Horizontal to Vertical Spectral Ratio (HVSR)

Introduction

The Horizontal to Vertical Spectral Ratio (HVSR) is a measure of the difference in power between ambient/microseismic waves in the horizontal direction against those in the vertical direction. Specifically, we want to know at what frequency do these two directions differ the most. The reason this is of interest is because the horizontal component of these microtremors will exhibit a resonance at a specific frequency. This frequency can be related to a depth, thus giving the depth to a seismically-signficant subsurface boundary (often, the top of bedrock or bedrock interfaces). With HVSR, most of this can be done with the "background" seismicity that exists everywhere on Earth at all times.

HVSR has been used by geologists, geophysicists, geotechnical engineers, and others to rapidly obtain information about the subsurface and even structures above the surface.

History

HVSR is one of the few scientific techniques to have been carried out on the Earth, the Moon, and Mars.

Although the origins of the method go back to at least the 1970s, the SESAME project of the early 2000s is often credited with formalizing and codifying the processes.

Here is a brief timeline

• 1971: Nogoshi and Igarashi determine that ambient seismic waves they are using for site classification can largely be explained by Rayleigh surface waves. They also observe that a single seismometer exhibits differences in horizontal and vertical components at specific frequencies that appear to be higher with shallower depths and lower with deeper depths to important subsurface interfaces.
• 1980: Nakamura uses the ratio of the horizontal and vertical components to bypass the need for reference sites and carry out site classification on a per-site basis.
• Early 2000s: The SESAME project carries out intense tests of the method and codifies statistical measures for determining the validity of a measurement. They also develop software used to carry out HVSR and other analysis on ambient seismic data.
• November 2017: The Incorporated Research Institutions for Seismology (IRIS) begins development/hosting of its python HVSR code (on which SpRIT is based) on its public github repository.

Theory

• Ambient seismic data is recorded by (most commonly) a three-component seismometer
• Fundamental Frequency is being measured.
  • The horizontally-polarized surface waves will have a resonance at a certain frequency (i.e., the fundamental frequency)
  • At this frequency, the horizontal components will record much greater amount of seismic energy than the vertical component
• This fundamental frequency is converted to a depth to determine depth to important geologic interfaces (commonly, the top of bedrock)

The phenomenon measured by HVSR is described by the U.S. EPA:

A material naturally vibrates at a fundamental resonance frequency and amplifies incident waves with the same frequency upon contact. This phenomenon (i.e., resonance) can be excited by seismic noise encountering the overburden-bedrock interface, at which acoustic impedance generally changes. Acoustic impedance is a measure of resistance to acoustic energy and depends upon seismic velocity and density. A sufficient (i.e., 2:1) contrast must exist at the bedrock-sediment interface for it to be identified by the HVSR method (Bard and others, 2004).

Per Xu and Wang, 2021:

The horizontal-to-vertical spectral ratio (HVSR) has been extensively used in site characterization utilizing recordings from microtremor and earthquake in recent years...The main applications of HVSR are site classification, site effect study, mineral exploration, and acquisition of underground average shear-wave velocity structure. In site response estimates, the use of microtremors has been introduced long ago in Japan, while it has long been very controversial in this research area, as there are several studies reporting difficulties in recognizing the source effects from the pure site effects in noise recordings, as well as discrepancies between noise and earthquake recordings. In practice, the most reliable way is the borehole data, and the theoretical site response results were compared with the HVSR using shear wave to describe site response.

HVSR Practice

Data Acquisition

• Passive seismic data
  • Seismic signal originates primarily from the Ocean
  • The largest source is a place in the Atlantic Ocean just south of Greenland where ocean currents and bathymetry align just right so that the ocean waves push down on the ocean bottom to shake the ocean.
• A single, three-component seismometer (with no active noise source) is all that is needed to acquire the data
  • This means the data can be acquired quickly and with only one or two scientists (very low cost)

Data Analysis

While there are many intermediate steps that can increase the quality of the data, the basic HVSR processing steps are as follows:

• Specify parameters/read data
• OPTIONAL: Remove any data with excess/aberrant noise
• Generate Power Spectral Density curves (SpRIT uses Welch's method via Scipy or Obspy/Matplotlib)
  • Break up data into windows by time (these windows can overlap)
  • Carry out Fourier analysis to calculate power spectral density (PSD) for each window
  • Average together the PSD curves across all time windows for each component
  • OPTIONAL: Remove outlier PSD curves for each component
• Calculate H/V ratio at each frequency/period step at each time window
  • Average the H/V curves across all time windows
  • OPTIONAL: Remove outlier H/V curves
• Pick peaks (local maxima) in the averaged H/V curve and determine which peak is associated with the fundamental frequency
• Check validity of the peak(s)
  • SESAME Protocols are the most common way to do this
  • Generate a report based on this
  • Primary result: Fundamental Frequency (primary peak)
• Convert Fundamental frequency to depth

Usage

HVSR has become an important method in near-surface geophysics, particularly in glaciated regions. Its applications include:

• Site Classification: Understanding site effects for engineering purposes.
• Site Response Studies: Assessing how sites behave during earthquakes.
• Shear-Wave Velocity Mapping: Unveiling underground structures.
• Geologic mapping: Determining depth to bedrock in areas where it is buried beneath glacial sediments