 100 second epoch.

• Solve for optical phase, p(t), at 105 sps

• Decimate to desired sample rate (~400 sps)

Femtometer

Functionality

1. Digitize x, y at 100,000 sps

2. Time stamp3. Fit ellipse4. Solve for optical

phase (100,000 arctancalculations/s

5. Filter6. Format, store, and

forward data

Example of Raw Output

Comparison of iSTS1 with Standard STS-1

Long-Period Noise comparison of iSTS1 and STS1

New DesignIn-line Vertical Component

Monolithic, electrical discharge machined (EDM)suspension springs

Comparison of in-line Optical Seismometer with Standard Trillium-240

Comparison of in-line Optical Seismometer with Standard Trillium-240

Horizontal-Component Optical Seismometer

Monolithic, electrical discharge machinedFlexure

Comparison of iTilt with Standard Trillium and STS-1

Variance Ratio = 1.05e-3

Comparison of iTilt with Standard Trillium 240

Some Advantages of the Optical Seismometer

1. The optical sensor is a linear, high-resolution displacement sensor, providing about a 30-bit resolution digital output without a high-resolution analog-to-digital converter.

1. Bandwidth and resolution sufficient to resolve the GSN low noise model from DC to > 15 Hz.

2. Dynamic range sufficient to record the largest teleseisms and most regional and local earthquakes.

3. No electronics in the sensor package. Only optical fiber connections to the seismometer. Eliminates heat and noise pickup from connecting electrical cables.

Some Advantages of the Optical Seismometer

5. Smaller package — our design is applicable to both vault and borehole installations and should be relatively easy to manufacture.

6. It measures absolute displacement referenced to the wavelength of light.

5. Unlike standard feedback seismometers whose response and calibration are dependent upon numerous electronic and mechanical components, the calibration and response the optical seismometers are simple using only three free parameters that can be determined at any time through examination of the data.

Absolute Calibration with tides

Comparison of iTilt with Standard Trillium 240

Example of Ellipse Fits

Two-Component Horizontal Borehole Optical Seismometer