{"id":15303,"date":"2026-07-28T14:35:19","date_gmt":"2026-07-28T14:35:19","guid":{"rendered":"https:\/\/blog.geostru.eu\/joint-masw-hvsr-analysis-non-uniqueness\/"},"modified":"2026-07-28T14:35:19","modified_gmt":"2026-07-28T14:35:19","slug":"joint-masw-hvsr-analysis-non-uniqueness","status":"publish","type":"post","link":"https:\/\/blog.geostru.eu\/en\/joint-masw-hvsr-analysis-non-uniqueness\/","title":{"rendered":"How many different profiles explain the same MASW dataset? We counted 122"},"content":{"rendered":"<p><strong>Every geophysical technique suffers from non-uniqueness: many different subsoil models are compatible with the same measurement.<\/strong> This is not a shortcoming of the instruments, it is a property of the information the measurement carries. We set out to measure how much it really weighs, and the result surprised us.<\/p>\n<h2>The experiment<\/h2>\n<p>We started from a <strong>known<\/strong> subsoil profile, eight layers, with a Vs30 of 325 m\/s. From that profile we generated the dispersion curve a MASW survey would have measured. Then we pretended not to know the answer and worked backwards: from the data, reconstruct the ground. Two hundred times, with different initial assumptions.<\/p>\n<p>The advantage of working this way is that <strong>we know the right answer<\/strong>. With field data you can never tell whether the profile you obtained is the true one; here you can, and the error can be measured.<\/p>\n<h2>One hundred and twenty-two profiles, all &#8220;correct&#8221;<\/h2>\n<p>Out of 200 attempts, <strong>122 produced a profile explaining the dispersion data with an error below 3%<\/strong>: a fit any operator would consider excellent.<\/p>\n<p>Those 122 profiles are not variations on a theme. They are different profiles:<\/p>\n<ul>\n<li>the lowest has <strong>Vs30 = 300 m\/s<\/strong><\/li>\n<li>the highest has <strong>Vs30 = 679 m\/s<\/strong><\/li>\n<\/ul>\n<p>The boundary between class B and class C \u2014 360 m\/s \u2014 falls in the middle of the distribution: <strong>83 profiles fall in class C, 39 in class B<\/strong>. One profile in three, from identical data, leads to a different seismic classification.<\/p>\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/blog.geostru.eu\/wp-content\/uploads\/sites\/9\/2026\/07\/fig-ventaglio-en.png\" alt=\"The 122 equivalent profiles\"\/><figcaption>In grey, the 122 profiles that explain the same MASW dataset equally well. Dashed blue: the true profile; gold: the one selected by adding the H\/V curve.<\/figcaption><\/figure>\n<p>This is the point that usually remains unspoken: when software returns <em>one<\/em> profile, it is not saying the others are wrong. It is saying that <strong>it has stopped searching<\/strong>.<\/p>\n<h2>What happens when you add the H\/V curve<\/h2>\n<p>We took those 122 profiles \u2014 all indistinguishable on the basis of dispersion alone \u2014 and asked each of them to explain <strong>also<\/strong> the H\/V curve measured at the same point with a three-component tromometer.<\/p>\n<p>The profile that explains it best has <strong>Vs30 = 324 m\/s<\/strong>. The true value was <strong>325 m\/s<\/strong>.<\/p>\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/blog.geostru.eu\/wp-content\/uploads\/sites\/9\/2026\/07\/fig-istogramma-en.png\" alt=\"Vs30 distribution\"\/><figcaption>Distribution of the Vs30 values of the 122 equivalent profiles, with the subsoil class bands. The dashed line marks the true value.<\/figcaption><\/figure>\n<p>This is not a marginal improvement: it is the step from a problem with hundreds of solutions to a problem with one. The H\/V curve alone would not have been enough to reconstruct the profile \u2014 but it is <strong>exactly the information MASW is missing<\/strong> in order to be decisive.<\/p>\n<blockquote>\n<p>The H\/V curve tells you <strong>where the bottom is<\/strong>. MASW dispersion tells you <strong>what lies above it<\/strong>. Neither of them, on its own, tells you both.<\/p>\n<\/blockquote>\n<h2>The limit almost nobody states: the spread length<\/h2>\n<p>There is a second, even more practical aspect, which emerged while working on a real case.<\/p>\n<p>A MASW survey reliably resolves wavelengths of the order of the <strong>spread length<\/strong>. Each picked point, at frequency <em>f<\/em> and phase velocity <em>v<\/em>, corresponds to a wavelength \u03bb = v\/f, and the investigated depth lies roughly between \u03bb\/3 and \u03bb\/2.<\/p>\n<table>\n<thead>\n<tr>\n<th>Spread length<\/th>\n<th>Depth actually investigated<\/th>\n<th>Vs30 determinable?<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>24 m<\/td>\n<td>8\u201312 m<\/td>\n<td>no, largely extrapolated<\/td>\n<\/tr>\n<tr>\n<td>48 m<\/td>\n<td>16\u201324 m<\/td>\n<td>partly<\/td>\n<\/tr>\n<tr>\n<td>72 m<\/td>\n<td>24\u201336 m<\/td>\n<td>yes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The comparison with the 30 metres required by Vs30 is immediate: <strong>with short spreads the deeper part of the profile is not measured, it is extrapolated<\/strong>. And that is precisely the portion the H\/V curve, which measures the resonance of the whole column, is able to constrain.<\/p>\n<p>In a real case with a 24-metre spread, two points had been picked at 4.7 and 5.0 Hz with velocities of 491 and 428 m\/s: wavelengths of <strong>104 and 85 metres<\/strong>, more than four times the spread. To explain them, the inversion placed a 717 m\/s substratum at 18 metres depth \u2014 <strong>a bedrock that does not exist<\/strong>. The fit remained excellent and no indicator flagged the problem. Once those two points were removed, the conflict disappeared.<\/p>\n<h2>The error that leaves no trace<\/h2>\n<p>Finally, there is an error that happens in the field, and it is invisible. In the velocity spectrum one identifies a well defined curve and interprets it as the fundamental mode. Sometimes it is not: when energy spreads onto the higher modes, the fundamental can be weak or entirely absent, and the most visible curve is in fact a higher mode.<\/p>\n<p>In our tests, attributing to the fundamental a curve that was instead the first higher mode shifted the Vs30 from 325 to <strong>451 m\/s<\/strong>: a wrong subsoil class, with a dispersion fit error <strong>below 1%<\/strong>. Repeated 155 times, the error proved systematic \u2014 always in the same direction, never random.<\/p>\n<p>A mode misinterpretation does not produce uncertainty. It produces a wrong answer, precise and consistent.<\/p>\n<h2>How it is done, in practice<\/h2>\n<ol>\n<li><strong>In the field<\/strong>: at the same point, the usual MASW spread and a 15\u201320 minute HVSR recording with a three-component tromometer, preferably at the centre of the spread.<\/li>\n<li><strong>In Easy MASW<\/strong>: pick the dispersion curve, assigning its own mode number to each curve, and export the modal curves.<\/li>\n<li><strong>In Easy HVSR<\/strong>: import the dispersion and run the joint inversion. A single Vs profile, consistent with both measurements.<\/li>\n<\/ol>\n<h2>What to take away<\/h2>\n<ul>\n<li><strong>A low misfit does not certify the result.<\/strong> It says the model is compatible with the data, not that it is the only one. The right question is: <em>how many other models get there too?<\/em><\/li>\n<li><strong>MASW alone is an under-determined problem.<\/strong> It is not a limitation of the software: it is a property of the data. No algorithm can recover information the measurement does not contain.<\/li>\n<li><strong>An HVSR recording at the same point costs fifteen minutes<\/strong>, and it is the missing information. The ratio between acquisition cost and uncertainty reduction is probably the best available in applied near-surface geophysics.<\/li>\n<li><strong>The mode must be identified, not assumed.<\/strong> A &#8220;clean&#8221; spectrum is not automatically a fundamental mode.<\/li>\n<li><strong>Beware of values close to class boundaries.<\/strong> 360 m\/s separates B from C: a result of 350 or 380 m\/s obtained from a single method is a design decision resting on an uncertainty that has never been measured.<\/li>\n<\/ul>\n<h2>A methodological note<\/h2>\n<p>The figures in this article come from <strong>synthetic data<\/strong>: known profile, computed curves, no instrumental noise. This is a deliberate choice \u2014 only this way is the exact answer known and the error measurable.<\/p>\n<p>With real data the situation is <strong>harder<\/strong>, not easier: noise, three-dimensional effects, H\/V peaks of anthropic origin. The non-uniqueness measured here is therefore an optimistic estimate.<\/p>\n<hr\/>\n<p><em>Joint MASW + HVSR analysis is available in <strong>Easy MASW<\/strong> and <strong>Easy HVSR<\/strong>. A complete technical guide, with the step-by-step procedure and practical advice for the inversion, can be downloaded as a PDF: <a href=\"https:\/\/blog.geostru.eu\/wp-content\/uploads\/sites\/9\/2026\/07\/Analisi-congiunta-MASW-HVSR-guida-en.pdf\">Joint MASW + HVSR analysis \u2014 guide<\/a>.<\/em><\/p>\n<p><em>Online manuals: <a href=\"https:\/\/help.geostru.io\/masw\/en\/\">help.geostru.io\/masw<\/a> \u00b7 <a href=\"https:\/\/help.geostru.io\/easyhvsr\/en\/\">help.geostru.io\/easyhvsr<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Every geophysical technique suffers from non-uniqueness: many different subsoil models are compatible with the same measurement. This is not a shortcoming of the instruments, it is a property of the information the measurement carries. We set out to measure how much it really weighs, and the result surprised us. The experiment We started from a&hellip;<\/p>\n","protected":false},"author":16658,"featured_media":15294,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2665,2662,2659,2658,2652,2661,1795,2663,2664,2653],"class_list":["post-15303","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ambiente","tag-applied-geophysics","tag-dispersion-curve","tag-easy-hvsr","tag-easy-masw","tag-hvsr","tag-joint-analysis","tag-masw","tag-seismic-microzonation","tag-subsoil-class","tag-vs30","category-1","description-off"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.0 (Yoast SEO v25.0) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Joint MASW + HVSR analysis: one technique is not enough<\/title>\n<meta name=\"description\" content=\"122 different profiles explain the same MASW dataset, with Vs30 from 300 to 679 m\/s. 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