H/V Spectrum

The Tab named H/V Spectrum is divided into five sections: "H/V curve reliability"; "Peak reliability"; "Model"; "Automatic search"; "Results". The fourth of these is only present when the automatic search option is selected, as explained further below.

This Tab gathers all the functions useful for identifying the possible stratigraphy associated with the H/V spectral ratio processed so far, and therefore for determining a reliable value of the code parameter Vs,equ.

H/V curve reliability

This section, together with the next one, indicates the checks suggested by the SESAME project regarding the reliability of the H/V spectral ratio curve and of its peak processed so far. These checks are not binding for the identification of the model in the following sections, but if the user wants them to be satisfied it is necessary to go back to the previous phases of the analysis. For clarification regarding the checks see the section concerning the description of the technique within this manual.

Peak reliability

As detailed in the description of the previous section, this is part of the checks required by the SESAME project.

Model

This section contains all the tools useful for identifying, and possibly storing and evaluating, the stratigraphic model that best approximates the behavior detected with the H/V spectral ratio obtained up to this phase of the analysis. This section provides two modes for searching the model: manual and automatic.

Fields common to both modes

Number of modes

This field allows you to set the number of ellipticity curves relating to the modes to be displayed on the H/V spectral ratio chart of the model currently present (or loaded) in the model table.

Show multiple models

By selecting this option it is possible to display on the H/V spectral ratio chart the ellipticity curve relating to the stored models, listed and selected in the models table below.

Models table

This table gathers the models that have been stored, showing the name and the misfit value if calculated. In the first column there is a check mark for each stored model that allows you to exclude it from display: if the check mark is present the ellipticity curve of the model is represented on the H/V spectral ratio chart, otherwise it is excluded from display.

Store

This button allows you to insert the model currently present in the main model table into the list of stored models, and therefore into the models table, assigning it a name whose root is "Model" and whose suffix is a progressive number depending on the number of models currently stored. If you store while in automatic search mode, the misfit value is also stored.

Remove (models table)

Removes the model selected in the models table from the list of stored models.

Add

This button adds a layer at the end of the model stratigraphy.

Remove

This button removes the layer currently selected in the table below from the model stratigraphy.

Insert

This button inserts a layer into the model stratigraphy immediately before the one selected in the table below.

Import

This button allows you to import a stratigraphy from an XML file of a previous export from another GeoStru software.

Synthesize

Launches the calculation procedure needed to evaluate the ellipticity curve (or the curves if a number of modes greater than 1 is set) of the model currently present in the table below. If automatic search mode is active, the misfit value is also evaluated.

Manual mode

This mode allows you to manually search for a model that approximates the behavior of the H/V spectral ratio calculated in the previous phases. This mode simply consists of entering, within the table below, a number of layers that the user deems appropriate, and entering for each of them the geotechnical characteristics: the layer thickness expressed in meters; the unit weight (if submerged, enter the dry one directly) expressed in kN/m3; the Poisson's ratio; the shear-wave velocity expressed in m/s. By then pressing the button named Synthesize you immediately get the graphical output of the ellipticity curve relating to the entered model within the H/V spectral ratio chart.

Automatic mode

This mode allows you to perform an automatic search of the geotechnical characteristics of the layers of the model present in the table. By activating this mode, selecting it from the option of the same name above the model table, the additional section named Automatic search becomes visible, in which some parameters useful for this search mode can be set.

Note that the automatic search works exclusively on searching for the thicknesses and the shear-wave velocity.

Within the model table, additional columns become visible immediately to the left and right of those of the thickness and of the shear-wave velocity (i.e. the parameters on which the search is carried out). These new columns serve to indicate the variability limits of the parameter for the single layer, i.e. they identify a search interval of the parameter and whether that parameter should actually be considered within the search. The automatic search only works on these two parameters because, as the SESAME project itself has been able to confirm, the unit weight and the Poisson's ratio have little influence on the variability of the model response.

Therefore, in this mode, for the thickness and the shear-wave velocity of each layer, it is possible to indicate whether the single parameter should be included in the search, and if so what its variability limits are. In addition, it should be considered that in the HVSR technique, for the procedure to have its validity, it is necessary to know the characteristics of the first layer. This is why Easy HVSR asks for confirmation to constrain the parameters of the first layer if, at the start of the automatic search procedure, these have not yet been selected. This does not prevent proceeding anyway with a search that also includes the parameters of the first layer.

The thickness of the last layer is in any case constrained since it does not participate in the calculation, representing the half-space lying below the stratigraphy, and of which only the shear-wave propagation velocity is searched for, if any.

A further consideration to take note of concerns the fact that the automatic search does not optimize the number of layers, which therefore remains at the exclusive discretion of the user.

In this mode it is in any case possible to perform a manual search (through the same procedure described above), with the only difference that in this way the misfit value is also evaluated.

In addition, even if the automatic search provides a first solution, this can be relaunched again starting from the solution just found, because the automatic search finds only one possible solution.

N.B.: Given the very nature of the problem, i.e. the lack of definition of the source that generates the noise of the recording both in terms of amplitude and position, it does not provide any reliability on the amplitude of the H/V spectral ratio, which is why the automatic search does NOT provide the exact solution in the identification of the stratigraphic model, but only a starting point from which to begin a MANUAL "tuning" and "refinement" of the model by the user, whose interpretive ability deriving from technical-practical experience of this kind of problem cannot be limited by any method or device. Therefore the automatic search present in Easy HVSR is simply a tool to support the user in the interpretation of the results.

Automatic search

This section contains some parameters and information useful for the automatic search of the stratigraphic model that best approximates the behavior of the H/V spectral ratio.

Increasing velocity profile

This option, if selected, sets a constraint on the search for the shear-wave velocity, i.e. it imposes that the difference in shear-wave velocity between a layer and the one above it be equal to or greater than zero.

Misfit value

This value indicates how well the identified stratigraphic model approximates the behavior deducible from the H/V spectral ratio according to a criterion whereby a smaller misfit value, compared to a larger one, results in a better correspondence. In practice, if this value were ideally equal to zero, you would have the correct stratigraphy. This condition is obviously impossible, even just taking into account the fact that all the measurements made are affected by error. Therefore this value is essentially useful for comparing several model solutions with one another, in order to possibly choose the one with the lower value.

Maximum number of iterations

Since the automatic search of the stratigraphic model is an iterative process, this value serves to set a maximum number of models to be generated. It has a purely applicative value in the sense that it does not directly affect the calculation, which could in any case terminate before reaching this limit value, and therefore a high value of it does not necessarily coincide with a better approximation of the solution.

In fact, reaching the maximum number of iterations (saturation of the calculation progress bar at the bottom right in the status bar of the application window) means that the search has not produced a reliable result, and that the returned solution is only the best one found during the search process.

Results

This section simply shows the results of the entire analysis procedure so that the user can make their own considerations:

• The value of the frequency at which the peak (the maximum value) of the H/V spectral ratio is located, with its confidence interval;
• The value of the frequency at which the peak (the maximum value) of the ellipticity of the fundamental mode of the stratigraphic model currently in the model table is located;
• The value of the code parameter Vs30 relating to the stratigraphic model currently present in the model table. Graphical configuration

In the case where no layer is present in the model table, the graphical configuration of the right-hand part of the application window takes on the same graphical configuration of the previous analysis phase (previous Tab). When even a single layer is entered, the following charts are displayed: at the top the H/V spectral ratio chart is displayed with any ellipticity curves of the model in the main table and of those possibly stored and selected in the models table; immediately below, two charts, of which the one on the left is a graphical representation of the stratigraphic model present in the main table, while the one on the right is the trend of the shear-wave velocity profile with depth.

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