Seismic Transducers

 

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The seismic transducers do not require contact with the reference frame. However, they give a speed relative to the transducer speed at the start of the test. The initial motion must be determined from other considerations in the test setup and added to the relative speed.

The devices discussed in the Reference-Based section required a link of some type between the reference and the moving object. Seismic devices do not have this requirement. A seismic device refers to a transducer, which is based on a mass attached to the transducer base, usually with a linear spring. The base is attached to the surface whose motion is desired, and the motion of the seismic mass relative to the base is recorded with a motion transducer. The following figure shows the principal components of this transducer type. Use of the governing equation of motion for the seismic mass permits the determination of the motion of the base from the relative motion function.

   
Equation (٭)

 If the motion transducer in the seismic instrument measures the displacement of the mass relative to the base, the output of the transducer is proportional to the acceleration of the transducer base for a specific frequency range and the device is called an accelerometer . Acceleration measurement using this type of device (or with other types of accelerometers) permits the determination of the velocity–time function by integration through the application of Equation (٭). In this equation, ay(t) would be determined from the output of the accelerometer.

The simplicity of this concept is evident and, because integration is a smoothing process, the numerically introduced noise encountered with a “differentiation of displacement” method of speed measurement does not occur. However, other errors can be introduced. First, any error in the acceleration measurement will be carried over. However, additional precautions are necessary to obtain good results for speed measurement. The problem areas include the following:
• The initial speed, Vi, must be known at the beginning of the time of interest. Because this quantity is added to the change in speed, an error in it will be a constant on each value.
• A bias, or zero shift, in the accelerometer signal will be included as a constant acceleration, and thus introduce a linearly increasing error in the calculated values throughout the time interval of interest. This bias may be introduced from electrical or thermal characteristics of the circuit, or, in the case of measurement of accelerations during impact after a free fall, by the 1 g acceleration of gravity.
• If the frequency content of the acceleration falls outside the usable bandwidth of the accelerometer and recording circuit, errors in acceleration occur. The low-frequency cutoff depends on the recording equipment and circuit, and the high frequency cutoff depends on the natural frequency and damping of the accelerometer, as well as the bandwidth of each piece of equipment in the recording circuit.
• Accelerometer theory is based on harmonic excitation of the system. For many velocity measurement applications, the input is a transient. Combination of these two factors can result in inaccurate accelerometer data; for example, ringing may occur, and cause errors in the calculated speeds. This problem is accentuated for lightly damped accelerometers.

When this method of speed measurement must be used, a series of check tests should be conducted to evaluate the accuracy of the method for that particular system.
A variation of the above method is to put an integrating circuit in the accelerometer and perform the integration with an analog circuit. Then, the output of the “velocity” transducer is proportional to the change in speed. This type of device is subject to all of the potential error sources discussed above.

It can be shown that if the electromechanical transducer in a seismic instrument gives an output which is proportional to the speed on one end relative to the other end, then the output of the seismic transducer is proportional to the speed of the transducer in an inertial reference frame, i.e., relative to the earth, for input motion frequencies well above the natural period of the seismic mass. Thus, use of a linear velocity transducer as the motion measurement transducer in a seismic instrument makes it a “seismic velocity transducer.” This type of device is called several different names, including seismometer, geophone, and vibrometer, as well as velocity transducer.

The natural frequency and damping in these instruments are selected to match the application. As with an accelerometer, the usable bandwidth depends on these two characteristics. The low- requency limit for this type of transducer is dependent on the accuracy required in the measurement. As an example, it can be used to show that if an accuracy of 5% is required, the lowest data frequency must be 4.6 times the natural frequency of the transducer, and that the upper data frequency is not limited. In fact, the higher the upper frequency, the more accurate the results.

Seismometers are used for recording and studying motion from earthquakes, and these devices can
be quite large. Natural periods can be in the range of 10 s to 50 s, and damping is normally selected as 0.7 of critical to extend the frequency range as much as possible. Geophones are commonly used for oil well logging and related work. Their natural periods are in the vicinity of 10 s.

A manufacturer of this type of transducer is Wilcoxon Research Inc.( View the products and datasheets ). The other supplier of seismic trancducers is Nanometrics Inc.(You can see Nanometric's products and technical data here). Teledyne Brown Engineering and GeoSpace Corp. is another producer for these devices.

 

 

 

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