Joint MASW + HVSR analysis¶

Full guide (PDF)

An in-depth guide to the joint inversion is available for download: Joint MASW-HVSR analysis — guide (PDF).

Joint analysis means interpreting together the dispersion curve obtained from a MASW survey and the H/V curve recorded with a tromometer at the same location, in order to derive a single shear wave velocity profile consistent with both measurements.

Why combining the two measurements pays off¶

Every geophysical technique suffers from non-uniqueness: many different subsoil models are compatible with the same measured data.

With MASW this effect is pronounced: markedly different soil profiles can produce virtually identical dispersion curves, with Vs30 differences large enough to change the subsoil category. When the software returns a profile, therefore, it is not stating that the others are wrong: it is returning one of the profiles compatible with the data.

The two techniques complement each other:

the dispersion curve resolves the first few metres well, but loses sensitivity with depth;
the H/V curve does not by itself provide the velocity profile, but accurately identifies the site resonance frequency and therefore the depth of the main impedance contrast, typically the transition to bedrock.

Requiring a single model to explain both curves strongly reduces the ambiguity: the resulting profile is more stable, extends deeper and defines the bedrock more clearly.

A very favourable cost/benefit ratio

An HVSR recording normally requires 15-20 minutes of ambient noise with a three-component tromometer. In exchange for this additional time, the uncertainty on the profile is substantially reduced.

What is needed in the field¶

At the same survey point:

the usual MASW spread (geophones and active source);
an HVSR recording with a three-component tromometer, preferably placed at the centre of the spread.

Workflow¶

Processing takes place in successive stages, in two separate programs:

Stage	Program	Task
1	Easy MASW	Process the traces, pick the dispersion curve and export the curves.
2	Easy HVSR	Process the H/V curve, import the dispersion curves and run the joint inversion.
3	Easy MASW	Import the final model and check it against the velocity-frequency spectrum, to document it in this report too.

In short: Easy MASW prepares and exports the dispersion data, Easy HVSR runs the joint inversion, and the final model can travel back to Easy MASW for checking and reporting.

Stage 3 is optional and is needed when the technical report is produced with Easy MASW.

Exporting the dispersion curves from Easy MASW¶

Once picking is complete in the spectral analysis stage:

select the Export dispersion command from the Export group;
enter the file name, with the .dsp extension;
the program confirms the number of exported points.

All modal curves present in the picking are exported, each with its own mode number: the fundamental mode (mode 0) and any higher modes.

The exported file¶

The .dsp file is a plain text file, readable and verifiable with any editor. It contains one line per picked point:

# GeoStru - curve di dispersione
# onda;modo;freq_Hz;vel_m_s
R;0;4.7312;491.680
R;0;5.0421;427.760
R;1;8.1515;367.600

where:

onda: wave type the curve refers to (R = Rayleigh);
modo: 0 for the fundamental mode, 1 for the first higher mode, and so on;
freq_Hz: frequency of the point, in Hertz;
vel_m_s: phase velocity, in metres per second.

Lines beginning with # are comments. Decimal values use the dot as separator, so that the file can be read regardless of the computer's regional settings.

Importing the final model from the joint analysis¶

The velocity model obtained in Easy HVSR can be brought back here and checked against the velocity-frequency spectrum, on top of the picked points. Without this step the Easy MASW project would keep the model of the MASW-only processing, which in general does not coincide with the result of the joint analysis: the report would document a profile other than the one adopted.

In Easy HVSR, at the end of the Search, use Export velocity model and save the .vsm file.
Here, with the project of the same test open, select Import velocity model from the Export group.

The program loads the layers into the inversion table and immediately computes their theoretical dispersion curve, which appears overlaid on the velocity-frequency spectrum together with the picked points. The Vs profile, the Vs30 with the subsoil category and the report images are updated accordingly.

Picking must already be done

The import is there to check the model against the data of this test: if the dispersion curve has not been picked, there is nothing to compare it with and the command says so.

How to read the result¶

The percentage error and the misfit factor shown after the import are computed by Easy MASW on the points picked in this project: they tell how closely the joint model follows the dispersion curve measured here. They are a different number from the H/V misfit computed by Easy HVSR, which concerns the spectral ratio: both are reported separately in the report.

A sound joint model follows the picked points reasonably well even though it was not obtained by minimising those alone. A discrepancy visibly larger than that of the MASW-only inversion is normal and is the price of the additional H/V constraint; a very large one, instead, means the two measurements are not compatible — usually tests carried out at different points, or a mode assignment that needs revisiting.

The layers arrive locked¶

After the import, Vs and thicknesses of all layers are locked (padlock in the Thickness locked and Fixed Vs columns): the documented model must remain exactly the one from the joint analysis, and a new computation leaves it unchanged.

If instead you want to start from that model for a new inversion with MASW data only, just clear the padlocks in the table: the search limits are already set around the imported values.

Provenance is lost if the model is modified

In the report, below the inversion table, a Model imported from line appears with the misfit and the resonance frequencies declared by Easy HVSR. That line disappears as soon as the model is modified — by unlocking the layers and recomputing, or by changing a value in the table — because the model is no longer the one from the joint analysis.

Which points to pick: the useful band depends on the spread length¶

This is the issue that most often spoils a joint analysis, and it does not concern the software: it concerns the geometry of the acquisition.

A MASW survey reliably resolves wavelengths of the order of the spread length. Each picked point, at frequency f and phase velocity v, corresponds to a wavelength:

\[\lambda = \frac{v}{f}\]

If λ exceeds twice the spread length, that point is beyond the reach of the measurement: it carries no information about the ground, only the uncertainty of the edge of the spectrum.

An out-of-band point does not raise an error: it produces a wrong result

With a 24 m spread, a point picked at 4.7 Hz and 490 m/s corresponds to λ = 104 m, more than four times the spread length. To explain it, the inversion is forced to place a very fast substratum at great depth — a bedrock that does not exist. The fit remains excellent and no indicator flags the problem.

Rule of thumb: before exporting, compute λ = v/f for the points at the lowest frequencies and compare it with the spread length. Points whose λ exceeds twice the spread length should be excluded from the picking.

The depth actually investigated¶

From the maximum usable wavelength follows the investigation depth, which is approximately between λ_max/3 and λ_max/2.

Spread length	Maximum useful λ	Investigated depth
24 m	~24-48 m	8-12 m
48 m	~48-96 m	16-24 m
72 m	~72-144 m	24-36 m

The comparison with the 30 m required by Vs30 is immediate: with short spreads the deeper part of the profile is not measured, it is extrapolated. That is exactly the portion the H/V curve, which measures the resonance of the whole column, is able to constrain.

In other words: the shorter the spread, the more joint analysis stops being a refinement and becomes a necessity.

Careful with mode identification¶

The mode number associated with each curve is not inferred by the program: it is the one the operator assigned during picking, and it is passed to the inversion unchanged.

This is the most delicate aspect of the whole procedure. The fundamental mode may be weakly energetic or entirely absent from the spectrum, so that the most visible curve is in fact a higher mode: interpreting it as the fundamental leads to a systematically overestimated velocity profile, with no anomaly appearing in the curve fit.

A good fit does not validate the interpretation

If the dispersion curve is attributed to the wrong mode, the inversion still converges to a solution with a very low error: the misfit value does not flag the mistake. Before exporting, check that the mode assignment on the spectrum is consistent with the energy distribution, and when in doubt consider the possibility that the visible curve is a higher mode.