Notes_on_piecewise_continuous_regression.15jul23.pdf. These notes discuss piecewise-continuous regression (aka "broken stick" regression, although the functions between break points [aka "hinge points"] need not be line segments; another name is segmented regression). There are a number of ways of implementing the regression; these notes show how to do it using basis functions. Examples of the regressions for various combinations of lines, flat segments, and quadratics are included in the accompanying document piecewise-continuous_regression_using_basis_functions.R.examples.01nov23.pdf, along with the R code used to create the examples. The text file with the R code is in piecewise-continuous.eric_thompson_basis_functions_program.R [Revised 01 November 2023]
Short description of how to compute RotD50 for Fourier acceleration spectra [Added 13 November 2022]
Thoughts on the acronyms GMPE, GMPM, and GMM.v2.pdf. As the file name indicates, these notes discuss various acronyms to describe models for predicting ground-motion intensity measures. In 2007 I invented "GMPE". which has gained wide acceptance, but now it seems that "GMM" will become the standard acronym. I agree that "GMPE" has limitations, but I prefer "GMPM" to "GMM". [Very minor revision 24 March 2022]
notes_concerning_SRI_amps_underestimating_FR_amps_for_gradient_models.2021-11-10.pdf. These notes discuss the relation between full-resonance (FR) and square-root-impedance (SRI) amplifications from velocity models that have a piecewise-continuous dependence on depth. For such models the FR amplifications are greater than the SRI amplifications. The notes speculate that because gradient models can be thought of as a series of many constant-velocity layers, the reason for the consistent difference is that the FR amplifications are controlled by the ratio of seismic impedances, rather than the square-root of the ratio as for the SRI amplifications. [Added 09 November 2021]
Constructing_equivalent_constant-velocity_layered_models.2021-10-26.pdf. These notes discuss how to use several programs in the SiteAmp suite of programs to construct layered models with constant-velocity layers equivalent to a more general model. Layer constant-velocity models are useful in computations of full resonance amplifications, using programs such as nrattle.for (in the SiteAmp suite of programs). [Revised version added 09 November 2021]
One_equation_for_smooth_transition_between_two_line_segments.application_to_BT15_FFF.v1.pdf. These notes show how to use a single equation to represent a two-line-segment function with a smooth transition between the line segments. The results are sonewhat more general than in the Geometrical_spreading_with_smooth_transition_between_linear_segments.pdf notes. [Added 16 August 2021]
Geometrical_spreading_with_smooth_transition_between_linear_segments.pdf. These notes show how to represent a two-line-segment geometrical spreading by a single equation with a smooth transition between the line segments. [Added 15 August 2021]
fas_narrow_band_filter_comparison.v01.pdf. These notes were prompted by the excellent paper by Wu et al. (2016) analyzing the distance decay of narrow-band filtered records from the Mineral, Virginia, earthquakes, in which they present convincing evidence that the amplitudes of the narrow-band filtered records decay as approximately 1/R1.5. I did a simulation study using the stochastic model, and I find that if the Boore and Thompson (2015) path duration model is correct, the underlying Fourier acceleration spectra (FAS) will decay at a rate only somewhat faster than 1/R, and not nearly as rapidly as 1/R1.5. The reason for the difference is that in the stochastic model the energy carried by the FAS is distributed over a duration that increases with propagation distance, and thus the peak of the filtered motions is reduced as a result of the energy being spread over an increasing duration. The conclusion of these notes is almost entirely dependent on the path-duration model, which has a rapid increase in duration from about 10 to 50 km. The next notes are a followup, computing durations for the Mineral mainshock and best recorded aftershock. [Added 23 May 2017]
durations_for_mineral_ms_and_as.v01.pdf. The Boore and Thompson (2015) (BT15) path-duration region for eastern North America did not use durations from the Mineral earthquakes. Using the same duration measure as in BT15, I find that the durations for the Mineral mainshock and best recorded aftershock (the two event analyzed) are consistent with those for the BT15 model. This would seem to provide some validation to the results in the previous notes regarding the rate of decay. But I did notice that the durations seem to be strongly influence by large amplitude coda waves, and it is not clear that applying the existing stochastic model to such motions is correct. I suggest that this is an important topic that should be studied by someone. [Added 23 May 2017]
daves_notes_on_interpolating_two_given_velocity_profiles_to_obtain_a_velocity_profile_with_specified_vz.v2.0.pdf. Discusses two methods for interpolating two given velocity profiles to obtain a profile with a specified time-averaged velocity from the surface to a depth Z (V(Z)). One method is contained in a paper by Cotton et al. (2006); small adjustments of the velocity profile from this method are required to give the specified V(Z). The other method is introduced here for the first time; the velocity profile resulting from this interpolation method requires no velocity adjustment to match the specified V(Z). [A revised version with a generalization of the interpolation method was added 24 July 2015]
Notes on relating density to velocity for use in site amplification calculations [Revised 23 August 2015]
f0_stress_relations_boore_allmann_shearer.add_equation_for_r.v04.pdf. These notes summarize some relations between corner frequency, source radius, and stress drop for circular faults (the relations are those used in the point-source stochastic simulations implemented in SMSIM). [Added 15 June 2021; includes some more detail on the equation derivation]
Adjusting_PSA_amplitudes_to_Vs30_3000.v02.pdf. These notes contain a procedure for adjusting PSA in eastern North America from sites with VS30 less than about 1.1 km/s to sites with VS30 = 2.0 km/s and 3.0 km/s. [Added 20 January 2015]
What_SCF_stress_param_is_consistent_with_the_AS00_source_model.pdf. These notes show that the best stress parameter to fit the high-frequency spectral level of the Atkinson and Silva (2000) source model is 88 bars. Comparisons are shown both for a single-corner frequency (SCF) model and for the generalized additive two-corner-frequency model. [Added 03 January 2014]
smsim_generalization_of_2-corner_frequency_source_models_v04.pdf. These notes describe two generalized 2-corner source models, both of which have a high-frequency spectral level equal to that of a songle-corner frequency source with a specified stress parameter. The new models have been incorporated into the stochastic method part of the SMSIM programs. [Revised 29 May 2013]
ab06_hard_rock_gmpes_and_bc_gmpes_vs_v30_v3.0.pdf. These are unpolished, draft notes discussing the extrapolation of the Atkinson and Boore (2006) ground-motion predictions from NEHRP BC (V30 = 760 m/s) to very hard rock, using the site factors from Boore and Atkinson (2008). One important conclusion is that using the site factors to go from very hard motions to softer site conditions will in general lead to an overprediction of the motions (by as much as a factor of 1.9 for PGA). [Added 11 September 2012]
daves_notes_on_ratios_of_source_spectra_v1.5.pdf. Equations for ratios of single-corner-frequency source spectra, for use in determining stress parameters from ratios of motions from two closely located events recorded at the same station (the "empirical Green's function" method). [Revised notes added 21 May 2012]
daves_notes_on_poissons_ratio.pdf (03/24/2007) .
daves_notes_on_program_wholespace_pointsource.pdf (07/08/2018). [Renamed notes added 08 July 2018]
comparisons_of_ground_motions_from_the_M_9_tohoku_earthquake_with_gmpes_v1.4.pdf (03/31/2011).
Some notes on Tmax for GMRotI50 penalty function.pdf (05/12/2016). These notes investigate the sensitivity of GMRotI50 to the maximum period (Tmax4Penalty) used in computing the penalty function (see Boore, D. M., J. Watson-Lamprey, and N. A. Abrahamson (2006). Orientation-independent measures of ground motion). Tmax4Penalty is chosen in two ways: fixed at 10 s, and computed on a record-by-record basis, taking into account the maximum usable period for each record. The results show that on average GMRotI50 is not very sensitive to the choice of Tmax4Penalty, although this should not be taken as a universal conclusion. [Added on 12 May 2016]
sensitivity_of_fas_from_high-cut_filtered_data_to_zero_pads_v01.pdf (07/02/2013). The Fourier amplitude spectrum at high frequencies for high-cut filtered data is sensitive to zero pads added before filtering (the mirror image of the situation for low-cut filtered data--see dependence_of_fourier_amplitude_spectra_at_low_frequencies_on_zero_pads_v02.pdf)] [Added on 02 July 2013]
dependence_of_fourier_amplitude_spectra_at_low_frequencies_on_zero_pads_v02.pdf (07/01/2013). [Updated on 01 July 2013: FAS computed using double precision were added to the FAS plot]
notes_on_revisions_to_smc2psa_rot_gmrot_v1.0.pdf. This note is a followup to Norm Abrahamson's suggestion for increasing the speed of the gmrot and rotd computations and resampling the time series to capture better the peak amplitudes. This builds on the note below. Both of these ideas were incorporated into a revision of my programs smc2psa_gmrot_rot (for smc-formatted files) and nga2smc_gmrot_rot (for files in the format used in the PEER NGA projects). The new programs are named smc2psa_rot_gmrot_interp_acc_rot_osc_ts.for and nga2psa_rot_gmrot_interp_acc_rot_osc_ts.for, to differentiate the new programs from the old ones. Comparisons of the results from the new and old programs are included for 24 pairs of horizontal component time series. [Added 02 October 2012]
the_effect_of_td_interpolation_on_rs_v1.0.pdf. This note confirms Norm Abrahamson’s finding that the straight line interpolation between sampled points used in the Nigam and Jennings (NJ) response spectral computation can lead to differences in response spectra compared with spectra computed from records for which the time series are interpolated properly, using the sampling theorem. My intention here is not to duplicate his work (an impossible task anyway), but simply to document the small amount of work that I have done, in the hope that others might find it useful. Norm deserves full credit for finding and investigating the issue. [Added 16 September 2012]
daves_notes_at_what_period_does_psa_equal_pga.pdf (09/30/2010).
filter_only_question_22april09.pdf (04/22/2009) .
properties_of_butterworth_filters.pdf (07/31/2008).
notes on smoothing over logarithmically spaced freqs.pdf (03/07/2008).
daves_notes_on_tapering_before_filtering.pdf (08/03/2007).
response_spectra_need_for_double_precision.pdf (06/06/2006).
notes_on_checking_shape_of_fas_for_locut.pdf (01/10/2006).
comments_pga_filtering_spectral_shape.pdf (07/30/2004).
lowest_usable_freq_for_response_spectra_v20.pdf (07/15/2004).
choice_of_filter_order.pdf (04/24/2004).
rs_same_fas_different_durations.pdf (04/06/2004).
causal_acausal_low_cut_filters.pdf (12/28/2003).
aa_pa_rv_pv_2.pdf (12/28/2003). (some notes on the definitions and asymptotic properties of various definitions of response spectra)
sd_for_directivity_pulses.pdf (11/22/2003).
notes_on_processing.pdf (09/03/2003).
acausal_filter_forward_reverse.pdf (07/21/2003). (making sure that the forward and reverse time-domain filtering is working)
interchange_filter_integration.pdf (07/21/2003).
dont_call_them_attenuation_relations.pdf (07/21/2006). These notes are an appeal to do away with the term "attenuation relations". These notes were repeated in section A.1 of Appendix A (). of Boore and Atkinson (2007), in which I proposed the term "Ground-Motion Prediction Equations", or "GMPEs". This term seems to have caught on and is now being used globally.
daves_notes_whats_wrong_with_duzce.pdf (11/17/2006).
pinyon_flat_locations_summary.pdf (11/15/2006).
questioning_sf71_pacoima_dam_filtering.pdf (11/15/2006).
m_for_big_bear_city_and_yorba_linda_eqs.pdf (11/15/2006).
daves_notes_smr_locations_anderson_dam_and_cedar_springs_dam.pdf (11/15/2006).
daves_notes_comparing_teamx_bjf_14augustjuly2005.pdf (10/25/2006).
daves_notes_on_including nonlinear_amps_26july2005.pdf (10/25/2006).
choice of rle400 or rle80 equations.pdf (10/24/2006).
daves_notes_mechrake_c3_stage1_stage2_pga_25july2005.pdf (10/24/2006).
daves_notes_compare_park04_anza_bbc_yl_psa.pdf (08/24/2006).
fault_classification_using_p_t_axes.pdf (12/06/2005).
lex_lgpc_comparison.pdf (12/06/2005).
more data for cape mendocino 1992.pdf (12/06/2005).
regarding_pump_station_10_record.pdf (12/06/2005).
notes_on_rinaldi_record.pdf (12/06/2005).
steidl_email_la00_10jan03.pdf (02/15/2005).
cm92_interface_or_not_4nga.pdf (01/12/2005).
notes_on_tabas_records.pdf (06/17/2004).