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 derives the shear wave velocity profile by interpreting at the same time the H/V curve measured in Easy HVSR and the dispersion curve obtained from a MASW survey carried out at the same location.

The problem it solves¶

The stratigraphic model obtained from the automatic search in Easy HVSR is not the exact model that generates the H/V curve: it is an estimate to be refined. This is not a limitation of the program, it is a property of the measurement.

The H/V curve accurately identifies the resonance frequency of the site, and therefore the depth of the main impedance contrast, but on its own it cannot determine how velocities are distributed along the profile: markedly different stratigraphic models can produce virtually identical H/V curves.

The MASW dispersion curve has the opposite weakness: it describes the sequence of velocities in the first few metres well, but loses sensitivity with depth and on its own leaves the position of the bedrock undetermined.

What ellipticity actually determines¶

Classic HVSR inversion, without dispersion, works like this: a stratigraphy is sought whose ellipticity — the theoretical H/V ratio produced by the model — is as close as possible to the measured H/V curve. Ellipticity is therefore the bridge between the data recorded by the tromometer and the stratigraphy: without it, the H/V curve would remain a graph that cannot be interpreted in terms of ground.

The result, however, is an estimate, not the solution. Ellipticity constrains the site resonance frequency well, and to a first approximation this depends on the ratio between the average velocity and the depth of the main contrast — not on the two terms taken separately. A slow, shallow soil and a faster, deeper one produce the same f0 and almost indistinguishable H/V curves.

This is precisely why the tutorial recommends locking the first layer with known values: without at least one piece of external information, the problem remains undetermined.

In one sentence: the H/V tells you where the bottom is, the MASW dispersion tells you what lies above it.

Requiring a single layered model to explain both curves removes most of the ambiguity: the dispersion fixes the shallow velocities, the H/V anchors the depth of the main contrast. Together they determine what each of them, on its own, leaves ambiguous.

A limitation worth knowing

The ellipticity of the fundamental Rayleigh mode is an approximate model of the H/V curve: real ambient noise also contains Love waves, higher modes and body waves. Moreover the absolute amplitude of the two curves is not directly comparable: what matters is the shape and above all the position of the peak. For this reason the ellipticity curve may appear lower than the average H/V curve in the chart without this indicating an error.

What you gain in practice

A more stable velocity profile, extending deeper, with a well defined bedrock and a Vs30/Vs,eq far less sensitive to the operator's choices.

What you need¶

The HVSR project processed as usual, up to the H/V curve.
A dispersion curve file with .dsp extension, exported from Easy MASW after picking. The MASW survey must have been carried out at the same location as the HVSR recording: if the two measurements belong to different points, joint analysis is meaningless.

Importing the dispersion curves¶

Select the Import MASW dispersion command and choose the .dsp file. The program confirms how many points and how many modes were read.

The file contains one line per point picked in Easy MASW, with the wave type, the mode number, the frequency in Hertz and the phase velocity in metres per second. It is a plain text file: if in doubt, it can be opened and checked with any editor.

Running the joint inversion¶

Once the dispersion has been imported, the automatic search evaluates models against both curves: the computed ellipticity is compared with the measured H/V curve, and the computed dispersion curve with the points imported from Easy MASW. The quantity being minimised is the weighted sum of the two residuals.

All the tools already available in the stratigraphic model remain valid:

locking thickness and velocity of individual layers, useful when the stratigraphy of the first few metres is known from a borehole or a direct test;
the search ranges (minimum and maximum thickness, minimum and maximum Vs) to narrow the solution space;
the increasing velocity constraint, where the geological setting justifies it.

Narrowing the search helps more than you would expect

Joint inversion is a problem with many possible solutions. Every independent piece of information you can impose - a known thickness, a measured velocity, a plausible range - reduces the search space and makes the result more reliable.

Automatic suggestions¶

At the end of each search the program analyses the result and reports, in the Suggestions box, the conditions that deserve attention. These are not error messages: the computation is valid, but something in the model or in the data is limiting the result. Among the checks:

model too simple to satisfy two curves (too few layers);
parameter stuck at a search limit — if a velocity or a thickness coincides with the minimum or maximum you set, it is the constraint deciding the result, not the data: widen it;
resonance not reproduced — the ellipticity peak departs too much from the measured one;
conflict between the two curves — the model reproduces one well and the other badly;
discarded dispersion points — for some points the indicated mode does not exist at the required frequencies, which often signals a mode assignment to be reviewed;
model depth insufficient for a controlled Vs30 estimate.

It is worth reading them before changing parameters by trial and error: in most cases they already point in the right direction.

The dispersion chart¶

When a dispersion has been imported, a chart appears comparing the points measured in Easy MASW with the curve computed from the current model, one colour per mode.

It is the most direct way to understand what is happening:

the computed curve does not reach the points at low frequencies → the model has no material fast enough at depth: raise the Vs max limit of the last layer. If the limit is already high and the curve still does not rise, check that those points lie within the useful band of the spread (see the Easy MASW manual);
the curve runs above the points at high frequencies → the shallow velocities of the model are too high. If the first layer is locked, it is the lock preventing it from coming down;
points of a higher mode fall close to the fundamental mode curve → the mode assignment in the picking needs reviewing.

Reading the result¶

When processing is complete, check both computed curves, not just one:

the model ellipticity overlaid on the measured H/V curve;
the model dispersion curve overlaid on the imported points.

An acceptable result reproduces both reasonably well. If one is reproduced well and the other clearly badly, the model is not reliable: this usually means the two measurements are not consistent with each other, and the cause should be looked for in the data before the search parameters.

The most frequent causes are: surveys carried out at different points, a dispersion picking assigned to the wrong mode, or an H/V peak of anthropic origin interpreted as stratigraphic.

Careful with mode identification¶

The mode number of each imported curve is the one assigned by the operator during picking in Easy MASW, and it is used unchanged.

If a curve is attributed to the wrong mode - typically a higher mode interpreted as the fundamental one - the inversion still converges to a solution with a very low residual, but the resulting profile is systematically overestimated in velocity.

A good fit does not validate the interpretation

The misfit value does not flag a mode assignment error. If the results are unexpected - in particular a Vs30 noticeably higher than the site geology would suggest - go back to the velocity spectrum in Easy MASW and review the mode assignment before changing the search parameters.