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No fitted scaling or shifted waveform used." } }, "referenceQuadratureAudit": { "officialGeneratorFile": "outputs/double-analytical-benchmark/analytical_solution_Aki.py", "sha256": "e7c268453971ba678c342d12b71e643b900ec7010669dcb7df27dd92d813f97e", "lineEvidence": [ { "line": 37, "text": "hdur = 2.0 / 1.628 # hdur/gauss (according to SPECFEM definition)" }, { "line": 38, "text": "dt = 0.001 # time step size" }, { "line": 63, "text": "nmin = int((r/alpha)/dt)" }, { "line": 64, "text": "nmax = int((r/beta)/dt)" }, { "line": 66, "text": "for i in range(nmin, nmax+1):" }, { "line": 68, "text": "val_conv += comp_source_time_function(t-time_temp,hdur) * time_temp * dt" }, { "line": 57, "text": "val_diff = (comp_source_time_function(t+dt,hdur)-comp_source_time_function(t-dt,hdur)) / (2.0*dt)" }, { "line": 280, "text": "# Mxz = Mrp" }, { "line": 294, "text": "ucar[2] = vec_r * cos(theta) - vec_t * sin(theta)" } ], "sourceUrl": "https://github.com/SPECFEM/specfem3d/tree/7a1c76454396f8dd2f5a67ea524ca372e2c91993/EXAMPLES/benchmarks/analytic_examples/analytic_solution_elastic/analytical_solution_Aki.py", "method": "At late time H=1, exact near-field integral is(b²-a²)/2; official int-truncated inclusive rectangular sum is DT²*sum(i,nmin..nmax). Cartesian near-field coefficient follows the original spherical tensors/rotation.", "pTravelTimeSeconds": 1.821078397711709, "sTravelTimeSeconds": 3.39934634239519, "nmin": 1821, "nmax": 3399, "lateDiscreteIntegralSeconds2": 4.1211899999999995, "lateContinuousIntegralSeconds2": 4.119614512471655, "integralBiasSeconds2": 0.0015754875283446879, "cartesianNearFieldCoefficientsMPerSeconds2": [ 0.001760436744431386, 0.0013898184824458312, 0.0037525099026037433 ], "independentKelvinFormula": "u=[(2-4nu)M*n+3*n*(n^T*M*n)-trace(M)*n]/[16*pi*mu*(1-nu)*r²]; mu=rho*Vs²,nu=(Vp²-2Vs²)/(2*(Vp²-Vs²)). 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Remaining solver residual can include spatial/time/source-start/boundary effects; no corrected-reference benchmark metric is calculated or accepted here." }, "boundaryCaution": { "earliestImageReflectionPTravelTimeFromCentroidSeconds": 10.063573431146693, "earliestPTravelTimeFromRecordedSourceStartSeconds": 6.063573431146693, "meaning": "Geometric top-face image path only, not measured reflected amplitude; finite source tails permit boundary influence before the centroid travel time." }, "failed24": { "status": "FAILED_DATABASE_STAGE", "logSha256": "4429ef9146dfa071b38bd47ad65095621088bbc2016a559a85a3a9adaa6dbf55", "recordedFact": "Regular-element equality check rejected~2e-18 metric differences; no24³ solver traces exist, and this audit changes neither engine nor tolerance." }, "nextStep": "Build and independently verify a separate continuous-integral/analytic-erf-derivative reference before any new solver comparison. 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