Galperin vs Orthogonal Seismometer Configurations: What’s the Difference and Why It Matters?

In seismic monitoring, triaxial seismometers are essential tools that capture ground motion in three dimensions. But not all triaxial sensors are designed the same way. Two dominant configurations exist: the orthogonal layout and the Galperin symmetric design. Understanding the difference between them is key when deciding how to choose a broadband seismometer or designing your seismic network.

Orthogonal Configuration: The Traditional Layout

Orthogonal seismometers use three sensing elements aligned at right angles:

  • X-axis (East-West)
  • Y-axis (North-South)
  • Z-axis (Vertical)

This configuration provides direct and intuitive measurements of ground motion along geographic axes. It is commonly found in strong-motion sensors and legacy seismic stations.

Pros:

  • Simple and direct mapping to geographic directions
  • Standard format for data processing
  • Useful in structural monitoring when orientation is controlled

Cons:

  • Requires precise alignment to true North and level installation
  • Uneven horizontal sensitivity
  • Prone to increased cross-axis coupling due to asymmetry

Galperin Configuration: The Modern Symmetric Design

First introduced by Evgeny Galperin, this configuration uses three identical sensors, each spaced 120° apart and tilted equally from vertical (typically ~35.26°). Rather than directly measuring along X, Y, and Z, these sensors capture intermediate components. Standard vertical and horizontal motion is then reconstructed through a simple mathematical transformation.

Galperin geometry forms the basis of modern broadband seismometers, including all broadband seismometers offered by QuakeLogic.

Pros:

  • Isotropic azimuthal sensitivity for uniform horizontal response
  • Mechanically balanced and compact design
  • Easier installation — no need for precise geographic orientation
  • Ideal for low-noise, high-fidelity broadband recording
  • Often includes self-leveling mechanisms

Cons:

  • Requires post-processing to derive standard components (Z, N, E)
  • May be unfamiliar to users expecting direct XYZ outputs

Coordinate Transformation in Galperin Systems

The raw sensor outputs (V1, V2, V3) from a Galperin layout are converted into vertical (Z) and orthogonal horizontal (X, Y or N, E) components through a transformation matrix. The result is functionally identical to orthogonal output — but with superior mechanical and dynamic performance.

To obtain standard seismic components — vertical (Z), north (N), and east (E) — from a Galperin-configured broadband seismometer, a mathematical transformation is applied to the raw outputs of the three equally tilted sensors.

Galperin sensors are mounted 120° apart in azimuth and tilted at approximately 35.26° from vertical. This symmetric geometry ensures equal sensitivity in all horizontal directions, making it ideal for high-fidelity broadband seismic recording.

The transformation to orthogonal components is handled by a fixed matrix derived from the Galperin geometry. Here’s a practical example in Python that demonstrates how to convert the raw Galperin outputs (V1, V2, V3) into Z, N, and E components:

import numpy as np

def galperin_to_orthogonal(V1, V2, V3):
    """
    Transforms Galperin outputs (V1, V2, V3) into orthogonal components (Z, N, E).
    
    Assumes Galperin sensors are tilted 35.26 degrees from vertical and 120 degrees apart in azimuth.
    """

    # Galperin angle in degrees and radians
    alpha_deg = 35.2643897  # approximately arccos(1/sqrt(3))
    alpha_rad = np.radians(alpha_deg)

    # Transformation matrix based on Galperin geometry
    # Source: Galperin 1985; commonly used form
    T = np.array([
        [np.cos(alpha_rad), np.cos(alpha_rad), np.cos(alpha_rad)],  # Z (vertical)
        [np.sin(alpha_rad), -0.5 * np.sin(alpha_rad), -0.5 * np.sin(alpha_rad)],  # N (North)
        [0, np.sqrt(3)/2 * np.sin(alpha_rad), -np.sqrt(3)/2 * np.sin(alpha_rad)]  # E (East)
    ])

    # Stack Galperin outputs into column vector
    V = np.array([V1, V2, V3])

    # Perform transformation
    Z, N, E = T @ V

    return Z, N, E

# Example usage
V1, V2, V3 = 0.1, 0.2, 0.15  # Example raw sensor outputs
Z, N, E = galperin_to_orthogonal(V1, V2, V3)

print("Vertical (Z):", Z)
print("North (N):", N)
print("East (E):", E)

This code is useful for researchers, engineers, or software developers integrating Galperin seismometers into their own data acquisition systems or post-processing pipelines.

Why Galperin Excels in Broadband Performance

Galperin-configured sensors offer lower cross-axis sensitivity, reduced internal noise, and azimuthal symmetry. This makes them particularly suited for high-precision seismological research.

Optimizing Your Network Design

Because Galperin-based instruments don’t require precise geographic orientation, they simplify field deployments and reduce installation error. This is especially helpful in large-scale projects and remote installations.

✅ QuakeLogic’s Seismometer Solution

At QuakeLogic, we exclusively offer Galperin-type broadband seismometers, engineered for superior sensitivity, symmetrical mechanical design, and fast, easy deployment. Our systems are:

  • Fully turnkey, with no licensing or calibration fees
  • Designed for broadband performance with low self-noise
  • Delivered with user-friendly software and optional remote monitoring tools
  • Compatible with standard seismic analysis workflows

Whether you’re deploying a temporary station or building out a national seismic network, Galperin configuration delivers the performance you need with the reliability you trust.

📞 Contact Us

Ready to upgrade your monitoring system? Reach out to our team at sales@quakelogic.net or browse our product line at products.quakelogic.net to explore QuakeLogic’s advanced broadband solutions.

DAM FAILURES IN MIDLAND, MICHIGAN – WHEN A DISASTER HITS, WILL YOU BE PREPARED?

When disaster strikes, we are all at risk! But the unprepared ones get hit the hardest.

The Edenville Dam collapsed and the Sanford Dam was breached in Midland, Michigan on last Tuesday (May 19) after days of heavy rain. In the midst of the Coronavirus pandemic, residents were ordered to evacuate because of rising waters. The collapsed Edenville Dam, built-in 1924, was rated in unsatisfactory condition while the Sanford Dam, which was built in 1925, was given a fair condition rating by the state.

Are other dams safe in the US?

On average, the nation’s dams are over 50 years old. At least 1,680 dams across the U.S. are currently rated in poor or unsatisfactory condition. These all pose potential risk according to this Associated Press article. Without urgent action, aging dams may not be able to adequately handle the intense rainfall and floods of a changing climate, as happened in the case of the Michigan dams. They may fail to protect people and property in cities and towns located nearby and downstream.

Introducing SMART DAMS

QUAKELOGIC is the only company using a cloud-based, AI-powered technology platform to perform continuous, autonomous structural assessments using data from sensors on the dam structure.

Deploying the QuakeLogic’s SENSOR DATA MANAGEMENT, ASSESSMENT, AND REPOSITORY TECHNOLOGY (SMART) on dams would significantly reduce needed search and inspection efforts in future events.

The SMART integrates manually and digitally read sensor recordings into a fully-automated unified monitoring system. It facilitates the acquisition and analysis of critical sensor data needed by the dam operators for proper operations and maintenance, and most importantly for the safety assessment of the dam.

The SMART helps to collect, organize, and evaluates sensor data routinely, sends immediate notifications upon exceedance of thresholds, and generate PDF reports regularly and on-demand.

The SMART is a cutting-edge system works with various types of sensors such as accelerometers, tiltmeters, potentiometers, strain gauges, thermocouples, weather stations, piezometers and seepage monitors. Comprehensive analytic information is visible in real-time on the mobile-friendly dashboard, providing proof and peace of mind that a dam is performing as expected.

In addition to SMART, our proprietary earthquake early warning (EEW) alerts provide a window of opportunity for action before earthquake shaking begins at the site. It can also trigger automated actions such as opening spillways, closing roads, etc. when every second counts.

Easy-to-understand, engineering-quality information about the real-time health of the dam supports operators to make informed decisions. Whether planning maintenance activities, or prioritizing critical response actions, QUAKELOGIC has you covered.

“Dams are vital in all communities. As we move toward recovery from COVID-19, it’s important to support the resiliency of dams by realtime monitoring and ensure that the dam owners have the support, tools, and resources to outsmart disasters.”

ON THE IMPORTANCE OF MONITORING TUNNELS FOR PROPER SEISMIC SAFETY ASSESSMENT AND RISK MANAGEMENT

Monitoring tunnels for vibrations and deformations is not only critical during the construction phase but also their service life.

In 2012, the Tokyo-bound Sasago Tunnel suffered significant damage when nearly 150 concrete ceiling panels collapsed and crushed three vehicles, including a van carrying six people that caught fire. The deficiencies in mounting components of the ceiling panels were to blame.

But, are tunnels safe during an earthquake?

A common belief that underground structures are safer because they move with the soil, while structures above ground sway back and forth during the earthquakes appears to be misleading. The impact of earthquakes on tunnels can be severe due to ground failures such as liquefaction, strong ground shaking, and fault crossing.

Liquefaction takes place when saturated soft soil deposits loose load-carrying capacity during strong shaking. This phenomenon can cause the ground surrounding tunnels to deform and shift, with potentially severe impacts. The slope instability and fault crossings may also create permanent deformations leading to a collapse of the tunnel.

After the 1906 San Francisco earthquake, the Wrights railway tunnel in southern Santa Cruz mountains was closed for more than a year due to the collapse of approximately 100-m-long part crossing the San Andreas Fault Zone. Another railway tunnel crossing the White Wolf Fault was seriously damaged during the 1952 magnitude 7.5 Kern County earthquake associated with this fault (Kontogianni and Stiros, 2003).

In 1999 a magnitude 7.2 hit the Duzce region in Turkey. Close to the fault rupture, twin highway tunnels on the major highway connecting Ankara to Istanbul were under construction. The tunnels were partially collapsed due to intense pulses of earthquake motion (near-fault effects) as their lines cross the shear zone of the North Anatolian Fault.

The excavation process during tunnel construction may itself trigger microearthquakes. The vibrations, therefore need to be monitored to identify such seismic activity whether they create any movements or cracks on the tunnel surface. The monitoring vibrations is also needed to estimate the rock formations ahead of the tunnel face to optimize the excavation parameters. Besides, the infrastructure surrounding the tunnel including buildings must be monitored especially in case of construction of new subway (metro) lines.

Structural health monitoring (SHM) system is essential for the seismic resilience of tunnels. A robust real-time SHM system not only allows for assessment of accelerations and deformations (displacements and strains) in tunnel linings but also facilitates the implementation of adaptive risk management. Such a system can assist the officials to make informed and timely decisions to protect people (such as drivers or construction workers) from life-threatening conditions. For example, the highway tunnel can be closed to traffic before any severe consequences take place. Such pro-active actions would not only save lives but also avoid liabilities.

QuakeLogic is the only company providing cloud-based AI-powered disaster risk management solutions to prevent and reduce human and economic losses risen during and after earthquakes. Our cutting-edge technology platform performs real-time autonomous structural assessments using sensor data and sends rapid notifications after an event with the level of shaking intensity and whether structural integrity is compromised. For tunnels, our platform provides meaningful and easy-to-understand information immediately after an earthquake. This timely and critical information helps the officials to plan their emergency response. We also provide a web-based display where the sensor information can be monitored in real-time. This solution can provide great benefits especially for tunnels under construction phase.

For emergency measures and safety of tunnels, QuakeLogic provides advanced monitoring systems together with real-time and autonomous data analytics.