{"id":15305,"date":"2026-07-28T14:35:20","date_gmt":"2026-07-28T14:35:20","guid":{"rendered":"https:\/\/blog.geostru.eu\/analiza-combinata-masw-hvsr-non-unicitate\/"},"modified":"2026-07-28T14:35:20","modified_gmt":"2026-07-28T14:35:20","slug":"analiza-combinata-masw-hvsr-non-unicitate","status":"publish","type":"post","link":"https:\/\/blog.geostru.eu\/ro\/analiza-combinata-masw-hvsr-non-unicitate\/","title":{"rendered":"C\u00e2te profiluri diferite explic\u0103 acelea\u0219i date MASW? Am num\u0103rat 122"},"content":{"rendered":"<p><strong>Orice tehnic\u0103 geofizic\u0103 sufer\u0103 de non-unicitate: aceleia\u0219i m\u0103sur\u0103tori \u00eei corespund numeroase modele de subsol diferite, toate compatibile cu datele.<\/strong> Nu este un defect al instrumentelor, este o proprietate a informa\u021biei pe care m\u0103sur\u0103toarea o con\u021bine. Am \u00eencercat s\u0103 m\u0103sur\u0103m c\u00e2t c\u00e2nt\u0103re\u0219te cu adev\u0103rat, iar rezultatul ne-a surprins.<\/p>\n<h2>Experimentul<\/h2>\n<p>Am pornit de la un profil de subsol <strong>cunoscut<\/strong>, cu opt straturi, av\u00e2nd Vs30 de 325 m\/s. Din acel profil am generat curba de dispersie pe care un sondaj MASW ar fi m\u0103surat-o. Apoi ne-am pref\u0103cut c\u0103 nu cunoa\u0219tem r\u0103spunsul \u0219i am mers invers: din date, s\u0103 reconstruim terenul. De dou\u0103 sute de ori, cu ipoteze ini\u021biale diferite.<\/p>\n<p>Avantajul de a lucra astfel este c\u0103 <strong>\u0219tim r\u0103spunsul corect<\/strong>. Pe date de teren nu se \u0219tie niciodat\u0103 dac\u0103 profilul ob\u021binut este cel real; aici da, iar eroarea poate fi m\u0103surat\u0103.<\/p>\n<h2>O sut\u0103 dou\u0103zeci \u0219i dou\u0103 de profiluri, toate \u201ecorecte\u201d<\/h2>\n<p>Din cele 200 de \u00eencerc\u0103ri, <strong>122 au produs un profil care explic\u0103 datele de dispersie cu o eroare sub 3%<\/strong>: o ajustare pe care orice operator ar considera-o excelent\u0103.<\/p>\n<p>Acele 122 de profiluri nu sunt varia\u021bii pe aceea\u0219i tem\u0103. Sunt profiluri diferite \u00eentre ele:<\/p>\n<ul>\n<li>cel mai mic are <strong>Vs30 = 300 m\/s<\/strong><\/li>\n<li>cel mai mare are <strong>Vs30 = 679 m\/s<\/strong><\/li>\n<\/ul>\n<p>Limita dintre categoria B \u0219i categoria C \u2014 360 m\/s \u2014 cade \u00een mijlocul distribu\u021biei: <strong>83 de profiluri se \u00eencadreaz\u0103 \u00een categoria C, 39 \u00een categoria B<\/strong>. Un profil din trei, pornind de la acelea\u0219i date, conduce la o clasificare seismic\u0103 diferit\u0103.<\/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-ro.png\" alt=\"Cele 122 de profiluri echivalente\"\/><figcaption>Cu gri, cele 122 de profiluri care explic\u0103 la fel de bine acelea\u0219i date MASW. Cu albastru \u00eentrerupt, profilul real; cu auriu, cel selectat prin ad\u0103ugarea curbei H\/V.<\/figcaption><\/figure>\n<p>Acesta este aspectul care de obicei r\u0103m\u00e2ne nespus: c\u00e2nd un program returneaz\u0103 <em>un<\/em> profil, nu spune c\u0103 celelalte sunt gre\u0219ite. Spune c\u0103 <strong>a \u00eencetat s\u0103 mai caute<\/strong>.<\/p>\n<h2>Ce se \u00eent\u00e2mpl\u0103 c\u00e2nd se adaug\u0103 curba H\/V<\/h2>\n<p>Am reluat cele 122 de profiluri \u2014 toate imposibil de deosebit pe baza dispersiei singure \u2014 \u0219i am cerut fiec\u0103ruia s\u0103 explice <strong>\u0219i<\/strong> curba H\/V m\u0103surat\u0103 \u00een acela\u0219i punct cu un tromometru cu trei componente.<\/p>\n<p>Profilul care o explic\u0103 cel mai bine are <strong>Vs30 = 324 m\/s<\/strong>. Valoarea real\u0103 era <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-ro.png\" alt=\"Distribu\u021bia valorilor Vs30\"\/><figcaption>Distribu\u021bia valorilor Vs30 ale celor 122 de profiluri echivalente, cu benzile categoriilor de teren. Linia \u00eentrerupt\u0103 indic\u0103 valoarea real\u0103.<\/figcaption><\/figure>\n<p>Nu este o \u00eembun\u0103t\u0103\u021bire marginal\u0103: este trecerea de la o problem\u0103 cu sute de solu\u021bii la una cu o singur\u0103 solu\u021bie. Curba H\/V singur\u0103 nu ar fi fost suficient\u0103 pentru reconstruirea profilului \u2014 dar este <strong>exact informa\u021bia care \u00eei lipse\u0219te metodei MASW<\/strong> pentru a fi decisiv\u0103.<\/p>\n<blockquote>\n<p>Curba H\/V arat\u0103 <strong>unde este fundul<\/strong>. Dispersia MASW arat\u0103 <strong>cum este alc\u0103tuit deasupra<\/strong>. Niciuna dintre ele, singur\u0103, nu arat\u0103 ambele lucruri.<\/p>\n<\/blockquote>\n<h2>Limita pe care aproape nimeni nu o declar\u0103: lungimea dispozitivului<\/h2>\n<p>Exist\u0103 un al doilea aspect, \u0219i mai practic, ap\u0103rut lucr\u00e2nd pe un caz real.<\/p>\n<p>Un sondaj MASW rezolv\u0103 \u00een mod fiabil lungimi de und\u0103 de ordinul <strong>lungimii dispozitivului<\/strong>. Fiecare punct selectat, la frecven\u021ba <em>f<\/em> \u0219i viteza de faz\u0103 <em>v<\/em>, corespunde unei lungimi de und\u0103 \u03bb = v\/f, iar ad\u00e2ncimea investigat\u0103 este cuprins\u0103 aproximativ \u00eentre \u03bb\/3 \u0219i \u03bb\/2.<\/p>\n<table>\n<thead>\n<tr>\n<th>Lungimea dispozitivului<\/th>\n<th>Ad\u00e2ncimea efectiv investigat\u0103<\/th>\n<th>Vs30 determinabil?<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>24 m<\/td>\n<td>8\u201312 m<\/td>\n<td>nu, \u00een mare parte extrapolat<\/td>\n<\/tr>\n<tr>\n<td>48 m<\/td>\n<td>16\u201324 m<\/td>\n<td>par\u021bial<\/td>\n<\/tr>\n<tr>\n<td>72 m<\/td>\n<td>24\u201336 m<\/td>\n<td>da<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Compara\u021bia cu cei 30 de metri ceru\u021bi de Vs30 este imediat\u0103: <strong>cu dispozitive scurte, partea ad\u00e2nc\u0103 a profilului nu este m\u0103surat\u0103, ci extrapolat\u0103<\/strong>. \u0218i este exact por\u021biunea pe care curba H\/V, care m\u0103soar\u0103 rezonan\u021ba \u00eentregii coloane, reu\u0219e\u0219te s\u0103 o constr\u00e2ng\u0103.<\/p>\n<p>\u00centr-un caz real, cu un dispozitiv de 24 de metri, dou\u0103 puncte fuseser\u0103 selectate la 4,7 \u0219i 5,0 Hz cu viteze de 491 \u0219i 428 m\/s: lungimi de und\u0103 de <strong>104 \u0219i 85 de metri<\/strong>, de peste patru ori lungimea dispozitivului. Pentru a le explica, inversia a plasat un substrat de 717 m\/s la 18 metri ad\u00e2ncime \u2014 <strong>un substrat care nu exist\u0103<\/strong>. Ajustarea r\u0103m\u00e2nea excelent\u0103 \u0219i niciun indicator nu semnala problema. Dup\u0103 eliminarea celor dou\u0103 puncte, conflictul a disp\u0103rut.<\/p>\n<h2>Eroarea care nu las\u0103 urme<\/h2>\n<p>\u00cen fine, exist\u0103 o eroare care se produce pe teren \u0219i este invizibil\u0103. \u00cen spectrul de vitez\u0103 se identific\u0103 o curb\u0103 bine definit\u0103 \u0219i este interpretat\u0103 ca mod fundamental. Uneori nu este: c\u00e2nd energia se distribuie pe modurile superioare, modul fundamental poate fi slab sau complet absent, iar curba cea mai evident\u0103 este \u00een realitate un mod superior.<\/p>\n<p>\u00cen testele noastre, atribuirea modului fundamental unei curbe care era \u00een schimb primul mod superior a dus Vs30 de la 325 la <strong>451 m\/s<\/strong>: o categorie de teren gre\u0219it\u0103, cu o eroare de ajustare a dispersiei <strong>sub 1%<\/strong>. Repetat\u0103 de 155 de ori, eroarea s-a dovedit sistematic\u0103 \u2014 mereu \u00een aceea\u0219i direc\u021bie, niciodat\u0103 aleatorie.<\/p>\n<p>O eroare de interpretare a modurilor nu produce incertitudine. Produce un r\u0103spuns gre\u0219it, precis \u0219i coerent.<\/p>\n<h2>Cum se procedeaz\u0103, \u00een practic\u0103<\/h2>\n<ol>\n<li><strong>Pe teren<\/strong>: \u00een acela\u0219i punct, dispozitivul MASW obi\u0219nuit \u0219i o \u00eenregistrare HVSR de 15\u201320 de minute cu tromometru cu trei componente, de preferin\u021b\u0103 \u00een centrul dispozitivului.<\/li>\n<li><strong>\u00cen Easy MASW<\/strong>: picking-ul curbei de dispersie, atribuind fiec\u0103rei curbe propriul num\u0103r de mod, \u0219i exportul curbelor modale.<\/li>\n<li><strong>\u00cen Easy HVSR<\/strong>: importul dispersiei \u0219i inversia combinat\u0103. Un singur profil Vs, coerent cu ambele m\u0103sur\u0103tori.<\/li>\n<\/ol>\n<h2>Ce r\u0103m\u00e2ne de re\u021binut<\/h2>\n<ul>\n<li><strong>Un misfit mic nu certific\u0103 rezultatul.<\/strong> Arat\u0103 c\u0103 modelul este compatibil cu datele, nu c\u0103 ar fi singurul. \u00centrebarea corect\u0103 este: <em>c\u00e2te alte modele ajung acolo?<\/em><\/li>\n<li><strong>MASW singur\u0103 este o problem\u0103 subdeterminat\u0103.<\/strong> Nu este o limitare a programului: este o proprietate a datelor. Niciun algoritm nu poate recupera informa\u021bii pe care m\u0103sur\u0103toarea nu le con\u021bine.<\/li>\n<li><strong>O \u00eenregistrare HVSR \u00een acela\u0219i punct cost\u0103 cincisprezece minute<\/strong> \u0219i este exact informa\u021bia care lipse\u0219te. Raportul dintre costul achizi\u021biei \u0219i reducerea incertitudinii este probabil cel mai bun disponibil \u00een geofizica aplicat\u0103 de suprafa\u021b\u0103.<\/li>\n<li><strong>Modul trebuie identificat, nu presupus.<\/strong> Un spectru \u201ecurat\u201d nu \u00eenseamn\u0103 automat un mod fundamental.<\/li>\n<li><strong>Aten\u021bie la valorile apropiate de limitele categoriilor.<\/strong> 360 m\/s separ\u0103 categoria B de C: un rezultat de 350 sau 380 m\/s ob\u021binut printr-o singur\u0103 metod\u0103 este o decizie de proiectare sprijinit\u0103 pe o incertitudine care nu a fost m\u0103surat\u0103.<\/li>\n<\/ul>\n<h2>O not\u0103 metodologic\u0103<\/h2>\n<p>Cifrele din acest articol provin din <strong>date sintetice<\/strong>: profil cunoscut, curbe calculate, f\u0103r\u0103 zgomot instrumental. Este o alegere deliberat\u0103 \u2014 numai astfel se cunoa\u0219te r\u0103spunsul exact \u0219i se poate m\u0103sura eroarea.<\/p>\n<p>Pe date reale situa\u021bia este <strong>mai dificil\u0103<\/strong>, nu mai u\u0219oar\u0103: zgomot, efecte tridimensionale, v\u00e2rfuri H\/V de origine antropic\u0103. Non-unicitatea m\u0103surat\u0103 aici este, prin urmare, o estimare optimist\u0103.<\/p>\n<hr\/>\n<p><em>Analiza combinat\u0103 MASW + HVSR este disponibil\u0103 \u00een <strong>Easy MASW<\/strong> \u0219i <strong>Easy HVSR<\/strong>. Un ghid tehnic complet, cu procedura pas cu pas \u0219i recomand\u0103rile practice pentru inversie, poate fi desc\u0103rcat \u00een format PDF: <a href=\"https:\/\/blog.geostru.eu\/wp-content\/uploads\/sites\/9\/2026\/07\/Analisi-congiunta-MASW-HVSR-guida-ro.pdf\">Analiza combinat\u0103 MASW + HVSR \u2014 ghid<\/a>.<\/em><\/p>\n<p><em>Manuale online: <a href=\"https:\/\/help.geostru.io\/masw\/ro\/\">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>Orice tehnic\u0103 geofizic\u0103 sufer\u0103 de non-unicitate: aceleia\u0219i m\u0103sur\u0103tori \u00eei corespund numeroase modele de subsol diferite, toate compatibile cu datele. Nu este un defect al instrumentelor, este o proprietate a informa\u021biei pe care m\u0103sur\u0103toarea o con\u021bine. Am \u00eencercat s\u0103 m\u0103sur\u0103m c\u00e2t c\u00e2nt\u0103re\u0219te cu adev\u0103rat, iar rezultatul ne-a surprins. Experimentul Am pornit de la un profil de&hellip;<\/p>\n","protected":false},"author":16658,"featured_media":15298,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2671,2674,2672,2659,2658,2675,2652,1795,2673,2653],"class_list":["post-15305","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ambiente","tag-analiza-combinata","tag-categorie-de-teren","tag-curba-de-dispersie","tag-easy-hvsr","tag-easy-masw","tag-geofizica-aplicata","tag-hvsr","tag-masw","tag-microzonare-seismica","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>Analiza combinat\u0103 MASW + HVSR: o singur\u0103 tehnic\u0103 nu ajunge<\/title>\n<meta name=\"description\" content=\"122 de profiluri diferite explic\u0103 acelea\u0219i date MASW, cu Vs30 de la 300 la 679 m\/s. 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